A theory that describes how matter produces and responds to 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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19
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375 views

Mass of empty AdS$_5$

Five dimensional empty AdS$_5$ space has mass $$ E = \frac{3 \pi \ell^2}{32 G}. $$ Is the above equation correct? Let's do some dimensional analysis to confirm. In natural units, in 5 dimensions ...
14
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1answer
258 views

Positivity of Total Gravitational Energy in GR

I read the following statement in the introduction to an article: Over the last 30 years, one of the greatest achievements in classical general relativity has certainly been the proof of the ...
9
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1answer
227 views

“Redshifting” of forces in stationary space - times

Here's the problem statement: Let $(M,g_{ab})$ be a stationary spacetime with timelike killing field $\xi ^{a}$. Let $V^{2} = -\xi _{a}\xi ^{a}$ ($V$ is called the redshift factor). (a) Show that the ...
8
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187 views

Materials with different gravitomagnetic permeability?

If you start with general relativity, and assume small perturbations around a nearly flat metric, it is possible to obtain linearized equations of gravity that look a lot like Maxwell's equations, ...
7
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1answer
562 views

warp drive with gravitational waves in the nonlinear regime

gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, ...
5
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1answer
368 views

Surface gravity of Kerr black hole

I'm going through Kerr metric, and following the 'Relativist's toolkit' derivation of the surface gravity, I've come to a part that I don't understand. Firstly, the metric is given by ...
4
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1answer
162 views

The Aharonov-Bohm effect is purely classical, right?

Every discussion I've ever seen of the Aharonov-Bohm effect makes a big deal of its being a quantum effect with no classical analogue. But as far as I can tell it is present already at the classical ...
4
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1answer
70 views

Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?

The definition of the SI unit "second" is stated as The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground ...
4
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1answer
93 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 ...
4
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1answer
289 views

Tensor equations in General Relativity

In the context of general relativity it is often stated that one of the main purposes of tensors is that of making equations frame-independent. Question: why is this true? I'm looking for a ...
4
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1answer
130 views

Rotation of Spacetime => Change in orbit/path

Along the idea of frame-dragging; Will the rotation of a black hole, which has some velocity v and angular momentum, influence its path in 3D space? I've seen the fact that depending on the ...
3
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1answer
35 views

Bondi-Metzner-Sachs (BMS) symmetry of asymptotically flat space-times

I started studying the BMS symmetry in connection with the paper: http://arxiv.org/abs/1312.2229 and there are a few strange things I noticed. First of all, from reading the original papers by Bondi, ...
3
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1answer
91 views

Black hole temperature in an asymptotically de Sitter spacetime

I am trying to calculate the Hawking temperature of a Schwarzschild black hole in a spacetime which is asymptotically dS. Ignoring the 2-sphere, the metric is given by ...
3
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1answer
118 views

Gravitational waves as information carriers

Is it possible to utilize gravitational waves as a delivery system for information between two observers straddling the event horizon of a black hole? And why ?
2
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1answer
94 views

Angular momentum, what is it, is it conserved, and how do we know?

Firstly, most definitions of angular momentum assume a point about which you define angular momentum. I realize that you can consider the angular momentum about any point, and have many angular ...
2
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1answer
43 views

Christoffel symbol

For two nearby points in General Theory of Relativity. The change in the vector components when parallel transported is given by Now, since the parallel transport change must depend on the path ...
2
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1answer
86 views

The relationship between Lorentz Lie algebra and curvature

Here I transfered the question from the comment The relationship between spin and spinor curvature How $\mathcal{R}_{ab} = \frac{1}{4}R_{abst}\gamma^s \gamma^t$ is from $\Psi \mapsto \Psi + ...
2
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1answer
98 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
144 views

Energy-Momentum Tensor under Lorentz Transformation

In relativity, the symmetric energy-momentum tensor is given by $$ T^{ij}, $$ where $T^{00}$ is the energy density and $\frac{1}{c}T^{10}$ is the momentum density. Thus: $$ \left(\frac{1}{c}T^{00}dV, ...
2
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1answer
137 views

If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole ...
2
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1answer
80 views

Are there bounds or measurements on the derivative of acceleration (jerk)

The title says it all. Is there a physical maximum value to the 3rd derivative of position? Common Lore says that there is not and that jerk does not play any role in physics. My guess is that there ...
2
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1answer
283 views

Why dynamic Casimir effect does not appear in static gravity field?

Dynamic Casimir effect tells us that a constantly-accelerated mirror should emit radiation due to interaction with vacuum. Following principle of equivalence, a similar mirror placed in static ...
1
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1answer
32 views

If a point r lies in the boundary of the chronological future of another point p, why does the chronological future of r belong to that of p?

I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in ...
1
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1answer
30 views

Robertson-Walker metric and stable orbits

The RW metric is defined using 4 spatial dimensions, but stable planetary orbits require 3 spatial dimensions. Does this indicate a problem with the assumption of the RW metric to describe the cosmos? ...
1
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1answer
28 views

Luminosity distance from angular diameter distance

Consider that I know the cosmological angular diameter distance at a given redshift : $$D_{A}\left(z\right)=\frac{x_{object}}{\theta_{observer}}$$ Is there a general formula to compute the ...
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38 views

Hubble's law for the Kasner solution

I'm puzzled with the following question: find an analog of the Hubble's law for the Kasner solution. Kasner metric is a solution to the vacuum Einstein equations ...
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20 views

Method of determining peculiar speed of the galaxy which moves on celestial sphere and emits the light

This question is the continuation of this one. I came up with solution, but I'm not sure that it is correct. Can someone check it? Let's introduce transverse (to the observer) proper speed ...
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42 views

How to find proper speed (relate to homogeneous cosmic background) of the galaxy by given redshift z and observing angular velocity?

The galaxy moves of the celestial sphere. It is given that proper speed is transverse to the observer and it must to find this speed in the moment of light emission. The motion is in the FLRW ...
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43 views

Differential equation for speed relate to the homogeneous cosmological background in FLRW metric

How to derive DE for the speed (which relate to the homogeneous cosmological background) of the observer which moves with constant proper acceleration in spatially flat FLRW universe?
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58 views

One more time about the connection of Weyl tensor and gravitational waves

There is differential identity with Weyl tensor and energy-momentum tensor: $$ D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + ...
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83 views

How to use The Schwarzchild Metric formula to get distribution representing “free-fall”

Given formula: How I can use to calculate distribution of points in space, so if i choose path which contains most of the points I get path that close to "free-fall path". As far as I know i should ...
0
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0answers
86 views

On motivation for the definition of ADM mass

The ADM mass is expressed in terms of the initial data as a surface integral over a surface $S$ at spatial infinity: $$M:=-\frac{1}{8\pi}\lim_{r\to \infty}\int_S(k-k_0)\sqrt{\sigma}dS$$ where ...
0
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87 views

Interpretation of contribution of gravitational potential energy to the gravitational field

In terms of General relativity we have as a matter of principle that anything that has inertial mass contributes to gravity. All forms of potential energy have inertial mass, it follows that the ...
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72 views

Trapping Light in a shell

I was curious about this. Is it theoretically (mathematically) possible to create a shell such that when a photon 'hits' the shell, the spacetime at the shell surface is such that the photon travels ...
0
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0answers
50 views

Geodesic in general relativity aproaching ellipse

In the gravity well-like 2d surfaces that are used in documentaries to illustrate the fact Earth orbits the Sun, I don't seem to find any kind of geodesic that will at least resemble an ellipse... ...
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0answers
69 views

Closed linear cosmology implies G M / R = c^2?

I have a question about a linear FRW cosmology with $k=+1$. Assuming zero cosmological constant the first Friedmann equation can be written: $$\left(\frac{\dot R}{R}\right)^2 + ...
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0answers
79 views

How to get general relativity from linear gravity theory?

I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the ...
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40 views

Dark energy lorentz invaraince

Dark energy (or the cosmological constant) is stated as Lorentz Invariant, form websites like: http://cerncourier.com/cws/article/cern/28917 In newtonian mechanics, this is correct. But time dilation ...
0
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0answers
53 views

Photon detection time in NMR rotating frame

I think of an NMR experiment, but with a single spin half nucleus initially set to the excited state. When the nucleus finally returns to its ground state, it will emit a photon. An observer in the ...
0
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0answers
51 views

metric extension outside the light cone

Could anyone explain what "extending the solution" beyond the past light cone means? Say, for example, if I have a metric (no coordinate singularities), how can I extend it to the outside of the past ...
0
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0answers
156 views

The interior of a cylinder as an Einstein manifold

The interior of a curved cylinder is an Einstein manifold (the Ricci Curvature Tensor is proportional to the Metric $R_{\mu\nu}=kg_{\mu\nu}$) since it has a constant curvature. Using the metric $$ ...
0
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0answers
80 views

What is the physical meaning of charges at light-like infinity in asymptotically flat space-times?

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 ...
0
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0answers
58 views

Switching from an accelerated frame of reference to a locally inertial reference system

Using the equivalence principle, show that the interval for an accelerated observer ($\textbf{g}$ uniform and constant) has the form $$ ds^2|_{\text{first order in ...
0
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0answers
274 views

covarient derivative of electromagnetic field tensor

I'm trying to prove the energy momentum tensor in curved spacetime for Electromagnetic field is Divergence-less directly(Without using general lie derivative method which can prove any energy momentum ...
0
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0answers
49 views

Curved space to flat space calculation

When changing the curved space co-ordinate into a flat space co-ordinate if a cone. I got the result transformation that i cannot get a transformation at the vertex(apex) why?
0
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0answers
51 views

Why does the local inertial compass coincide with the stellar compass?

I found this physics paper via a non-duality site and I wished that I could understand it. Could someone please either read it and explain it to me or else point me to pages that would help me ...
0
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0answers
155 views

Can Parallel Transport always move a Vector Parallel to Itself?

Consider two tiny plane(flat) surfaces A and B meeting at a straight line L.We have a preassigned vector on A at some point P on it.Is it always possible to have a vector parallel to the first one ...
0
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80 views

Counterpart of the Klein Gordon Equation on the “Coordinate Shell”

The relation $$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$ satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$. Now let's think in the reverse direction. ...
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0answers
50 views

Emitting gravitational radiation

Is the following true: Two massive bodies with variable distance between them do not emit GR in any direction Two bodies that revolve around common center will not emit in the plane of their orbits ...
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180 views

Comparing Lagrangian in Special Relativity vs General Relativity for a weak gravitational field

This is a sequel to this question. Who knows a difference between the Lagrangian in SR and GR for a weak gravitational field in non-relativistic case? What is the reason of this difference?