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.

learn more… | top users | synonyms (1)

2
votes
1answer
164 views

Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
7
votes
1answer
133 views

Should all theories of gravity have Schwarzschild solution?

A consistent theory of gravity must include the Newton's classical theory of gravity as a weak field approximation. Moreover, to satisfy the experiments in the solar system, the Schwarzschild ...
1
vote
1answer
152 views

Covariant derivative as a tensor

$$\nabla_{j} v^{i}~=~g^{ik}\nabla_{j}v_{k}.$$ Does this equality involve an intermediate step, where I take the metric inside the derivative, and then use the fact that covariant derivative of the ...
7
votes
3answers
856 views

Do gravitational waves cause time dilatation?

The effect of gravitational waves in transverse traceless gauge on matter is represented by the expansion and contraction of a ring of test particles in the direction of polarization of the wave. ...
4
votes
1answer
99 views

Derivation of metric of space time with a point source in 2+1 dimension using ADM formalism

In "Quantum Gravity in 2+1 dimension" by S Carlip, Sec 3.1 (where the metric of a spacetime with a point source is derived, using the ADM formalism), equation 3.8 states that (this is the momentum ...
0
votes
0answers
61 views

Questions about four-momemtum

I am reading a note about Kerr metric, following is some screen shot where I have problems. First of all, I think the author made a mistake. It should be $$ E=-u_\mu k^\mu=u^t\;\;\;L=u_\mu ...
2
votes
0answers
78 views

Questions about deduction the dual form of Frobenius's Theorem

I am reading Page 435, General Relativity by Wald. Let $T^*\subset V^*$ be a subspace of the dual tangent space of a manifold, $W\subset V$ be the subspace of the tangent space annihilated by $T^*$, ...
1
vote
1answer
150 views

What's the meaning of the age of the universe?

I'm not asking about how we worked backward from an expanding universe to the age of the big bang, but rather what is the meaning of time in a near infinitely dense point in the context of general ...
3
votes
1answer
262 views

Any simple reason why spin 2 polarization tensor should be symmetric in $\mu\nu$?

Perhaps this is obvious to the not so tired one, but is there any reason why the five spin 2 polarization tensors $\epsilon_{\mu\nu}^{a}, a=1,\dots,5$ should be symmetric in $\mu\nu$? While I'm at ...
3
votes
0answers
389 views

Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
1
vote
0answers
265 views

How did the scientific community receive Einstein's theories when he published them? [closed]

By now, we have had multiple indications through observations and experiments that Einstein's theories on general and special relativity are correct. We recently had our second observation of ...
1
vote
0answers
76 views

Schwarzschild diagram in Einstein Cartan theory

I'm a very visual learner and I would like to know if the diagram representing the Schwarzschild solution is altered at all when the torsion tensor is non zero. Of particular interest - what is the ...
2
votes
2answers
731 views

Frames, Tetrads and GR

Given a general metric, $g_{ab}$ I can select an orthonormal basis $\omega^{a}$ such that, $$g_{ab} = \eta_{ab}\omega^a \otimes \omega^b$$ where $\eta_{ab}$ = $\mathrm{diag}(1,-1,-1,-1).$ We may ...
0
votes
1answer
157 views

What is the solution of general relativity for our universe? [duplicate]

So I just finished off learning quantum mechanics and special relativity. I just realized that in general relativity, there is Einstein field equation which must be solved in order to talk about ...
17
votes
2answers
701 views

Why isn't general relativity the obvious thing to try after special relativity?

To preface my question, I ask this as a mathematics student, so I don't have a very good sense of how physicists think. Here is the historical context I'm imagining (in particular taking into account ...
12
votes
2answers
506 views

Doesn't the Schwarzschild metric combined with Hawking radiation imply that nothing ever gets past the event horizon of a black hole?

According to the General Theory of Relativity, the coordinate time distance per spacetime distance traveled by a particle freely falling into a black hole gets closer and closer to $0$ as the particle ...
0
votes
0answers
43 views

Gravity propagation speed [duplicate]

Related to: The speed of gravity? In the related question and in many other questions here, it seems as if the propagation speed of the gravitational interaction is $c$. To my understanding, the only ...
3
votes
1answer
142 views

Why can a killing vector field be determined globally by its value and first derivative at one point?

It is said in Weinberg's Book, Gravitation and Cosmology, page 377, that a killing vector field (which we a priori assume exists globally) can be uniquely determined by its value and first derivative ...
1
vote
0answers
254 views

Tetrad formalism: getting back to coordinate basis

Let $\omega^{\hat{a}}$ be an orthonormal basis, and $\theta^{\hat{a}}_{\hat{b}}$ be the associated connections. From Cartan's second structure equation, we may compute the curvature 2-form, i.e. ...
4
votes
1answer
431 views

What is the minisuperspace Lagrangian for gravity plus a scalar field?

In this paper by Sean Carroll and Grant Remmen, in equation (11) they write a Lagrangian of the form $$\boxed{\mathcal{L}=3a\left(k-\dot{a}^2\right)+a^3\left[\frac{1}{2}\dot\phi^2-V(\phi)\right]}$$ ...
5
votes
1answer
273 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 ...
0
votes
2answers
75 views

Direction of expansion of the universe

From what I understand the expansion of the universe has no "center". If we're flying through space away from the "center of the big bang", there's basically no way to tell. Every two given points in ...
0
votes
1answer
232 views

Null Geodesics in flat 2+1 dimensional Minkowski space

For a given line element in flat 2+1 dimensional Minkowski space $$ g = ds^{2} = − dz \otimes dz + dx \otimes dx + dy \otimes dy .$$ The null geodesics are supposedly given by: $$ x = lu + l' $$ ...
0
votes
0answers
121 views

Einstein frame vs. Matter frame

What is the difference between Einstein frame and Matter frame in General Relativity? -A brief comment on each could be useful too. These two frames were used in this manuscript ...
3
votes
0answers
204 views

Computing the Einstein tensor for a spherically symmetrical metric using the tetrad formalism

I am having some trouble understanding how to use the tetrad formalism. I will start with what I have so far, my question will be after that. I begin with the metric $$ \text{d}s^2 = e^{2a} \text{ ...
3
votes
2answers
123 views

Asymptotic flatness implies existence of rotation axis

Suppose we have an asymptotically flat, globally hyperbolic spacetime $M$ endowed with two one-parameter isometry groups $\sigma_t$ and $\chi_{\phi}$ which commute (i.e. $\sigma_t \circ \chi_{\phi}= ...
2
votes
2answers
198 views

What are the factors affecting the spacetime curvature?

Large masses in space as stars and planets cause a curvature in the spacetime fabric. What are the factors that affect this curvature? Is it only mass? And can we conclude these factors using Tensors? ...
3
votes
1answer
2k views

Minimal vs. Non-minimal coupling in General Relativity

What is the difference between Minimal vs. Non-minimal coupling in General Relativity? A brief introduction to Minimal Coupling in General Relativity could be useful too.
2
votes
0answers
79 views

Topology of spacetime in 2+1 dimension

In the book Quantum Gravity in 2+1 dimension by S. Carlip, in the second chapter (section 2.1), he comments that a compact 3-manifold with a flat time orientable Lorentzian metric and a purely ...
2
votes
0answers
100 views

General formula to compute the redshift (first order perturbations)

Consider an expanding universe with the following metric in conformal time/co-moving coordinates: ...
1
vote
0answers
63 views

Very specific type of GR paper hunt [duplicate]

My General relativity skills suck. I need a good paper that does not start with equivalence principle and pages of elevator experiments derives principles mathematically, not by physical intuition ...
10
votes
2answers
1k views

Why can we assume torsion is zero in GR?

The first Cartan equation is $$\mathrm{d}\omega^{a} + \theta^{a}_{b} \wedge \omega^{b} = T^{a}$$ where $\omega^{a}$ is an orthonormal basis, $T^{a}$ is the torsion and $\theta^{a}_{b}$ are the ...
1
vote
1answer
159 views

What happens if a body free-falls at a certain speed?

It is known that a body falling to the ground is affected by gravity, and its velocity increases by 9.8 m/s per second. But when this body is falling, and it reaches the speed of 340 m/s (the speed of ...
1
vote
1answer
238 views

Stress-Energy Tensor

As of recent, I've been doing a bit of self education in GR, equipped with a working knowledge of the key elements of the differential geometry in GR, and in looking at the Einstein-Rosen bridge, I ...
7
votes
1answer
481 views

Was Einsteins work with relativity necessary for successful space travel?

So I know that Einstein and general relativity had huge impacts on the way we view the world, but how crucial were these scientific advancements to the success of our space programs? Would Newtonian ...
1
vote
0answers
186 views

Covariant Derivative with a Torsion Free Metric

Where $\triangledown$ is the covariant derivative and we are to assume that the connection is torsion free (that is, we can exchange the lower indices of the connection coefficients), how can I prove ...
12
votes
2answers
3k views

How can a singularity in a black hole rotate if it's just a point?

I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely ...
3
votes
1answer
161 views

Can geodesics in a Lorentzian manifold change their character?

From a physics perspective, it's pretty easy to see why a a massive particle will be restricted to timelike paths, etc. but does the math guarantee that on its own or do we have to impose it? More ...
1
vote
0answers
46 views

Space time curvature due to electric charge or magnetic charges [duplicate]

since we know that gravitational force is nothing but a curvature in space-time. I have a similar analogous for the electric or magnetic charges. Similarity is that both electromagnetic and ...
0
votes
2answers
1k 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 ...
4
votes
1answer
338 views

Interpreting perturbation theory in general relativity

In quantum mechanics we start with a Hamiltonian $H_0$ for which we know the exact eigenstates and energy eigenvalues. We perturb it by a known term $H$, and then attempt to compute (approximately) ...
89
votes
5answers
26k views

Why would spacetime curvature cause gravity?

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" ...
1
vote
0answers
347 views

Induced metric on the boundary of a manifold

The Gibbons-Hawking-York term which supplements the Einstein-Hilbert action is, $$S_{GH} = \frac{1}{8\pi G} \int_{\partial M} d^3 x\sqrt{-h} \, K$$ where $\partial M$ is the boundary of the manifold ...
2
votes
1answer
520 views

Stress energy tensor and the covariant derivative of the 4-momentum

Another basic question. I have usually seen the stress energy tensor $T^{ij}$ described as the flow of the 4-momentum field $p^i$ along direction $x^j$ in spacetime with $p^0$ as energy and $x^0$ as ...
4
votes
1answer
402 views

Computing Curvature via Cartan Formalism

Given a metric $g_{\mu \nu}$, one can select an orthonormal basis $\omega^{\hat{a}}$ such that, $$ds^2= \omega^{\hat{t}}\otimes\omega^{\hat{t}} - \omega^{\hat{x}} \otimes \omega^{\hat{x}} - ...$$ By ...
1
vote
0answers
52 views

How to calculate the minimum number of extrinsic dimensions of a metric tensor?

The Question How does one calculate the minimum number of dimensions of an extrinsic space that can be used to define the metric tensor \begin{align} g_{mn} = \dfrac{\partial y^k}{\partial x^m} ...
1
vote
0answers
41 views

Positive Mass Theorem [duplicate]

I'm a third year maths undergrad doing a project on minimal surfaces. However I'm really struggling to understand what the PMT is trying to explain? Could anyone help explain this (as simply as ...
10
votes
5answers
3k views

Naive visualization of space-time curvature

With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus: "If you throw a ball, it will move along a parabola. Initially its vertical ...
0
votes
1answer
509 views

General relativity, gravity and spacetime curvature [duplicate]

There is a very fundamental flaw in the common explanation given of the space-time curvature due to massive objects. It is said that a massive object curves space time just like a bowling ball on a ...
1
vote
0answers
170 views

Reissner-Nordström Black Holes

The Reissner-Nordström black holes are described by the metric, \begin{align} ds^2 = -\left(1-\frac{2M}{r}+\frac{Q^2}{r^2}\right)dt^2 + \frac{1}{1-\frac{2M}{r}+\frac{Q^2}{r^2}}+r^2d\Omega^2 ...