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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Life of a photon in gravity?

I have a simple thought experiment and I am not sure about the answer: What would happen to a photon that is emitted by an excited hydrogen in an otherwise empty universe? Would gravity of the atom ...
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0answers
75 views

Does rest mass increase in the FRW metric?

The flat FRW metric can be written in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ where $\eta$ is conformal time. Let us assume that $a(\eta_0)=1$ when $\eta_0$ is the present ...
3
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1answer
120 views

Tensor decomposition

I came across what a Physicist called "decomposing a tensor with respect to a congruence", something I simply cannot grasp. I searched a lot and I couldn't find any reference on that. I know that ...
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0answers
31 views

Black Holes should take infinite time to form with the increase in mass to form one [duplicate]

How can black hole form because as the density begins to increase gravity also start to increase and time starts to slow. wouldn't it take infinite time to form a black hole. how can anything fall ...
2
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0answers
47 views

Quasilocal stress tensor

I have been reading through the paper hep-th/9902121 and have a few questions about the first five lines of the introduction: 1) "In a generally covariant theory, it is unnatural to assign a local ...
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41 views
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156 views

Can space have angular momentum that can be transfered to/from physical objects?

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum. ...
0
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1answer
83 views

Variation of det metric tensor

I have the metric tensor $g_{\mu\nu}$. I want to make the variation of $\sqrt{-g}$ where $g=detg_{\mu\nu}$. Can I make this work? ...
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0answers
18 views

Traveling to the future is possible, but not to the past? [duplicate]

I understand how going to the future is possible: If you go really fast, time around you slows down for observers. But is it true that time traveling into the past isn't even theoretically possible?
2
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1answer
72 views

Why not all timelike world lines have infinite total length?

I don't understand this stament by Geroch(1968), when discussing the definition of singularity: We could not have required that all timelike world lines have infinite total length, for this ...
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1answer
40 views

How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity? [duplicate]

How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity? Most say that light cannot escape a black hole. Then gravity cannot escape a black hole either, so ...
0
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1answer
43 views

How is electromagnetic binding energy introduced in the stress-energy tensor

Take the hydrogen atom. It is easy to imagine that the gravitational pull it creates is smaller than the sum of those of the proton plus the electron, because a photon of 13.6 eV was created when the ...
2
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0answers
110 views

Why can't we fix the metric and its derivatives at boundary, with the variational method?

In general relativity and for its Einstein-Hilbert action, we usually ask that the metric variations $\delta g_{\mu \nu}$ cancel on the boundary $\partial \, \Omega$ of some region $\Omega$ of the ...
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47 views

Definition of Energy in Friedmann equations?

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density $\rho(t)$ is given by: $$\rho(t) \propto ...
5
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2answers
382 views

Gravitational waves and time

Two questions. It is said that time can only go slower in gravity fields and if you move faster. I have heard that when a gravitational wave pass earth then the space/time vibrate and time change ...
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1answer
104 views

If Alice is moving at relatavistic speeds compared to Bob, is collapse still simultaneous?

I have read some papers about experimental proof of non-locality involving a laser that goes through a beam-splitter and then each "half" goes to an observer (traditionally "Alice" and "Bob"). It has ...
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1answer
63 views

Distortion of body in Schwarzschild black hole

Suppose I toss a cloud of matter into a Schwarzschild black hole; for the sake of argument, have it be timelike dust. As we know, the dust is "spaghettified" by tidal forces: simultaneously compressed ...
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2answers
183 views

Conservation of energy and Killing-field

In general relativity we have no general conservation of energy and momentum. But if there exists a Killing-field we can show that this leads to a symmetry in spacetime and so to a conserved quantity. ...
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1answer
64 views

Is there a point at which spaghettification is highest?

I've read anything getting close to a regular black hole would experience spaghettification but not when you get close to super-massive black hole. Is there a point of "peak spaghettification" where ...
1
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1answer
50 views

Is there a principal difference in acceleration from an impulse and the free fall of a body in the orbit around a gravitational mass?

Especially taking in account that acceleration need a force which leads to some conversion of energy. This is not the case for orbital motion, such a acceleration does not convert energy. That seems ...
4
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225 views

Variation of the Einstein-Hilbert action in D dimensions without the Gibbons-Hawking-York term

Consider the standard Einstein-Hilbert action in $D \ne 2$ dimensions spacetimes : \begin{equation} S_{EH} = \frac{1}{2 \kappa} \int_{\Omega} R \; \sqrt{- g} \; d^D x, \end{equation} where $\Omega$ is ...
23
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5answers
5k views

Could gravity accelerate light? [duplicate]

Gravity causes anything with energy to accelerate toward the source. Black holes, for example, have such strong gravity that they pull in light and don't let any escape. But can acceleration still ...
2
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1answer
153 views

Infalling light signals seen by a free falling observer

In this question/answer Does someone falling into a black hole see the end of the universe?, it is stated that an observer free falling toward/into a black hole will not see the end of the Universe ...
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0answers
18 views

Effect of a photon on curvature of spacetime [duplicate]

Since light has no rest mass, is it reasonable to assume that the curvature of spacetime is not affected (distorted) by a single photon? Sure, a photon is attracted due to gravity. But could be ...
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0answers
34 views

How to derive the relation satisfied by “gravitational magnetic field” from an equation of the Weyl tensor?

Let us call the spacetime $M$ with a metric $g_{ab}$. There is a unit spacelike vector field $\eta^a$ orthogonal to a hypersurface. So that we can define the so-called gravitational electric and ...
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1answer
54 views

Describing the shape of a singularity

Hawking and Ellis write about the difficulty of describing the shape of a singularity when presented with a manifold that has curves of finite length that don't reach a point in the manifold. ...
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77 views

Why is special relativity still in use, if general relativity is more broad?

I always thought special relativity is only there because it is the building block for "The General theory of Relativity", until recently I encountered a text from my course book given below. A ...
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2answers
106 views

What general relativity predicts in such a situation?

If there's a system of a point mass or point particle with mass 'm' and a structure such that - The structure is made of many concentric spheres (shells) with certain thickness and the radius of those ...
0
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1answer
36 views

Nomenclature “Material System”

This is just a quick question about nomenclature from General Relativity. Most textbooks refer to "material systems"; 1) Does a material system have to be a system with mass? or can it just be a ...
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1answer
51 views

Constant-speed, straight-line spacetime trajectories and light

If orbiting objects are actually following constant speed, straight line paths in spacetime, why is it that massless particles (light) do not follow these paths?
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3answers
297 views

What would be the implications for current theories if gravitational waves are not detected? [closed]

Let's assume that scientists trying to detect gravitational waves get a huge raise in funding, design even better experiments, and run them for decades, but just can't find any gravitational waves ...
2
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2answers
67 views

Local Lorentz transformations

If $\gamma^m$ denotes a tangent space gamma matrix, and $\gamma^\mu$ denotes a curved space gamma matrix, then they are related by $$\gamma^\mu(x) = \gamma^m e_{m}^{\mu}(x)$$ where $e_{m}^{\mu}(x)$ ...
6
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3answers
486 views

“Warp-drive” thought experiment

Why wouldn't this "warp-drive" work? Assuming we can build a flywheel that can survive near light speed and have an onboard power storage or beamed energy that can spin it up to that speed and back ...
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1answer
65 views

Deriving the motion equation for a minimally-coupled scalar field in general relativity [closed]

From the following Lagrangian $$ L = \sqrt{-g} (R+\epsilon\partial^\mu\phi\partial_\mu\phi) $$ I'm getting the motion equation (for the field $g_{\mu\nu}$ and vaccum)as: $$ R_{\mu\nu} - ...
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0answers
24 views

Book recommendation for self study of General relativity [duplicate]

I am a second year Chemical Engineering student. However out of interest I wish to learn General theory of relativity. Can anyone please suggest some books for learning this subject?
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2answers
82 views

How does general relativity explain the impact force after radial inward fall toward Earth?

I understand that, in the context of the Schwarzschild spacetime (General Relativity), a radially inward falling observer follows a time-like geodesic with zero four-acceleration. There are no forces ...
2
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1answer
62 views

Universe Expansion - Could galaxies be moving away from each other due to photon bombardment?

We know galaxies are moving apart from each other due to the ability to look at the color shift of those galaxies. The fact that galaxies are moving apart seems to be most-widely attributed to the ...
0
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1answer
60 views

Why is spatial conformal infinity a point

One property of spatial infinity is that all spacelike geodesics end at it. Since spacelike geodesics can have different directions, I do not understand why spatial infinity is a point. It looks more ...
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1answer
89 views

How to get null tetrad by metric?

How to get null tetrads ${l^a,n^a,m^a,\overline{m}^a}$ for this metric? This on is from Ryder's book (Introduction to general relativity) page 268 $g^{\mu\nu}=\begin{pmatrix} 0 & \frac{1}{c} ...
7
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1answer
214 views

Homotopy proof of the lack of foliation of the Gödel metric

A common proof of the lack of foliation of the Gödel universe, apparently mostly copy pasted from Hawking and Ellis, goes thusly : A closed timelike curve must cross a spacelike hypersurface ...
6
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3answers
266 views

Why does the FLRW metric assume constant curvature?

So the FLRW metric takes the following form in reduced-circumference polar coordinates. $$\mathrm ds^2 = -c^2 \mathrm dt^2 + a^2(t) \left(\frac{\mathrm dr^2}{1 - k\, r^2} + r^2 (\mathrm ...
2
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0answers
28 views

How fast can an object spin? [duplicate]

Without any forces in space to stop it, assuming an object does not collide with anything or enters any kind of gravitational pull, how fast could the object spin. I mean the earth spins quite fast, ...
3
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2answers
151 views

Why is “gravitational” red-shift neglected in galaxy and galaxy cluster scales?

The red-shift of the light of a star in a galaxy or that of a galaxy in a cluster of galaxies is generally interpreted as how fast the star or the galaxy is moving, i.e. it is interpreted in a purely ...
2
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0answers
56 views

Full form of the Pauli-Fierz action

In Deser's paper on the fully interacting version of the Pauli Fierz theory, he does a rather simple method of treating the Pauli Fierz equation without going with infinite sums, just by treating the ...
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0answers
35 views

Local Translation of frame field- Geometric Picture

In order to phrase my question I review my geometrical picture of the first order formulation of gravity: Given some d-dimensional manifold $\mathcal{M}$ one constructs the Frame bundle $FM$, a ...
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1answer
114 views

Does $g_{\mu\mu}$ in an expression follow the Einstein summation convention?

Assume that I have the expression for a Christoffel symbol: $$ \Gamma^\mu_{\alpha \beta}=\frac{1}{2}g^{\mu \lambda}(\partial_\alpha g_{\beta \lambda}+\partial_\beta g_{\alpha \lambda} - ...
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0answers
33 views

Solving the Stress-energy-momentum tensor with metric

Let's say I want to find an expression for $T_{00}$ in Einstein field equations given a particular metric. I need to find first $g_{00}$, which is not complicated to find, and $R_{00}$ which is ...
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2answers
143 views

Einstein field equations and SEM tensor + Alcubierre

I wonder how I can find, using the Einstein field equations, the SEM tensor in a region of space with a function $k(x,y,x)$ that describes the curvature of space in that region at a moment (so it is ...
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0answers
20 views

Do clocks near the centre of the galaxy run slower than clocks at the edge? [duplicate]

Does an astronaut floating in space near the center of the galaxy, where the mass density is higher (let's ignore the dark matter halo for this example) have a clock that runs slower than an astronaut ...
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1answer
72 views

Einstein equivalence principle cannot entirely predict gravitational time dilation

The Einstein equivalence principle can be used to derive the gravitational redshift of photons, but it does so in an unusual way. The derivation is as follows. Consider an source of photons on the ...