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Questions tagged [general-relativity]

A theory that describes how matter interacts dynamically with the geometry of space and time. It was first published by Einstein in 1915 and is currently used to study the structure and evolution of the universe, as well as having practical applications like GPS.

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Innermost stable circular orbit in Schwarzschild solution

I've been reading about GR recently and I can follow the derivation of a Schwarzschild solution to it's final and well known form in Schwarzschild coordinates. The orbit stability argument (for a ...
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Kaluza-Klein theory metric

What are the physical dimensions of the 5x5 Kaluza-Klein metric? ( the metric should be dimensionless but doesn't look so with the inclusion of the four potential and the scalar field)
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How do we explain this new take on the old Twins Paradox?

Here's a new take on the age old Twins Paradox that I have not been able to figure out. We have two twins in two separate space ships at the same place and time. Twin A fires his thrusters for 1 year ...
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Is the BMS approach to asymptotic flatness more general than Penrose/Hawking's?

It seems there are two main approaches to asymptotic flatness: one due to Bondi-Metzner-Sachs and another due to Newman-Penrose and explained in Hawking's GR textbook "The Large Scale Structure of ...
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Why are coordinate systems used in General Relativity if it is a background independent theory?

I am studying topological manifolds as a prerequisite to studying General Relativity and although this question is premature since I have not yet begun the latter it is bothering me. From basic ...
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Under what circumstances are general relativistic coordinate transformations physically meaningful?

Although the field equations of GR are covariant under arbitrary coordinate transformations, such as the transformation given by Dirac (in Princeton Landmarks pp 34) that eliminate the singularities ...
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Simulating the spherical halo of dark matter around the galaxy using Einstein's GR

So far as I understand, the distribution of dark matter in the form of an invisible spherical halo embedding the galactic disc is simulated using Newtonian gravity. Has there been any enterprise of ...
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What is the relationship between how time is viewed in thermodynamics and how time is viewed in general relativity?

From my limited understanding of physics, it seems that the second law of thermodynamics, in which entropy never decreases over time in a closed system, relates to how time can only go forward i.e. ...
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Simple question about change of coordinates

Suppose we have two coordinate systems (Cartesian and spherical) $$x^{\mu} = (t,x,y,z)$$ $$x'^{\mu'} = (t',r,\theta,\phi)$$ where $r= \sqrt{x^2 + y^2 + z^2} , \theta = \cos^{-1}(z/r), \phi = \tan^{-...
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How can velocity be a tensor?

I have just begun studying general relativity and have a question. I know that if a tensor is zero in one coordinate system, it will be zero in all coordinate systems. So how can the $\mu$'th ...
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Gravitational time dilation and a race [on hold]

If there is a person far away from a gravitational source(higher gravitational potential) the faster time passes relative to a person closer to that gravitational field. Is this correct?(this is how I ...
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Derivation of the energy-momentum tensor from matter Lagrangian

We know that the energy momentum tensor for a perfect fluid is given by $$ T_{\mu\nu} = \left(\rho+{p\over c^2}\right) v_\mu v_\nu + p g_{\mu\nu}. $$ How can we derive it from a Lagrangian? Which ...
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Problem in finding relationship between coordinates using metric tensor transformation rule

If suppose we are given with two metrics of spacetime. $$ds^2=(1+h)^2d\tau^2 -dh^2$$ and $$ds^2=\rho^2dt^2 -d\rho^2$$ Then is it possible to find the relationship between these two coordinate ...
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expression for pressure and energy density given stress tensor

I'm playing with a metric of the form $ds^{2} = f(r)dt^2 +a(t)[g(r)dr^2 + r^2 d\theta^2 +r^2 \sin^{2}\theta d\phi^2]$ From this I constructed the einstein tensor and then using the einstein field ...
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Do white holes encode the future evaporation of the black hole?

In General Relativity, white holes arise when one formulates Maximal extensions (the process by which coordinate singularities are mapped to new non-degenerate coordinates) to a geometric solution (...
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non-zero divergence of stress energy tensor

are there spacetime metrics where $\nabla_{\nu}T^{\mu\nu} \ne 0$ ? if the divergence of the energy momentum tensor is non-zero, what does that tell us about the spacetime aside from the fact that ...
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Lorentz covariant derivative of the vielbein determinant

Denote by $\mathcal{D}_m$ the Lorentz covariant derivative, $$\mathcal{D}_m=\partial_m-\frac{1}{2}\omega_m{}^{ab}M_{ab} \tag{1}$$ where indices $m,n,p,\dots$ are world indices, indices $a,b,c,\dots$ ...
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Calculating surface gravity

I have some trouble with understanding how surface gravity/Killing horizon equation works, for example in following form: $$κ^2=-\frac 12 (\nabla^aK^b)(\nabla_aK_b)$$ with Killing vector $K$. I'm ...
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String theory and background independence

I have read that string theory assumes strings live in spacetime defined by general relativity which make the theory background dependent (although general relativity is a background independent ...
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Mercury perihelion advancement [on hold]

By Newton's gravity equations 5557 out of 5600 arc sec Mercury perihelion advancement derived from other planets gravitational attraction. Whether regular asteroids striking force could explain ...
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Is 4 Vector related to mass in changing axis geometry? [on hold]

Am I getting this right? Mass is the deviation of the rest level of the grid (space/time); as defined by the four vector. Mass is the Lorentz Transformation on the axis (x, y, z, and time) where the ...
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What condition do global coordinates fulfil?

This may be a dumb or vague question: Is there any criterion that a metric tensor needs to fulfill such that coordinates it is expressed in can be called global. Or alternatively what is the ...
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Trading clocks in two different reference frames

I'm a high school student, just learned relativity. I understand that observed time is different between two different inertial reference frames. I vaguely understand that time is different in two ...
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31 views

General Relativity Lagrangian Part 2

This is a continuation of this. I am asked to calculate the second order correction to h in T. So I wrote $h=h_0+h_1+h_2+...$ where $h_0$ is the first order, $h_1$ is the second and so on. Plugging in ...
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Relativity of simultaneity in train experiment-doesn't Doppler effect reveal simultaneity?

In Einstein's simultaneity thought experiment with the "moving" train and lightning strikes, wouldn't the observer on the train be able to deduce the simultaneity of the lighting strikes from the fact ...
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General Relativity Lagrangian

The Lagrangian density for the $h=h^{00}$ term of the Einstein gravity tensor can be simplified to: $$L=-\frac{1}{2}h\Box h + (M_p)^ah^2\Box h - (M_p)^b h T$$ The equations of motion following from ...
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What is the physical meaning of a vector space, basis and tangent bundle? [closed]

I've been studying General Relativity, mostly from Spacetime and Geometry by Sean Carroll and I don't really understand the physical meaning of all the mathematical terms used. I know what the ...
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Is it possible to test the physical reality of extra dimensions predicted by string theory?

I have no business asking this question since I am not a string scientist but I like to follow science news in phys.org and I read an article dated today Gravitational waves provide dose of reality ...
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what does the Thermal redshift mean?

I am reading a paper on UHE neutrinos, it talks about the importance of considering the thermal effects for components of cosmic neutrino background in the scattering with UHE neutrinos. and the ...
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Black Holes as a collection of unreachable events [closed]

I recently watched this video on YouTube by PBS Space Time called "Do Events Inside Black Holes Happen?" https://www.youtube.com/watch?v=vNaEBbFbvcY This video talks about many misconceptions about ...
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Why does the lowered Riemann tensor only have 20 independent components for the Schwarzschild metric?

I have seen quite a bit online about how there are only 20 independent components for the (lowered) Riemann tensor $R_{abcd}$ for the Schwarzschild metric. I've been told this follows from the ...
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Cookie Cutter Relativity

A situation similar to this arose in my high-school modern physics course, and I had a question to ask that I hope someone is willing to answer. Suppose a circular pad of cookie dough is being rolled ...
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Why there are these two angular coordinates in a general spacetime?

In the paper "Gravitational Waves in General Relativity. VIII. Waves in Assymptotically Flat Space-Time" by R. Sachs, the author constructs a system of coordinates in section 2 for a general spacetime....
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Why "an interval along $\mathscr{I}^-$ is $(v^0-v)=2(r^0_\ast-r_\ast)$?

In this paper the author reviews the derivation of Hawking radiation on a gravitational collapse spacetime. They point out on p. 3 that an essential part of the derivation is that if $u^0,v^0$ are ...
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Formula for Christoffel Symbols in Terms of Derivatives of Riemannian Metric with Contravariant Indices? [closed]

The following formula represents the usual textbook way of computing the Christoffel symbols of the second kind ${\Gamma^i}_{jk}$ via the Riemannian metric with covariant indices $g_{mn}$ and spatial ...
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1answer
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The theater, the actors and the 'graviton' [duplicate]

In my perception of the universe, there's the theater which is the 'spacetime' and the actors meaning the 'particles'. If i got it right, GR claims that the 'actors' effect the 'theatre' by 'bending' ...
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Could it be really possible to go through a tunnel into a new universe like in the movie Coraline? [duplicate]

I originally asked this question at Worldbuilding Stack Exchange and now I see that it doesn't seem very suitable there so I think here might be a better place. I don't understand how general ...
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The $t$-coordinate bounds inside a black hole

In case of the Schwarzschild black hole, the $t$ coordinate inside the event horizon becomes spacelike. Hypothetically, if one had too much time inside a grand-super-massive black hole and decided to ...
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Black hole inside of a singular (not a galaxy) macro object?

I understand that black holes have so much stress-energy, that even light cannot escape them. Now based on that, I would understand it so, that it the black hole gets near enough to anything, the ...
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rewriting the graviton propagator

The graviton propagator is usually given by $P^{\mu\nu\alpha\beta}= \frac{1}{2}(\eta^{\mu\alpha}\eta^{\nu\beta}+\eta^{\mu\beta}\eta^{\nu\alpha}-\eta^{\nu\mu}\eta^{\alpha\beta})$ This may be ...
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Irreducible mass of a charged black hole merger

The irreducible mass $ \rm m_{irr} $ of a black hole with charge $ \rm Q $ is (in natural units) $$ \rm m_{irr} = \frac{r_{+}}{2} = \frac{M}{2} + \sqrt{\frac{M^2}{4} - \frac{Q^2}{4}} $$ which is ...
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Minkowski Space is not truly conformally compact

We say a manifold $(M,g)$ is conformally compact if it is the interior of some $(\overline M, \overline g)$, such that $$g = r^{-2}\overline g|_M,\quad \mathcal Z(r) = \partial M,\quad \text{and}\quad ...
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elevator moving near the speed of light

Imagine that you are in an elevator that is moving downward at a constant speed that is near the speed of light (let's say close to the surface of the earth: toy problem, needless to say). Now say ...
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How are different metrics for spacetime constructed?

is a metric something derived? for example where does the extremal Reissner Nordstrom metric come from?
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62 views

Gravitational waves energy source in linearized theory

By linearizing the metric in the following way (approach in most textbooks): $g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\text{ with } |h_{\mu\nu}|\ll 1$ and choosing the transverse-traceless gauge a wave ...
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Black holes within scalar fields: is the problem self-consistent?

Many times I see papers devoted to "scalar black holes" or related to black holes with "scalar hairs". All of which confuses me. As an example, consider this 2004 paper from Phys. Rev. Lett. From the ...
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Do electric charges warp spacetime like stress-energy?

I have read these questions: Does charge bend spacetime like mass? Why is spacetime curved by mass but not charge? Where John Rennie says: "Charge does curve spacetime." And where Frederic Thomas ...
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Why is it so hard to form a theory of everything? [duplicate]

If quantum mechanics predicts that gravity doesn't exist and we observe that it does exist, all we have to do is form a new theory of quantum mechanics. It's really easy to show that a theory that's ...
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Energy-momentum tensor non-minimal scalar field

If we consider a non-minimal coupling term between gravity and scalar field for inflation, we can have some modifications for density and pressure of scalar field. I have some problems to obtain the ...