text stringlengths 81 47k | source stringlengths 59 147 |
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Question: <p>From my understanding of relativity, gravity is not a force, but a result of the curvature of spacetime. If Object1 moves past Object2, even though it's moving in a straight line, its direction may change due to the distortion caused by Object2's mass.</p>
<p>However, what about the situation where Object... | https://physics.stackexchange.com/questions/79676/why-is-there-a-gravitational-attraction-between-two-objects-at-rest-with-respect |
Question: <p>What are the direct real life applications of general relativity other than nuclear technology? </p>
<p>What I meant was, was there any technology developed based on general relativity that can benefit mankind today? </p>
<p>Secondly, are there any adverse effects quantum technology today?</p>
Answer: | https://physics.stackexchange.com/questions/82121/what-are-the-direct-real-life-applications-of-general-relativity-and-quantum-phy |
Question: <p>I have a question. I want to know the difference between the sphere and the geodesic sphere.
Another question:
given a vector field, $Y$, on a manifold $M$ defined by: $Y(p)=p$ for every point $p \in M$, I tried to calculate the divergence of $Y$. I think that it is equal to $n$, where $n$ is the dimension... | https://physics.stackexchange.com/questions/94459/about-divergence-of-a-vector-field-and-geodesic-sphere |
Question: <p>If a scalar field component has to be added to the Einstein field equations (see below) to solve dark matter/energy, then how would string theory need to be modified and do black holes still exist?</p>
<p>The proposed modified equations are (ignoring physical constants)
$$ R_{ij} - \frac12 R g_{ij} = T_{i... | https://physics.stackexchange.com/questions/35863/what-does-adding-a-scalar-field-component-to-the-einstein-field-equations-mean-f |
Question: <p>So there are so many solutions for general relativity - then how does one "choose" the solution that is right one? By checking with observation? (though I also know that it is currently unknown which one is the correct solution.)</p>
Answer: <p>Generally speaking we start with a known stress-energy tensor... | https://physics.stackexchange.com/questions/55435/how-to-choose-a-solution-from-all-possible-solutions-of-general-relativity |
Question: <p>$u^{\mu}$ - 4-velocity</p>
<p>$b^{\mu}$ - 4-vector of magnetic field</p>
<p>$
u_{\mu}u^{\mu}=-1, \qquad u_{\mu}b^{\mu}=0
$</p>
<p>$$
u_{\beta}u^{\alpha}\nabla_{\alpha}b^{\beta}-u_{\beta}b^{\alpha}\nabla_{\alpha}u^{\beta}+\nabla_{\alpha}b^{\alpha}=0
$$
I don't understand why this equation gives this
$$
u... | https://physics.stackexchange.com/questions/60251/help-me-to-understand-this-conversion-4-vectors |
Question: <p>In the case of charges defined at space-like infinity, I can understand the physical meaning of them because they can be related to measurements made by a physical observer (that is an observer whose wordline is time-like). For example in four dimensions, for the Schwarschild solution, the ADM mass coincid... | https://physics.stackexchange.com/questions/60748/what-is-the-physical-meaning-of-charges-at-light-like-infinity-in-asymptotically |
Question: <p>Ok, this question is more a result of my lack of knowledge of how to manipulate equations involving index notation rather than about physics...</p>
<p>I have the geodesic equation with $U^\lambda\equiv\dot{x}^\lambda$:-</p>
<p>$$
\dot{U^\lambda} + \Gamma^\lambda_{\mu\nu} U^\mu U^\nu
$$</p>
<p>And I want... | https://physics.stackexchange.com/questions/61641/transforming-an-equation-to-the-co-vector-version |
Question: <p>Is the definition of $$d s^2=-d \tau^2$$ assuming that $c=1$, so that we always have $$\left({ds\over d\tau}\right)^2=-1$$?
Is there a reason for this definition?
Don't we get an imaginary ${ds\over d\tau}$?</p>
Answer: <p>It depends on what convention you're using for the metric's signature. Some people ... | https://physics.stackexchange.com/questions/61353/interval-and-proper-time |
Question: <blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="https://physics.stackexchange.com/questions/8659/invariant-spacetime-distance-circular-motion">Invariant spacetime - distance - Circular Motion</a> </p>
</blockquote>
<p>I understand that the closer something travels to the speed of lig... | https://physics.stackexchange.com/questions/8671/a-question-about-the-relativity-of-time |
Question: <p>Suppose two pointed masses are given in space. Suppose further that one of the masses has a given velocity at (local) time 0. Is there a way to compute its position in a future time?</p>
<p>Neglecting general relativity, I will simply compute an integral, but with general relativity, we see that the metri... | https://physics.stackexchange.com/questions/10870/calculating-position-in-space-assuming-general-relativity |
Question: <p>Relativistic gravity affects particle in motion, does it affect particle that are resting too? How? and if not could one say that the matter at 0K is not affected by gravity?</p>
<p>I'm not a physicist; is just a thought and probably really naive.</p>
Answer: <p>Yes, gravity affects particles at rest, an... | https://physics.stackexchange.com/questions/14338/general-relativity-at-0k |
Question: <p>As I've said elsewhere, I've not had the opportunity to take a class in general relativity. Nonetheless, I understand that two major aspects of the standard cosmological model are the <a href="http://en.wikipedia.org/wiki/Cosmological_principle" rel="nofollow">cosmological principle</a> and the observatio... | https://physics.stackexchange.com/questions/16090/how-do-we-resolve-a-flat-spacetime-and-the-cosmological-principle |
Question: <p>My copy of Feynman's "Six Not-So-Easy Pieces" has an interesting introduction by Roger Penrose. In that introduction (copyright 1997 according to the copyright page), Penrose complains that Feynman's "simplified account of the Einstein field equation of general relativity did need a qualification that he d... | https://physics.stackexchange.com/questions/16725/intuitively-what-is-the-source-term-of-the-einstein-field-equation |
Question: <p>We may consider a "local" region in curved spacetime (local in respect of the spatial and the temporal coordinates). A "local inertial frame" may be constructed by some transformation that produces flat spacetime locally. This transformation produces the diagonal [1,-1,-1,-1] in an approximate manner.</p>
... | https://physics.stackexchange.com/questions/16951/local-charts-in-general-relativity |
Question: <p>Let's consider the equation y=x in the x-y rectangular Cartesian frame in flat space time. We use the transformations in the first quadrant:
$$y=y'^2$$
$$x=x'$$
$$t=t'$$
For the first transformation we are taking the positive values of $y'$ only.
The equation of y=x in the transformed cond... | https://physics.stackexchange.com/questions/19429/the-light-ray-bends-round |
Question: <p>Let's consider two points A an B separated by a finite distance in curved space time. A light ray flashes across an infinitesimally small spatial interval at B. </p>
<p>Metric:
$$ds^2=g_{00}dt^2-g_{11}dx^2-g_{22}dy^2-g_{33}dz^2$$ ----------- (1)</p>
<p>We may write,</p>
<p>$$ds^2=dT^2-dL^2$$
Where,</p>
... | https://physics.stackexchange.com/questions/27908/pseudo-superluminal-motion-and-the-synchronization-of-clocks |
Question: <p>The question is somewhat related to
<a href="https://physics.stackexchange.com/questions/220055/what-is-the-sum-of-the-angles-of-a-triangle-on-earth-orbit">What is the sum of the angles of a triangle on Earth orbit?</a> but still not quite what I think of.</p>
<p>Consider a real world triangle made of st... | https://physics.stackexchange.com/questions/419477/how-exactly-does-a-real-object-e-g-a-triangle-behave-considering-the-effects |
Question: <p>A common example of acceleration is a ball hanging from the top of the car. The angle this hanging ball makes from zero is dependent on the acceleration of the car.</p>
<p>What happens as we <em>allow</em> the car to <em>attempt</em> to approach the speed of light at constant acceleration?</p>
<p>My expe... | https://physics.stackexchange.com/questions/432698/angle-of-a-hanging-ball-in-system-trying-to-approach-speed-of-light |
Question: <p>I am studying about Mathisson-Papapetrou-Dixon equations which govern the motion of a test particle around a central massive object in the pole-dipole approximation.</p>
<p>Given that <span class="math-container">$S_a=-\frac{1}{2}\epsilon_{abcd}V^bS^{cd}$</span> I want to prove that <span class="math-cont... | https://physics.stackexchange.com/questions/443795/mathematical-question-on-mathisson-papapetrou-dixon-equations |
Question: <p>In examining black holes in Schwarzchild Coords (ie without resorting to other coords) the r coord becomes timeline within the event horizon and the t coord spacelike.</p>
<p>Therefore the light cone is tilted by 90 degrees. However, how do we say which direction in r is future and which is past? (textboo... | https://physics.stackexchange.com/questions/448884/future-pointing-light-cones-in-black-hole-in-schwarzschild-coordinates |
Question: <p>I think about the precession of the perihelion of the trajectory as the probe comes closer to the sun than Mercury, which was the first successful test for the general relativity.</p>
Answer: | https://physics.stackexchange.com/questions/485500/are-the-effects-of-general-relativity-accounted-for-in-the-calculation-of-the-tr |
Question: <p>Consider the metric </p>
<p><span class="math-container">$$ds^2=dv^2-dt^2+v^2 \mathcal{R}^2 d\Omega^2_3,$$</span></p>
<p>where <span class="math-container">$d\Omega^2_{3}$</span> is the metric of the <span class="math-container">$3$</span>-sphere, and <span class="math-container">$\mathcal{R}$</span> is ... | https://physics.stackexchange.com/questions/498407/flat-space-limit-of-metric-blows-up-in-different-coordinates |
Question: <p>In the <a href="http://www.scholarpedia.org/article/Spin-coefficient_formalism" rel="nofollow noreferrer">Newman-Penrose formalism</a>, one rewrites the Einstein equations in terms of a system of linear transport equations for the Newman-Penrose scalars. I am considering the initial value problem for this ... | https://physics.stackexchange.com/questions/531467/consistent-initial-data-for-evolution-in-time-with-the-newman-penrose-formalism |
Question: <p>In the Wikipedia article on "Geodesics in general relativity" we can find the following statement:</p>
<blockquote>
<p>In general relativity, gravity can be regarded as not a force but a
consequence of a curved spacetime geometry where the source of
curvature is the stress–energy tensor (representin... | https://physics.stackexchange.com/questions/552566/projection-of-4d-geodesic-in-spacetime-onto-3d-space-is-an-ellipse |
Question: <p>I am but a humble college dropout with a keen interest in physics, but one way or another I feel I have discovered some key information that will lead to a solid theory of everything that should satisfy all parties it concerns, that is, if I can correctly format and word it. My hope here is simply some res... | https://physics.stackexchange.com/questions/658803/regarding-nothingness-and-motion-in-the-ocean-of-matter-energy |
Question: <p>In general relativity, if a volume of particles moves unrestricted through spacetime, is their volume always conserved?</p>
<p>Say we let a collection of particles at rest wrt each other, fall freely in a gravitational field. Will tidal forces keep the volume they occupy constant? My intuition says yes, bu... | https://physics.stackexchange.com/questions/709750/does-a-volume-stay-constant-when-freely-falling |
Question: <p>Correct and direct me when I am wrong.
That is how I understand the logical flow of the formulation of the general theory of relativity:
First we have the equivalence principle, that one tells us that if want to see the effect of gravity just figure out the Physics in some frame accelerating with g in a se... | https://physics.stackexchange.com/questions/731841/correct-my-understanding-of-the-logical-flow-of-the-formulation-of-general-relat |
Question: <p>I first read about it on A Brief History of Time(Stephen Hawking). In 1962, a relativity experiment was executed: identical (classical) watches put on a water tower, one is on very high, other one is at the bottom. And of course, after a certain time, the one which is closer to ground was slower than the o... | https://physics.stackexchange.com/questions/223645/relativity-a-modification-on-sea-tower-experiment |
Question: <p><a href="https://i.sstatic.net/VDHUg.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VDHUg.jpg" alt="enter image description here"></a>Imagine that the Sun is not rotating. It also has a tunnel throughout its body exactly through the core. Please disregard any other effect then gravity.
From... | https://physics.stackexchange.com/questions/289025/which-photon-would-win-the-race |
Question: <p>I was studying a book which claims that, after a lot of math, the metric of the isotropic spacetime around a spherically symmetric is, approximately <span class="math-container">$$ds^2 = -A(r)dt^2 + B(r)dt^2 + r^2 d\Omega^2$$</span></p>
<p>So, the motion of a planet around this mass is given by the Lagran... | https://physics.stackexchange.com/questions/596430/motion-of-a-planet-around-a-spherically-distributed-mass |
Question: <p>Roger Penrose says in the Big Bang there was no mass!!
<a href="https://www.youtube.com/watch?v=OFqjA5ekmoY" rel="nofollow noreferrer">https://www.youtube.com/watch?v=OFqjA5ekmoY</a>
because E=M.c2. ( minute ca. 6). So where came the mass from.</p>
Answer: <p>The big bang was before the spontaneous symm... | https://physics.stackexchange.com/questions/605193/no-mass-in-the-big-bang |
Question: <p>I am reading <a href="http://www.fis.puc.cl/%7Erbenguri/3.pdf" rel="nofollow noreferrer">this paper</a> (link to pdf) by Benguria et al. <em>Aspects of the Hamiltonian dynamics of interacting grvitational gauge andd Higgs fields with application to spherical symmetry</em></p>
<p>At page 13 of the paper the... | https://physics.stackexchange.com/questions/607861/where-do-these-vectors-come-from |
Question: <p>Here's the concept. We see a very dense 1.5 km radius asteroid, and my friend Charlie and I fly up in our spaceship to check it out. I fly close on my bathroom scale, equipped with rocket thruster, and hover above the non-rotating asteroid. I have 100 kg mass.</p>
<p>My scale reads 2.05864e15 Newtons, s... | https://physics.stackexchange.com/questions/608614/if-gravity-impacts-length-measurements-and-length-measurements-impact-gravity |
Question: <p>This is a question from a mathematics student trying to visualize the fact that general relativity is based on a concept of, “identifying gravity with the curvature of spacetime” (sincere apologies for probable physics inaccuracies and useless details).</p>
<p>Suppose an absolute spacetime, a time-dependen... | https://physics.stackexchange.com/questions/611328/using-relativity-to-suppress-classical-inertial-acceleration |
Question: <p>If I understand the relativistic explanation of gravitation - that it is curvature of spacetime - then a particle left alone will travel along that curved spacetime in a path that depends on the local curvature at each instant in time (right?). If so, then the orbit of a small body without significant eff... | https://physics.stackexchange.com/questions/574129/how-does-the-gravitational-field-of-a-massive-body-affect-the-orbit-of-that-body |
Question: <p>In both Sean Carroll's book and Misner,Wheeler,Thorne, the authors take the gravitational redshift experiments to show that spacetime has a curved geometry.
There is a paper by Harvey R Brown(published in American Journal of Physics) that challenges this viewpoint by pointing out how this is a misconceptio... | https://physics.stackexchange.com/questions/575694/misconception-in-the-implications-of-the-gravitational-redshift-experiments |
Question: <p>I have been trying to understand the implications of general relativity. I unfortunately don't have a good knowledge of advanced topics and I may have made some silly assumptions.</p>
<p>As far as I understand, spacetime dictates the trajectory of an object, and the object curves spacetime. Objects follow ... | https://physics.stackexchange.com/questions/581982/would-gravity-still-act-if-all-objects-in-a-closed-system-somehow-became-station |
Question: <p>I'm reading the book "Einstein Gravity in a nutshell" by Anothy Zee and I'm a bit stuck on one of the steps in the derivation for divergence in an arbitrary coordinate system. The proof goes as follows,</p>
<p>since we know
<span class="math-container">$$W^\mu\partial_\mu\phi$$</span>
where <spa... | https://physics.stackexchange.com/questions/584772/coordinate-invariant-divergence |
Question: <p>I am reading <a href="https://doi.org/10.1016/S0370-2693(00)01125-4" rel="nofollow noreferrer">this paper</a> <em>The Bardeen model as a nonlinear magnetic monopole</em> by Eloy Ayón-Beato Alberto Garcı́a. A the end where the authors prove the that the weak energy condition is satisfied, they say that the ... | https://physics.stackexchange.com/questions/591847/why-are-these-vectors-perpendicular |
Question: <ol>
<li><p>One has that <span class="math-container">$ds^{2} = g_{ij}(x)dx^{i}dx^{j}$</span>. I often see that the interval is re-expressed with a time "seperation" of the form:
<span class="math-container">$$
ds^{2} = g_{00}(x)dt^{2} + \tilde{g}_{ab}dx^{a}dx^{b} \;\; a,b = 1,2,3
$$</span>
When ca... | https://physics.stackexchange.com/questions/594680/1-when-can-a-time-coordinate-be-separated-in-the-interval-general-relativity |
Question: <p>What does gravity look like in a compact space, such as a universe with spatial periodic boundary conditions equivalent to a 3-torus, or a ball with opposite points on the surface of the ball identified? In particular, what is the equivalent to the Schwarzschild vacuum solution to the Einstein field equati... | https://physics.stackexchange.com/questions/595287/gravity-in-compact-space-like-three-torus-or-a-ball-with-ends-identified |
Question: <p>Reading through the original <a href="https://aip.scitation.org/doi/10.1063/1.1666410" rel="nofollow noreferrer">GHP paper</a>, I notice that some of the <a href="http://www.scholarpedia.org/article/Spin-coefficient_formalism" rel="nofollow noreferrer">Newman-Penrose scalars</a> do not have definite spin w... | https://physics.stackexchange.com/questions/526164/make-newman-penrose-scalars-definite-spin-weight |
Question: <p>Suppose we do an experiment on earth and light a monochromatic light near a highly dense object. Does it cause any change in the wavelength of light? </p>
Answer: | https://physics.stackexchange.com/questions/525469/does-curvature-of-spacetime-changes-the-wavelength-of-light |
Question: <p>I have a question regarding the Gödel metric. Supposedly the Gödel universe is filled with rotating pressure-less dust.
However, checking different sources, it seems like Einstein's field equations are satisfied in this case for a perfect fluid without pressure and 4-velocity <span class="math-container">... | https://physics.stackexchange.com/questions/525772/rotating-dust-in-g%c3%b6del-universe |
Question: <p>I came across this question:</p>
<p><strong>"If there are two point masses in free space(i.e., there is no other mass/force/field acting in their vicinity), will those two point masses get closer to each other, or will they remain stationary as they are?"</strong></p>
<p>I approached this question throug... | https://physics.stackexchange.com/questions/526989/gravitational-motion-of-2-point-masses-in-free-space |
Question: <p>Observer independence means that the physic involved is independent of the reference frame of the observers but observers can't agree on the vacuum temperature due to the the Unruh Effect, does this not violate GR's principle? If we can't agree on the energy we can't agree on curvature, correct?</p>
Answe... | https://physics.stackexchange.com/questions/528820/does-the-unruh-effect-violate-observer-independence-in-general-relativity |
Question: <p>Ok, I apologize in advance if this has been asked before. I tried googling for it, but didnt find anything related. Im a comp sci guy, not a physics guy, so its possible Im not googling the right terms. </p>
<p>So my understanding is that: </p>
<p>A) Photons of light do not experience time in their refer... | https://physics.stackexchange.com/questions/532814/if-a-photon-does-not-experience-time-how-is-it-affected-by-gravitational-pull-o |
Question: <p>A black hole would distort spacetime time to a greater degree than planet Earth. That is, both the radius and the gradient of the distortion are greater. </p>
<p>Is there a term that combines "greater radius" and "greater gradient" into one?</p>
<p>In layman terms, a black hole distorts spacetime more "a... | https://physics.stackexchange.com/questions/541651/term-for-radius-and-gradient-of-spacetime-distortion |
Question: <p>I was reading about "vacuum solution" in wiki, <a href="http://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity)" rel="noreferrer">http://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity)</a>. There are some words I'm confused.</p>
<blockquote>
<p>1.In general relativity, a vacu... | https://physics.stackexchange.com/questions/137153/do-gravitational-fields-exist-in-vacuum-region |
Question: <p>This question is mainly inspired after watching the movie known as Interstellar</p>
<p>We knew that for time dilation caused by relativistic motion between A and B. A will measure <strong>B's clocks slowing down</strong>, and B will measure <strong>A's clock slowing down</strong> by the same rate, while th... | https://physics.stackexchange.com/questions/154061/gravitational-time-dilation-does-time-of-the-observer-at-a-lower-gravitational |
Question: <p>Let's say that we have two homogeneous spherical balls - one with mass <span class="math-container">$m_1=1000m$</span> and radius <span class="math-container">$r_1=1000r$</span> and second with mass <span class="math-container">$m$</span> and radius <span class="math-container">$r$</span>. Distance between... | https://physics.stackexchange.com/questions/561508/how-would-einstein-calculate-acceleration-of-a-ball |
Question: <p>I think I have found a way to easily understand time-like and space-like paths with the contect of a little linear algebra. My question is: is my understanding, below, correct?</p>
<p>When I learned General Relativity, one source of some confusion was how to find the actual time or distance from a metric. ... | https://physics.stackexchange.com/questions/565750/an-easy-way-to-determine-the-space-like-and-time-like-paths-on-a-spacetime-manif |
Question: <p>In general theory of relativity the Einstein field equations e.g. relate the geometry of space-time with the distribution of one body within it.
<span class="math-container">$$R_{\mu\nu}-\dfrac{1}{2}g_{\mu\nu}R+g_{\mu\nu}\Lambda=\dfrac{8\pi G}{c^4}T_{\mu\nu}.$$</span></p>
<p>What will be the "Einstein... | https://physics.stackexchange.com/questions/566281/what-will-be-the-einstein-field-equations-for-two-or-three-bodies |
Question: <p>While reading $\textrm{Present status of the Penrose Inequality}$ by Marc Mars, 2009, I was confused with the following statement:</p>
<blockquote>
<p>... in order to determine whether a space-time is a black hole, detailed knowledge of its global future behaviour is required.</p>
</blockquote>
<p>Why ... | https://physics.stackexchange.com/questions/233034/when-is-a-spacetime-a-black-hole |
Question: <p>One basic result of general geometry (from math) in curved spaces or on curved surfaces is that if you are in a surface of variable curvature, things like the Euclidean congruence postulates and theorems for triangles and other simple figures fail, and the reason this is is because those are actually stron... | https://physics.stackexchange.com/questions/244842/elementary-question-about-non-euclidean-geometry-in-general-relativity-cannot |
Question: <p>Einstein's equation is</p>
<p>$$8πT_{ab}=G_{ab}$$</p>
<p>where the left side contains the stress-energy tensor and the right side contains the Einstein tensor. </p>
<p>Is there exactly one unique stress-energy tensor corresponding to a given spacetime curvature? Or is it possible for one curvature (i.e.... | https://physics.stackexchange.com/questions/244884/can-we-distinguish-between-two-mass-distributions-in-spacetime-having-the-same-e |
Question: <p><span class="math-container">$R_{\mu v}=\frac{\partial}{\partial x^{\lambda}} \Gamma_{\mu v}^{\lambda}+\Gamma_{\mu \lambda}^{\eta} \Gamma_{v \eta}^{\lambda}$</span></p>
<p>equation (2) after the multiplication of the meteric tensor</p>
<p><span class="math-container">$g^{\nu\sigma}R_{\mu v}=\frac{\partial}... | https://physics.stackexchange.com/questions/696194/i-cant-understand-where-the-minus-sign-in-the-second-equation-is-coming-from |
Question: <p>Often the Penrose diagram is drawn for pure AdS or AdS-Schwarzschild black hole. What is the Penrose diagram for a star that is not collapsing in AdS?</p>
Answer: | https://physics.stackexchange.com/questions/527460/penrose-diagram-of-a-star-in-ads |
Question: <p>This is really a philosophical question, which I've already asked at Phil.SE but I'm asking here with more physics detail.</p>
<p>In Newtonian Mechanics, space and time are independent of each other, and of motion; in that the geometry of space time is independent of the distribution of matter and energy a... | https://physics.stackexchange.com/questions/167044/does-gr-reflect-aristotelian-time |
Question: <p>I am trying to derive Teukolsky equation on Kerr spacetime using SageMath and</p>
<p>(1) [(Δ+3γ−γ∗+4μ+μ∗)(D+4ϵ−ρ)−(δ∗−τ∗+β∗+3α+4π)(δ−τ+4β)−3ψ2]ψ4=0.</p>
<p>Like he did in his <a href="https://articles.adsabs.harvard.edu/pdf/1973ApJ...185..635T" rel="nofollow noreferrer">paper</a>. But I did not have succes... | https://physics.stackexchange.com/questions/713899/derivation-of-teukolsky-equation-doesnt-match |
Question: <p>Suppose we have a object with mass "M" with small density and a object with same mass "M" but different density (like a large density). Does the curvature of spacetime same for the two object with same mass but different densities?</p>
Answer: <p>To start with, as pointed out in the comments, your questi... | https://physics.stackexchange.com/questions/275562/does-curvature-of-spacetime-depend-upon-the-mass-or-density-of-a-object |
Question: <p>Is the curvature of space-time a smooth function everywhere (except at black holes) in view of General relativity. By 'smooth' it is meant that it possesses derivatives of all order at a given point. </p>
Answer: <p>No, not at the boundary of a solid object like a planet. There's a step function in the s... | https://physics.stackexchange.com/questions/1628/is-the-curvature-of-space-time-a-smooth-function-everywhere-except-at-black-h |
Question: <p>A previous <a href="https://physics.stackexchange.com/questions/1628/is-the-curvature-of-space-time-a-smooth-function-everywhere-except-at-black-ho">Stack question</a> (before I joined) asking about continuity in GR received replies which suggested that Curvature would be discontinuous at say a planetary b... | https://physics.stackexchange.com/questions/3751/the-matter-vacuum-boundary-in-general-relativity |
Question: <p>I am speaking about GR with classical fields and energy. One question, spread over three increasingly strict situations:</p>
<p>Is there an energy density limit in GR? (literally, can the energy density have an arbitrarily large value at some point in space at some point in time)</p>
<p>Is there an energ... | https://physics.stackexchange.com/questions/7771/is-there-an-energy-density-limit-in-gr |
Question: <p>According to Rindler the geodetic effect can be considered as consisting of Thomas precession combined with the effect of moving through curved space.</p>
<p>Wolfgang Rindler (2006) Relativity: special, general, and cosmological (2nd Ed.) p234</p>
<p>However according to Misner, Thorne, and Wheeler, Grav... | https://physics.stackexchange.com/questions/8043/decomposing-geodetic-de-sitter-effect-into-thomas-precession-and-spatial-curvatu |
Question: <p>If we have a perfect Schwarzschild black hole (uncharged and stationary), and we "perturb" the black hole by dropping in a some small object. For simplicity "dropping" means sending the object on straight inward trajectory near the speed of light.</p>
<p>Clearly the falling object will cause some small (... | https://physics.stackexchange.com/questions/8307/perturbation-of-a-schwarzschild-black-hole |
Question: <blockquote>
<p>"A four-dimensional differentiable (Hausdorff and paracompact) manifold $M$ will be called a space time if it possesses a pseudo-Riemannian metric of hyperbolic normal signature $(+,-,-,-)$ and a time orientation. There will be no real loss of generality in physical applications if we assume... | https://physics.stackexchange.com/questions/10329/a-question-on-an-assumption-of-space-time |
Question: <p>If a person has a good grounding in classical mechanics, electrodynamics and special relativity, is Einstein's 1916 paper a recommended way of learning about the subject?</p>
<p>After looking through it briefly, I like what I see because he explains all about tensors from first principles. On the other ha... | https://physics.stackexchange.com/questions/14241/is-einsteins-1916-general-relativity-paper-a-recommended-way-to-start-learning |
Question: <p>Why, if the Schwarzschild metric is a vacuum solution ($T_{\mu\nu}=0$) , do textbooks state that $T=\rho c^{2}$ when approximating Poisson's Equation from the Einstein Field Equations? </p>
<p>Thank you.</p>
Answer: <p>There is a coordinate slicing known as the Kerr-Schild coordinate system where one ca... | https://physics.stackexchange.com/questions/15187/schwarzschild-metric |
Question: <p>In Hartle's General Relativity book ("Gravity"), one of the problems (chapter 8 problem 6) is to prove that $g_{\mu\nu}u^\mu u^\nu$ is conserved along geodesics (really not hard to show), where $u^\mu$ is the 4-velocity. My question is: Isn't it true that $g_{\mu\nu}u^\mu u^\nu$ is equal to $-1$ for <em>an... | https://physics.stackexchange.com/questions/16852/is-4-velocity-normalized-to-1-even-for-non-geodesic-timelike-curves |
Question: <p>I'm trying to understand proper distance equation in Schwarzschild spacetime.</p>
<p>$d\sigma=\frac{dr}{\left(1-\frac{R_{S}}{r}\right)^{1/2}}$.</p>
<p>I'm sure I'm missing something really obvious here, but how do I use this to find the coordinate distance $r$
for a particular proper distance $\sigma$
... | https://physics.stackexchange.com/questions/18553/proper-distance-and-embedding-diagrams |
Question: <p>A Thought Experiment:</p>
<p>We are in flat spaceime provided with a reference frame—a rectangular Cartesian frame. The coordinate labels[the spatial labels] are visible to us. Each spatial point is provided with a clock—and the different clocks are synchronized wrt to each other. Gravity is now turned on... | https://physics.stackexchange.com/questions/18616/projective-transformations-in-gr |
Question: <p>The de Donder gauge is often used to simplify the linearised equations of motion of general relativity. If the metric is linearised as $g_{ab} = \bar g_{ab} + \gamma_{ab}$, then the de Donder gauge reads<br>
$\nabla^a(\gamma_{ab} - \frac{1}{2}\bar g_{ab}\gamma) = 0$.</p>
<p>The partial differential equati... | https://physics.stackexchange.com/questions/19684/modification-of-de-donder-gauge |
Question: <p>This may be obvious but I have limited experience in physics , The generators of Spatial translation symmetry commutes with each other i.e [P(i),P(j)] = 0 but if Spacetime is a curved manifolds then the value of the commutator should not be zero but some invariant property related to curvature i.e a Functi... | https://physics.stackexchange.com/questions/21628/what-should-be-the-equation-satisfied-by-the-momentum-commutators-in-a-curved-ba |
Question: <p>Consider a mass 'm' suspended in the gravitational field of a massive star. Assuming the Schwarzschild metric it is easy to calculate the gravitational acceleration at the location of the mass and thus the tension in the cable. The question is: how does this tension propagate up the cable?</p>
<p>I've t... | https://physics.stackexchange.com/questions/22292/tension-on-a-cable-in-a-gravitational-field |
Question: <p>I'm interested in the derivation of the Gauss equation (Gauss-Codazzi). Usually we consider the definition of the Riemann tensor on the hypersurface.</p>
<p>$$^{(n-1)}R_{abc}^{~~~~~~~d}~w_d=[D_a,D_b]w_c$$</p>
<p>where $D$ is the connexion associated to the induced metric ($h$) on the hypersurface.</p>
<... | https://physics.stackexchange.com/questions/23749/derivation-of-the-gauss-codazzi-equation |
Question: <p>Events in relativity[SR or GR]are marked by coordinate values and not by physical values.We write a metric for motion along the x-axis:
$$ds^2=g_{00}dt^2-g_{11}dx^2$$ ----------- (1)</p>
<p>For physical values we may write:</p>
<p>$$ds^2=dT^2-dL^2$$ ------------ (2)</p>
<p>Where $dT^2=g_{00}dt^2$ and $d... | https://physics.stackexchange.com/questions/24514/the-light-cone-in-gr-a-flickering-one |
Question: <p>there is a relation between time and space in special theory of relativity:
$$t^2c^2-L^2=\tau^2.c^2$$
what is relation between time and space in general relativity?</p>
Answer: <p>The remarkable property of spacetime in GR is that it is <em>locally</em> that of SR. Or, more technically, tangent to every ... | https://physics.stackexchange.com/questions/30877/what-is-relation-between-time-and-space-in-general-relativity |
Question: <p>Imagine that I have a radioactive material with a long half life. The atoms in this material decay at a certain rate $R$. The rate is the decay constant times the number density $R = \lambda N $. It has dimensionality:</p>
<p>$$ \left( \frac{ \text{decays} }{m^3 s} \right) $$</p>
<p>Imagine that the ... | https://physics.stackexchange.com/questions/38986/is-a-volumetric-rate-frame-invariant-in-general-relativity |
Question: <p>Do <a href="http://mathworld.wolfram.com/ChristoffelSymbol.html" rel="nofollow">Christoffel symbols</a> commute? For example, does $\Gamma^{e}_{db}\Gamma^{c}_{ea} = \Gamma^{c}_{ea}\Gamma^{e}_{db}$?</p>
Answer: <p>In classical theory, all observables commute. The components $\Gamma^a_{bc}$ are just real nu... | https://physics.stackexchange.com/questions/41437/do-christoffel-symbols-commute |
Question: <p>The classical theory of spacetime geometry that we call gravity consists of the Einstein equation, which relates the curvature of spacetime to the distribution of matter and energy in spacetime.
$ds^2=g_{\mu\nu}dx^{\mu}dx^{\nu}$
<strong>Mathematically</strong>, how do the Einstein's differential equation o... | https://physics.stackexchange.com/questions/45307/how-do-the-einsteins-differential-equation-of-the-curvature-of-spacetime-come-o |
Question: <p>How can I go from the 'standard' Einstein equations
$R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = \frac{8\pi G}{c^4}T_{\mu\nu}$ to these equations:
$R_{\mu\nu} = \frac{8\pi G}{c^4}(T_{\mu\nu} - \frac{1}{2}g_{\mu\nu}T)$?</p>
Answer: <p>Take the trace of the equation by contracting it with $g^{\mu\nu}$:</p>
<p>$$... | https://physics.stackexchange.com/questions/50141/how-does-one-write-the-einstein-field-equations-in-terms-of-ricci-tensor |
Question: <p>Is Einsteins Equivalence theorem in General Relativity correct? It seems to me that it neglects the fact that gravitational acceleration depends upon separation distance squared, thus neglecting the effect of tidal forces. </p>
<p>For example, as I sit on earth, I experience the affect of earth's gravity;... | https://physics.stackexchange.com/questions/55496/general-relativity-equivalence |
Question: <ul>
<li>Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A.</li>
<li>Suppose there is another habitable star with a much smaller mass, also with a clock, called St... | https://physics.stackexchange.com/questions/56998/general-relativity-paradox-different-local-times-of-two-frames-a-constant-dist |
Question: <p><a href="http://en.wikipedia.org/wiki/Einstein_field_equations">Einstein's field equation</a>:</p>
<p>$$G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} - g_{\mu\nu}\Lambda$$</p>
<p>I'm trying to understand each of the terms in this equation intuitively, but I'm struggling.</p>
<p>Basically, I want to understa... | https://physics.stackexchange.com/questions/61179/understanding-einsteins-field-equation |
Question: <p>My question concerns the following definition</p>
<blockquote>
<p><strong>Definition:</strong> The <em>timelike</em> (resp. null) <em>generic condition</em> in GR is fulfilled if
$$u_{[\alpha} R_{\rho]\mu \nu [\sigma}u_{\beta]}u^\mu u^\nu \ne 0$$
at some point of each timelike (resp. null) geodesi... | https://physics.stackexchange.com/questions/70193/timelike-null-generic-condition-in-general-relativity |
Question: <p>I am reading the original paper by Bondi, van der Berg and Metzner (<a href="http://rspa.royalsocietypublishing.org/content/269/1336/21" rel="nofollow">link</a>) regarding gravitational waves in asymptotically flat axisymmetric spacetimes. In the introduction, he makes the following comment - </p>
<blockq... | https://physics.stackexchange.com/questions/71952/conservation-of-energy-and-birkhoffs-theorem |
Question: <p>This is a question about an historical theory of gravitation, studied by Einstein quite a bit <em>before</em> he settled on General Relativity. At that time, Einstein did not know that gravity was a consequence of curved space-time. He identified the variations of gravity with the variations of light speed... | https://physics.stackexchange.com/questions/72054/about-an-einstein-equation |
Question: <p>I am reading the paper on Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems by H. Bondi, M. G. J. van der Burg, A. W. K. Metzner. (<a href="http://rspa.royalsocietypublishing.org/content/269/1336/21" rel="nofollow noreferrer">link</a>) Here is a quote(s) from that pa... | https://physics.stackexchange.com/questions/72074/axial-symmetry-constraints-on-the-metric |
Question: <p>It seems if I reverse velocities then things begin orbiting backwards, at least in classical mechanics.</p>
<p>From <a href="https://en.wikipedia.org/wiki/Orbital_mechanics#Laws_of_astrodynamics" rel="nofollow">here</a>:</p>
<blockquote>
<p>Every orbit and trajectory outside atmospheres is in principle... | https://physics.stackexchange.com/questions/72359/are-orbits-reversible-in-general-relativity |
Question: <p>After the work from Breitenlohner and Freedman, we know matter fields in asymptotically AdS spacetime can be stable out of the black hole under some special conditions.</p>
<p><strong>My question:</strong> In such a spherically symmetric spacetime, could the matter field has the non-radial variable of the... | https://physics.stackexchange.com/questions/78608/is-it-possible-that-a-matter-field-has-a-dependent-on-non-radial-space-like-coor |
Question: <p>Consider a point mass $A$ with mass $m$ in empty space. The point mass $A$ does not have a velocity and does not rotate.
Since gravity is symmetric for nonmoving objects, the spacetime curvature around $A$ is also symmetric.</p>
<p>So at a distance $d$ from the point mass $A$ how strong is the curvature $... | https://physics.stackexchange.com/questions/92769/how-strong-is-the-spacetime-curvature-at-distance-d-for-a-nonmoving-point-mass |
Question: <p>I don't know much about <a href="http://ncatlab.org/nlab/show/tangent+bundle" rel="nofollow noreferrer"><i>tangent spaces</i>, or <i>tangent vectors</i>, "as such"</a>; nor about <a href="http://en.wikipedia.org/wiki/Schild%27s_ladder#affine_parametrization" rel="nofollow noreferrer"><i>affine parametrizat... | https://physics.stackexchange.com/questions/93037/is-it-possible-to-express-free-ness-of-a-time-like-world-line-without-referrin |
Question: <p>Considering a static spacetime of the metric form
\begin{equation}
\mathrm{d}s^{2}=-V^{2}\mathrm{d}t^{2}+h_{ij}\mathrm{d}x^{i}\mathrm{d}x^{j}
\end{equation}
with a timelike killing field $\xi^{\mu}=(\partial_{t})^{\mu}$ we
can choose a function space on each constant time hypersurface $\Sigma$
as$\mathcal... | https://physics.stackexchange.com/questions/100996/sobolev-norm-for-schwarzschild-metric |
Question: <p>In General Relativity, if the system accelerates, the inside of the system and the outside of the system will have different speed of time.</p>
<p>Where is the boundary of the system? </p>
<p>If a human accelerates closer to the speed of light, does that mean the human exist inside of their specific syst... | https://physics.stackexchange.com/questions/111766/the-border-of-the-system |
Question: <p>I have some confusion about the concept of stationary and static.</p>
<p>A metric $g$ is called <strong>stationary</strong> if there is a time like Killing vector $K$.</p>
<p>$g$ is called <strong>static</strong> is further HSO (hyper surface orthogonal), i.e. there exists a foliation of hyper surface or... | https://physics.stackexchange.com/questions/112670/stationary-and-static |
Question: <p>What is the <em>effective</em> physical difference between a large region of curved space-time and an equally large region of a polarized vacuum? Consider the fact that vacuum polarization amounts to an effective deviation in speed of light in a local region due to the deviation in electric permittivity o... | https://physics.stackexchange.com/questions/114091/what-is-the-effective-physical-difference-between-a-massive-region-of-a-polarize |
Question: <p>The Boyer-Lindquist coordinate coordinate of the Kerr Solution is
$$
ds^2=\left(1-\frac{2Mr}{\Sigma}\right)dt^2+\frac{4Mar\sin^2\theta}{\Sigma}dtd\phi - \frac{\Sigma}{\Delta}dr^2-\Sigma d\theta^2-\left(r^2+a^2+\frac{2Ma^2r\sin^2\theta}{\Sigma}\right)\sin^2\theta d\phi^2
$$</p>
<p>Let
$$
K=\frac{\partial}{... | https://physics.stackexchange.com/questions/117325/hyper-surface-orthogonal-vector-in-boyer-lindquist-coordinate |
Question: <p>As far as I have the knowledge of GTR that a mass bends the space time around it.But why does this bend occur?The example from real life that when a mass is placed on a net then the net bends but it us very difficult for me to visualise the situation of bending of spacetime due to a mass.What is actually h... | https://physics.stackexchange.com/questions/132481/why-do-the-space-time-get-curved-around-a-massive-objectwhat-problems-do-we-fac |
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