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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On four-vectors

When one starts learning about physics, vectors are presented as mathematical quantities in space which have a direction and a magnitude. This geometric point of view has encoded in it the idea that ...
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0answers
6 views

If all motion is relative, how does light have a finite speed?

Firstly, I'd like to apologize. This is probably a dumb question for whoever can answer it. My question is a conceptual one. I've often heard that Einstein shattered the notion of absolute motion ...
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0answers
7 views

Was the impossibility of the second degree perpetuum mobile in the General Relativity ever proven?

Somewhere I've heard, that gravity often likes to work against the entropy. For example, the surprisingly low temperature of the black holes. Or see the gravitational separation of different elements ...
4
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1answer
43 views

Does geodesic incompleteness in Penrose-Hawking theorems imply curvature blow up?

The singularity theorems in General Realtivity roughly stated say that given: A global causal condition An energy condition The existence of a closed trapped surface then spacetime must be ...
0
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2answers
121 views

Gravitational time dilatation calculation [on hold]

I'm proving an example case from Kip Thorne's book, Science of Interstellar for time dilatation at a Kerr black hole with the following data: \begin{align} a & = 0.998, \\ r & = ...
2
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1answer
126 views

Null geodesic equation

For a null geodesic curve $X^i$, $$0=g_{ij}V^iV^j.$$ When we derive the geodesic equation from E-L equations, will this affine parametrization cause it to blow up? How is it justified to use the ...
3
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5answers
339 views

Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
3
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2answers
110 views

How can laser interferomerty be used to measure path difference smaller than wavelength of laser light?

The currently proposed Gravitational wave detection apparatus consists of Michelson Interferometer which is supposed to measure distances of the order of $10^{-22}$m. But the wavelength of the light ...
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1answer
145 views

Big Bang…or…Everywhere Stretch?

Recently I watched a minute-physics video that suggested that a better name for the beginning of time would be "Everywhere stretch" because there wasn't a space-time singularity that formed where the ...
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0answers
67 views

If the stress energy tensor $T=0$, does that mean $\delta{T}=0$? [on hold]

If the stress energy tensor $T=0$ in the vacuum, does that mean the variation of $T$ with respect to $g_{\mu\nu}$ equal zero? $$ \delta{T}=0 $$
2
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2answers
87 views

Is the stress energy tensor continuous at the interface between an object and vacuum?

The stress energy tensor has (as I understand) zero value in the region where there is no matter and non-zero value where there is matter. Suppose there is one matter object in space, now how does the ...
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1answer
131 views

Does gravitational field has gravitational mass?

Other questions closely related to the one of the title (as I will show) are Does speak about work done on photon has sense? Does photon has a gravitational mass? Does exists a modern (and more ...
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2answers
724 views

The uncertainty principle and black holes

What are the consequences of applying the uncertainty principle to black holes? Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
7
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1answer
255 views

Pressure and density using a general Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
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0answers
26 views

Does a graviton impart negative momentum?

Picture a massive system on an axis. If a graviton is generated and emitted by a system in the positive direction, will that system also be accelerated in the positive direction? Another system ...
2
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1answer
71 views

Symmetry of extrinsic curvature tensor

I am trying to solve following problem: In a spacetime of signature (+, −, −, −), let $$ u^au_a = 1, \quad A_{ab} = \nabla_cu_dh^c_{\; a}h^d_{\; b}, \quad h_{ab} = g_{ab} - u_au_b $$ Show that ...
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1answer
53 views

Wave equation on Schwarzschild background

I am trying to follow the solution of the wave equation for a scalar field on Schwarzschild background from http://batteringram.org/science/gr/scalar_wave.pdf. I have a problem on page 2 where they ...
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0answers
37 views

Scalar field in Reissner-Nordstorm metric

I am trying to solve this kind of problem: For a scalar field $ \psi $ in Reissner-Nordstorm metric \begin{align} g_{ab} dx^{a} dx^{b} = - f dt^{2} + f^{-1} dr^{2} + r^{2} d \Omega_{S^{2}}^{2} ...
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1answer
115 views

How to find a metric of a general observer?

Yes, that's it. How to find a particular metric of an observer in general relativity? Let's say we have a static metric: ...
2
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1answer
170 views

Is there any evidence against the Cosmological Principle?

I have been slowly getting more into math, but haven't gone into differential geometry or anything like that yet, so this question might be basic. Trying to get a deeper understanding of the ...
0
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1answer
70 views

Could electromagnetic charge curve something like spacetime in analogy with general relativity? [duplicate]

Newtonian gravity and electrostatics have the same form; this analogy is extended when we look at full dynamic electromagnetism, and correspondingly "gravitomagnetism". We are quite capable of ...
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3answers
65 views

Path of light as it travels between two black holes

What would happen to light passing through a narrow space between the event horizons of two equal-mass black holes? Would it deviate or follow a straight path?
5
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4answers
224 views

Is gravitational Chern-Simons action “topological” or not?

Here are the 2+1D gravitational Chern-Simons action of the connection $\Gamma$ or spin-connection: $$ S=\int\Gamma\wedge\mathrm{d}\Gamma + \frac{2}{3}\Gamma\wedge\Gamma\wedge\Gamma \tag{a} $$ $$ ...
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2answers
111 views

Can anyone explain me how time can bend according to Einstein in simple way? [duplicate]

I am just 16 and curious to learn about Theory of Relativity. Can any one explain it simple enough for me to understand? I read that it is bending of time-space or space-time that causes gravity. How ...
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1answer
51 views

Stress-energy tensor on spacetime satisfying Klein-Gordon equation

Consider the stress-energy-momentum tensor $$T_{\alpha \beta}=(\nabla_\alpha \phi )\nabla_\beta \phi -\frac{1}{2}g_{\alpha \beta}((\nabla^\nu \phi ) \nabla_{\nu} \phi +m^2 \phi^2$$ where the ...
16
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2answers
471 views

Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, ...
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0answers
42 views

Are there any $f(R, T)$ models of gravity?

For the past few months I have been studying $f(R)$ models of gravity. Recently I came cross $f(R, T)$ modified models of gravity. For the past few days I have tried to work out the difference between ...
5
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0answers
50 views

Do metric theories with torsion contradict solar system observations?

Obviously, the answer to this question can be "maybe, if you make the torsion tensor small enough", but my question is, given some "typical" size to the torsion tensor, do the spin-orbit couplings ...
2
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0answers
89 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric : $ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$ And then I ...
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0answers
48 views

Question on time dilation [duplicate]

When i studied physics we had this example where someone climbes into a rocked flyes into space comes back the time that passes for him one year time on earth 86 years. I think most know what thinking ...
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0answers
52 views

The Golden Ratio and universe [on hold]

It is well known that golden ratio is "almost everywhere", also it is in Milky Way galaxy Can general relativity (or Newton's gravity) explain why the arm of Milky Way galaxy is approximately ...
2
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1answer
52 views

Raychauduri equation for Milne universe

I am trying to solve this kind of problem: Consider the Milne model, i.e., the empty $ \kappa = −1 $ Friedmann model. Verify by a direct calculation that the expansion $ \Theta $ of the unit ...
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3answers
542 views

How much choice did Einstein have in choosing his GR equations?

General relativity was summarised by Wheeler as "Spacetime tells matter how to move; Matter tells spacetime how to curve". I have a fairly good mental picture of how the first part works. However, I ...
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0answers
41 views

Is the Cauchy Horizon of Anti deSitter spacetime stable?

The Cosmic Censorship Conjecture are two mathematical conjectures about the structure of spacetime. In particular the so called Strong Cosmic Conjecture asserts heuristically that generically, ...
3
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1answer
228 views

Wave Packet in Curved Spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
2
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1answer
109 views

Does all of spacetime exist?

In Brian Greene’s 2004 book, The Fabric of the Cosmos, he quotes Einstein on the meaning of time, …the distinction between past, present and future is only an illusion, however persistent. ...
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1answer
51 views

Gauge freedom in tetrad

I asked the question in the MathOverflow, but didn't get any response. I thought maybe better luck here. I'm reading the following paper about Petrov type D space times called "Type D vacuum ...
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0answers
64 views

Can tachyons escape the gravitational pull of a black hole?

Anything that crosses the event horizon of a black hole cannot escape the pull since it has crossed the Schwarzschild radius and thus, the escape velocity is greater than the speed of light, and since ...
1
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2answers
602 views

Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
5
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3answers
237 views

Has anyone tried Michelson-Morley in an accelerated frame?

After doing much more digging than I thought I had to do, I found out that the speed of light is NOT invariant in an accelerated reference frame. Has anyone done any experiments to confirm this? In ...
3
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1answer
101 views

Resource for mass-charge interaction

My GR professor mentioned that trajectories of charged particles in GR are not the same as those of non-charged particles (i.e. charged particles don't move on geodesics). As I understood it, the ...
2
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1answer
153 views

Obtaining a copy of Hawking's Ph.D thesis - Properties of Expanding Universes

Due to its popularity, I am interested to know the 4 chapter titles and topics covered in S.W. Hawking Ph.D, Properties of Expanding Universes. I also ask this because that thesis is hardly available. ...
21
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0answers
893 views

A dictionary of string - standard physics correspondences

Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 ...
2
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1answer
66 views

General relativity and quantum fields evolution in curved space [closed]

There are many cases when we have to discuss the problem of evolution of quantum fields on GR background (inflaton evolution during inflation, axion field evolution etc). But GR isn't quantized as ...
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2answers
106 views

What would a closed timelike curve look like?

What exactly are closed timelike curves. In a metric in which they would exist, what would they look like. What would it be like travelling through them? It obviously wouldn't look like a door. Would ...
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0answers
43 views

How did Weyl's 1918 paper; Gravitation and Electricity, influence classical physics? [migrated]

The main-stream view seems to be that Weyl's 1918 paper Gravitation and Electricity was initially considered a failure for reasons first pointed out by Einstein. But these initial ideas were reapplied ...
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2answers
60 views

First fundamental form in the Gibbons-Hawking-York boundary term

Let me expose my problem, I am trying to perform the explicit variation of the Gibbons-Hawking-York boundary term, $$S_{GH}=\int_{\partial M} d^{n-1}x\sqrt{\left|h\right|}K$$ The problem I have is ...
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0answers
52 views

Travel thorough the time by Wormholes [closed]

My question is that are we humans with our technology able to make a wormhole stable and travel through the time by it? Because due to Einstein's theory, wormholes are unstable and on the other word, ...
5
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2answers
286 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu ...
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3answers
129 views

I Think I am Misunderstanding Einstein's Equivalence Principle and His Elevator

I'm having difficulties understanding why a gravitational acceleration can be guaranteed to be locally equivalent to an accelerating frame. Doesn't it matter on how the force is being applied? If the ...