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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On the coordinate independence of general relativity

I've been having a bit of trouble with the idea of coordinate independence in general relativity. Let me start with a simple example that I think illustrates my question conceptually: Say you have ...
0
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0answers
16 views

Is there some other name used for “ping rigidity”?

In MTW, p. 398, "Box 16.4 (continued)", there's an interesting sketch (which can also be seen on p. 15 of this excerpt (www.pma.caltech.edu/~ph236/yr2008/readings/MTW_Chapter16.pdf). (It's not the ...
0
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1answer
82 views

Why point mass leaves it's own gravitational well? [closed]

I suppose that point mass has its own gravitational well. Why this point mass is still attracted by other gravitational waves. I expect that this point mass is surrounded by "gravitational hills". Why ...
2
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0answers
63 views

How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
4
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1answer
71 views

Geodesics in Kerr

I'm interested in plotting the trajectories of null geodesics near an uncharged rotating black hole (described by the Kerr solution) which involves a system of first order differential equations. Kerr ...
0
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1answer
31 views

Given two events such that either one of them is 'on the light cone' of the other, do they constitute a 'null interval'?

One basic part of determining a metric (or applicable generalization) of a given set $\cal S$ of events (up to an arbitrary non-zero constant) is to determine to which pairs among those events, ...
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0answers
49 views

Ghosts in theories of gravity and holographic theories

I want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?
2
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1answer
49 views

Are there more distinctive names of “null curves” with certain additional properties (absence of “chord curves”)?

In this answer (to the question "In general relativity, are light-like curves light-like geodesics?", PSE/q/76170) a particular example of a curve is discussed whose "tangent is everywhere null" and ...
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0answers
76 views

How should a math undergrad student prepare himself to study GR and QM? [duplicate]

I'm quite sure that similar questions like this have been asked for more than thousands of times on here but since each person's background and interests are unique I believe questions like this ...
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3answers
1k views

Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
1
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3answers
180 views

Space-time curvature creates gravity or is it (could it be) vice-versa too?

Mass (Energy) creates space-time curvature and thus it forms the reason for gravity. Can it be vice-versa too? Like, mass created gravitational field, gravitational field created space-time curvature? ...
1
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3answers
108 views

Do massless particles follow the curved spacetime or not?

I am assuming that zero (rest) mass particles don't interact gravitationally with each other and other particles. Does that mean they experience a "flat" spacetime instead of a curved one? I find it a ...
2
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2answers
211 views

Why “light cones” have different shapes near black holes?

There is theory that light cone shape does not depend on the reference frame in which it is viewed. So why we draw light cones near black hole differently? I thought that if I am observing (from the ...
4
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2answers
188 views

Metric tensor in special and general relativity

I'm having trouble understanding the metric tensor in general relativity. What I've understood so far has come from my course lecture notes used in conjunction with "The Road to Reality" by Roger ...
3
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2answers
115 views

Frame dragging — is there a “non-tiny” example?

Now. As I understand it, in fact, the earth (10^25 kg) creates a very small, very tiny, frame dragging effect. Indeed, we have measured this using satellite experiments. So, the Earth (10^25 kg) ...
2
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0answers
49 views

Avoiding Pseudo-tensors when addressing global conservation of energy in GR

Discussions about global conservation of energy in GR often invoke the use of the stress-energy-momentum pseudo-tensor to offer up a sort of generalization of the concept of energy defined in a way ...
1
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0answers
43 views

Laplacian in tensor [closed]

Find $\vec \nabla^2\phi $ when $$ds^{2}=-dt^{2}+a^{2}(t)[dx^{2}+dy^{2}+dz^{2}] $$ or $$g_{ij}=\begin{bmatrix} -1 & 0 &0 &0 \\ 0 &a^{2}(t) &0 &0 \\ 0&0 ...
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0answers
53 views

Are there any known (closed form even if approximate) solutions to problems in relativistic elasticity?

There are several useful known solutions to the EFE with relatively simple / trivial stress-energy-momentum tensor, such as the Schwarzschild solution. Despite the idealizations made therein they are ...
2
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0answers
64 views

Gravitational atraction of fast object [duplicate]

Let's imagine a asteroid that travels with 0.99999999999999999c. (I know it's impossible). Anyway... Relativistic mass of such object would be almost equal to earth's stationary mass. Now let's ...
1
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1answer
60 views

How has the age of the Universe been derived from the observations made by the Planck mission?

The parameters of $\rm\Lambda CDM$ model have been determined to an amazing high precision from the measurements made by the Planck mission. In particular, the Hubble "constant" (the value of Hubble ...
3
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3answers
109 views

The Hole Argument

I have read explanations of this but haven't really understood. Given a spacetime $(M,g)$ I have read that if I represent the metric in some coordinates $(x,y,z,t)$ as $g(x,y,z,t)$ and then in another ...
1
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1answer
131 views

Finding the metric tensor from the Einstein field equation?

I have have set my self a challenge to learn all the maths behind the Einstein field equation (EFE), and from reading it seems that the Metric tensor is the thing we are trying to find (from the 10 ...
2
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0answers
79 views

How to properly construct the electromagnetic tensor in curved space-time? (Part II)

In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book - Introducing ...
0
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1answer
98 views

Does physics recognize the particle of light separately from the wave of light? [closed]

To frame this question, we need to assume that time freezes when traveling at the speed of light. This is theoretically congruent with Einstein's theory of relativity and the theory of time dilation, ...
1
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1answer
67 views

Ricci curvature tensor, definition of symbols

So I know that $$R_{μν}:=R^λ_{μλν}$$ is the Ricci curvature tensor (where $R^λ_{μλν}$ is the Riemann Tensor). This is in Einstein's field equations: $$R_{μν}-\frac{1}{2}g_{μν}R=\frac{8πG}{c^4}Τ_{μν}$$ ...
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1answer
125 views

GPS Satellite - Special Relativity

I'm going through an old relativity assignment, and I've been asked to calculate the time dilation for a satellite which orbits the earth in 12 hours at 26000km from the surface, and travels at a ...
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0answers
45 views

Frequency of a photon as related to the change of its frequency

I think that bob maybe already, at least partially, has answered my following question: "Is it true or false that the frequency of a photon is not related to the change of its frequency caused by ...
2
votes
1answer
202 views

How to properly construct the electromagnetic tensor in curved space-time?

How do I properly construct the electromagnetic tensor in curved space-time? I have my curved spacetime metric $(+,-,-,-)$ and my magnetic vector potential $A$. I tried two ways but not sure which is ...
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0answers
80 views

Is inertia actually a property of the force rather than the mass?

I ask this because it occurred to me that the inertial property of mass only actually arises in the context of forces (such as the EM force) as a resistance to their accelerating effect. Inertia plays ...
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0answers
27 views

Difference between Gravitational and Matter Scalar Fields

In the context of Scalar-Tensor theories of gravity (for example in Brans-Dicke) what is the difference between gravitational and matter scalar Fields? My doubt comes from "The scalar-tensor Theory ...
-1
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2answers
60 views

More about gravitation as the source of redshift of light beams [closed]

In the realm of physics there is no knowledge, the justification of which does not depend either upon experience or upon reason. In the light of the findings of the preconditions of knowledge made in ...
1
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1answer
90 views

Conservation of energy and momentum via the continuity equation in asymmetric time and space translation

I am confused about energy and momentum conservation, time and space translation symmetry, and the continuity equation. Suppose we have a mass $m$ in inertial space far from any gravitational ...
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0answers
76 views

Maybe photon energy is constant as the Universe expands?

This is a question following on from my previous post Time-like Killing vector in FRW metric? For simplicity I take the spatially flat FRW metric in cartesian co-ordinates given by: $$ds^2 = -dt^2 + ...
2
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1answer
63 views

Space Warps & Frame Invariance

The Alcubierre Warp Drive in Higher Dimensional Spacetime (H. G. White & E. W. Davis), among other sources, proposes that the x-axis symmetry paradox for Alcubierre-style warp drives can be ...
2
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1answer
96 views

Where are the time dilatational effects of orbital motion and gravitational acceleration equal?

Nearly four years ago, upon hearing of the observation of time dilation in two optical atomic clocks at an elevation one metre apart, due to acceleration towards earths centre of gravity by Chou, C. ...
3
votes
1answer
68 views

$c^4$ in Einstein field equations

I have read many derivations of Einstein field equations (done one myself), but none of them explain why the constant term should have a $c^4$ in the denominator. the $8{\pi}G$ term can be obtained ...
2
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1answer
102 views

Computing the Christoffel symbols with the geodesic equation

I would like to compute the Christoffel symbols of the second kind using the geodesic equation. To practice, I have tried the Schwarzschild Ansatz $$ g_{00} = \mathrm e^\nu,\quad g_{11} = - \mathrm ...
3
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1answer
165 views

Is the apparent lack of (Ricci) curvature in the Schwarzschild metric due to a choice of coordinates?

I've been lightly studying GR lately. Something that has been bothering me has been the lack of (Ricci) curvature produced from the Schwarzschild metric in the few lectures I've watched, as well as ...
1
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0answers
18 views

Lee Yang force and cosmology

The text I am reading (Stars and Relativity by Ya. B. Zel'dovich) discusses the possible existence of a repulsive force proportional to total baryon number. At the time of the book's publication it ...
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2answers
64 views

How fast to travel to end up where i started from?

I've heard that if one travels far enough in one direction through the universe, one ends up at the starting point, due to the "geometry" of the universe. What rate is space expanding at? Is it in ...
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0answers
57 views

Variation of the purely covariant Riemann tensor

I need to find the variation of the purely covariant Riemann tensor with respect to the metric $g^{\mu \nu}$, i.e. $\delta R_{\rho \sigma \mu \nu}$. I know that, $R_{\rho \sigma \mu \nu} = g_{\rho ...
3
votes
1answer
80 views

Geodesics in AdS3

I'm having some trouble doing an easy computation with the AdS space. I'm considering $\text{AdS}_3$ space with the Poincaré coordinates, so the metric reads $$ds^2 = \frac{R^2}{z^2}(dz^2 - dt^2 + ...
3
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0answers
46 views

Should a radiation-filled Universe be scale invariant?

Imagine a spatially flat Universe, without cosmological constant, filled only with EM radiation. As Maxwell's equations without charges or currents are scale invariant then should this Universe be ...
2
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2answers
71 views

Relativity and volume of black hole

Does Einstein's theory of special or general relativity incorporate volume? In a particle accelerator two particles smash together at relativistic speeds and "create" new particles (quarks etc) due ...
7
votes
3answers
959 views

Why does time stop in black holes?

Everyone says that time stops in the black hole. It's a "fact". However, I have never heard everyone explaining that. Of course, I know that observer in weaker gravitational field sees that something ...
2
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0answers
43 views

How to prove that a time-oriented spacetime possesses a nowhere vanishing timelike vector field?

Penrose gave a very brief proof to this question. Since the spacetime is paracompact, there exists a positive definite metric called $h_{ab}$. Then, the nowhere vanishing time-like vector field $V^a$ ...
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0answers
51 views

Null geodesics and rotation in stationary axisymmetric space-times

It is well known that in Schwarzschild space-time, a torque-free gyroscope in circular orbit at any permissible angular velocity at the photon radius will, if initially tangent to the circle, remain ...
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4answers
3k views

Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.
3
votes
1answer
68 views

Do alternate theories for Dark Matter (like MOND) explain it's effect on gravitational lensing?

For a long time, I was sceptical about the evidence for dark matter. To me, it seemed like a pretty big leap to make when we have no idea whether or not our current models of gravity should apply ...
6
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0answers
48 views

Role of the canonical ensemble and electric charge in AdS/CFT

If we consider a charged black hole in AdS spacetime, we can either do thermodynamics in the grand canonical or the canonical ensemble. In the former, we fix the electrostatic potential ...