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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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 ...
1
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1answer
160 views

Questions about MTW's _“thousand” tests of the Einstein principle_ (Box 16.4)

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which "Each geodesic clock is constructed and ...
13
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3answers
992 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 ...
7
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3answers
1k views

Understanding Einstein's field equation

Einstein's field equation: $$G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu} - g_{\mu\nu}\Lambda$$ I'm trying to understand each of the terms in this equation intuitively, but I'm struggling. Basically, ...
5
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2answers
346 views

How general relativity gets to an inverse-square law

I understand that a general interpretation of the $1/r^2$ interactions is that virtual particles are exchanged, and to conserve their flux through spheres of different radii, one must assume the ...
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1answer
55 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 ...
0
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1answer
97 views

How does it seem to be that space/time always equals c?

Given the way objects move, they seem to be going all the same "velocity" so to speak, that velocity being the speed of light. Except, velocity is displacement/time, so if something goes faster, the ...
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0answers
60 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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1answer
27 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 ...
6
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1answer
350 views

In general relativity, are light-like curves light-like geodesics?

Just as the title. If a curve is light-like, i.e. a null-curve, is it definitely a null geodesic?
7
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3answers
831 views

Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or ...
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1answer
112 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? ...
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99 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) ...
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3answers
88 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 ...
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2answers
142 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 ...
7
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1answer
168 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, ...
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0answers
40 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 ...
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2answers
48 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 ...
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0answers
54 views

Proving the contracted Bianchi identity [closed]

I know how to derive the contracted Bianchi identity $$\nabla_\mu(R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R) = 0.$$ But I am having trouble proving that the LHS of this is 0. Can someone help me please? ...
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0answers
29 views

Hodge star operator [migrated]

Again I have issues with notations. The hodge star operator is defined as : (m is the dimension of the manifold) $$\star: \Omega^{r}(M) \rightarrow \Omega^{m-r}(M)$$ $$\star(dx^{\mu_{1}} \wedge ...
2
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2answers
178 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 ...
8
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1answer
115 views

Evaluating the Einstein-Hilbert action

The Einstein-Hilbert action is given by, $$I = \frac{1}{16\pi G} \int_{M} \mathrm{d}^d x \, \sqrt{-g} \, R \, \, + \, \, \frac{1}{8\pi G}\int_{\partial M} \mathrm{d}^{d-1}x \, \sqrt{-h} \, K$$ ...
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0answers
39 views

Laplacian in tensor [on hold]

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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4answers
435 views

What does the equivalence principle mean in quantum cases?

We know that electron trapped by nuclear, like the hydrogen system, is described by quantum state,and never fall to the nuclear. So is there any similar situation in the case of electron near the ...
7
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1answer
544 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, ...
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0answers
42 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 ...
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0answers
56 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 ...
3
votes
3answers
100 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 ...
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0answers
49 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 ...
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1answer
97 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 ...
4
votes
3answers
451 views

Degrees of freedom of the graviton versus classical degrees of freedom

I have a puzzle I can not even understand. A graviton is generally understood in $D$ dimensions as a field with some independent components or degrees of freedom (DOF), from a traceless symmetric ...
0
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1answer
46 views

Does mutual gravitational attraction imply a negative pressure?

Imagine a small ball of gravitating dust particles initially at rest at the center of a large volume $V$. Following John Baez, Einstein's field equations say (in units of $c=8 \pi G=1$): ...
0
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1answer
52 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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1answer
62 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: $$R_{μν}-\frac{1}{2}g_{μν}R=\frac{8πG}{c^4}Τ_{μν}$$ ...
2
votes
1answer
181 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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votes
1answer
89 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, ...
3
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1answer
230 views

The most general form of the metric for a homogeneous, isotropic and static space-time

What is the most general form of the metric for a homogeneous, isotropic and static space-time? For the first 2 criteria, the Robertson-Walker metric springs to mind. (I shall adopt the (-+++) ...
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1answer
110 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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2answers
159 views

Does the stretching of space time have a limit?

Why does the stretching of spacetime have no limit? If multiple universes exist. Wouldn't each universe occupy a defined area? If these universes do occupy a defined area wouldn't there be a limit to ...
0
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3answers
225 views

The radius of the universe and time [closed]

Ok - fair warning - Non-physicist asking dumb-assed questions here again. I've been reading a lot of Einstein, Feynmann, Ferris etc. I'm just loving this stuff. But I suddenly found myself looking at ...
0
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0answers
38 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 ...
7
votes
3answers
398 views

Does Kaluza-Klein Theory Require an Additional Scalar Field?

I've seen the Kaluza-Klein metric presented in two different ways., cf. Refs. 1 and 2. In one, there is a constant as well as an additional scalar field introduced: $$\tilde{g}_{AB}=\begin{pmatrix} ...
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0answers
61 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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2answers
81 views

Principle of locality and forces

I have a silly confusion about the statement written in the link Einstein and Locality ''external influence on A has no direct influence on B; this is known as the Principle of Local Action.'' ...
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0answers
22 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 ...
3
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2answers
378 views

How to obtain the field equations in Brans-Dicke theory from the action?

The action for the Brans-Dicke-Jordan theory of gravity is $$ \\S =\int d^4x\sqrt{-g} \; \left(\frac{\phi R - \omega\frac{\partial_a\phi\partial^a\phi}{\phi}}{16\pi} + \mathcal{L}_\mathrm{M}\right). ...
2
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1answer
56 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 ...
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0answers
50 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 ...
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0answers
63 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
85 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. ...