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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Confused about equations for the Big Bang in general relativity ad loop quantum gravity?

I am trying to get a vague understanding of the mathematical equations for the Big Bang in GR and LQG. My understanding so far is that when the universe is assumed to be homogeneous and isotropic, ...
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1answer
66 views

Kaluza suggested metric

Is there a book or a paper that goes into the mathematical details of getting scalar curvature of the 5 dimensional metric that Kaluza wrote down? I am running into many mathematical issues for I am ...
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313 views

Non-trivial scalar quantity

Is there any scalar quantity made of only the Christoffel symbols, determinant of a metric and tensors, not derivatives? In other words, can we construct a scalar quantity which cannot be written in ...
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3answers
20k views

Does Gravity Really Exist? [closed]

As far as I understand some of the readings, Gravity does not exist in real terms. It's only a way of modeling motion as we see. Einstein for example explained the motion without having to have ...
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0answers
43 views

What topics should I develop complete concepts in before I begin the derivation of GR? [duplicate]

I had just been trying to understand GR but i just cannot understand where some of the formula of field came from. Apparently all those initial formula are from Newtonian physics so please anyone ...
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1answer
188 views

Modifying Newtonian gravity to fit observed precession of Mercury's orbit

The idea is to modify Newtonian gravity so that it fits measurements of orbits around the sun. For example the precession of Mercury's orbit unlike Newtonian $n$-body simulations. I'm currently not ...
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489 views

What made Einstein think that gravity was caused by the curvature of spacetime?

What observation/thought experiment led him to think this?
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53 views

What is the status of gauged gravity [duplicate]

The Standard Model of elementary particles is a gauge theory with gauge group $SU(3)\times SU(2)\times U(1)$, which is really a successful theory. We might be able to quantize gravity similarly. ...
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92 views

What's the meaning when Kerr-Newman metric's mass is zero?

Kerr-Newman metric represents the spacetime of a charged and rotating black hole. If the mass parameter is zero, this metric is still not the Minkowski spacetime. What's the meaning of a charged and ...
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394 views

Geometric meaning of parallel transport

The definition of parallel transport of a vector $v^b$ along a curve $C$ with tangent field $\it{t}^a$ is given by Wald's GR as $$t^a \nabla_a v^b = 0$$ Is it correct to think of $\nabla_a v^b$ as ...
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1answer
42 views

Tensors applied to vector and dual vector fields in GR

This is a specific question about tensor manipulation in Wald's GR. I'm asking for clarification of a trivial step, because I'm working through the text outside the context of a class, without prior ...
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0answers
99 views

How to derive the cigar soliton solution to the Ricci flow equation? [closed]

I am trying to derive the cigar soliton solution to the Ricci flow equation. Such solution has the form $$ {\frac {{{\it dx}}^{2}+{{\it dy}}^{2}}{{{\rm e}^{4\,t}}+{x}^{2}+{y}^{2 }}} $$ I am ...
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1answer
537 views

A Theorem Due to Hodge: Hawking/Ellis

This is probably quite an obscure question but hopefully somebody has a simple answer. I'm studying the proof of the topology theorem on black holes due to Hawking and Ellis (Proposition 9.3.2, p. 335 ...
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86 views

Newtonian potential defines size of Universe?

As I understand it the Newtonian potential $\Phi$ at the position of an observer in space is approximately given by: $$\Phi \sim \frac{G M}{R},$$ where $R$ is the radius of a sphere centered at the ...
3
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1answer
107 views

Riemannian curvature tensor [closed]

In Einstein's field equations, it includes only energy momentum tensor of the matter alone. However, it doesn't include the energy momentum tensor of the field. In Professor Hamber lectures on General ...
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0answers
41 views

Relation between the curvature of a manifold and the number of covariantly constant vector fields that it admits

Suppose that on a four dimensional manifold we are able to explicitly construct four linearly independent covariantly constant vector fields $K^a_{\mu}$: $$D_{\mu}K^a_{\nu}=0,$$ $a=1,2,3,4$ then it ...
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3answers
220 views

Generators of the Diffeomorphism Group

So what are the generators of a Diffeomorphism Group? For simplicity, let's consider $ Diff(R^2) $ (diffeomorphisms of the euclidean plane.) Diffeomorphisms are differentiable, invertible ...
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1answer
266 views

Does accelerating generate gravitons?

If gravity and acceleration are indistinguishable, then does that mean converting potential energy to kinetic energy generates gravitons... but only temporarily until you stop accelerating?
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1answer
200 views

Ricci Scalar of the five-dimensiional Reissner–Nordström metric is different to zero?

The Ricci scalar of the four-dimensional Reissner–Nordström metric is equal to zero. In the case of the five-dimensional Reissner–Nordström metric, the Ricci scalar is different to zero?
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2answers
142 views

Conserved quantity of Spactime Diffeomorphism Group

So it's my understanding that the underlying symmetry of GR is the Diffeomorphism Group of 3+1 spacetime. It's also my understanding that a symmetry implies a corresponding conserved quantity in a ...
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1answer
115 views

Does nature of singularity in black hole depend on material that fell in?

Electromagnetic waves have a tracesless stress energy tensor, and therefore if they are the only fields in a region of spacetime, the Ricci curvature scalar $R=0$ according to GR. However $R^{\mu\nu} ...
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1answer
235 views

How does gravity's space time distortion access energy to induce freefall? [closed]

An observer, standing on top of a building, has a gravity switch (use your imagination) which allows him to turn gravity on and off. He turns the switch off, then releases a pool ball over the edge ...
4
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2answers
231 views

FRW metric and its validity througout the age of the universe

Why do we think that the FRW metric should be valid throughout the entire history of the universe?
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2answers
91 views

Can time be interacted with? [duplicate]

Astronauts come back to Earth younger than they would have been had they stayed on Earth for that same period of time. They are traveling so fast relative to the Earth that time slows down for them. ...
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1answer
261 views

Variational principle for a point particle (massive or massless) in curved space

We know that for a point particle, the action is $$ S[x,e] ~=~ \frac{1}{2}\int_{\lambda_A}^{\lambda_B} d\lambda\left[e^{-1}(\lambda)~g_{\mu\nu}(x(\lambda))~\dot{x}^\mu(\lambda)~\dot{x}^\nu(\lambda) -...
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1answer
893 views

Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory

In Einstein-Cartan gravity, the action is the usual Einstein-Hilbert action but now the Torsion tensor is allowed to vary as well (in usual GR, it is just set to zero). Variation with respect to the ...
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0answers
124 views

Forward's frame-dragging accelerator

On 1962, Robert Forward studied the possibility of using General Relativity Frame-Dragging effects to accelerate probes inertially (that is, without feeling any internal G-forces) One of the ideas is ...
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830 views

When does a singularity start to exist during a black hole formation?

Excuse me if the question is naïve. I am not a physicist. Let's imagine formation of a black hole from a homogeneous collapsing star. At certain moment when enough of matter is inside of a small ...
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1answer
63 views

What's the definition of incompleteness of a coordinate system and a spacetime?

I always see in GR textbooks that some coordinates or some spacetime is incomplete, such as Rindler spacetime and spacetially flat FRW universe with only positive cosmological constant. This ...
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0answers
74 views

Does Hawking radiation need an apparent horizon and when does it switch on during stellar collapse?

I've read that Hawking radiation is implicitly linked with the existence of an apparent horizon (1). This seems a slightly less onerous than linking Hawking radiation with a genuine bona fide event ...
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2answers
295 views

Does General Relativity correctly explain the ellipsoidal shape of the earth?

Does General Relativity theory correctly explain the ellipsoidal shape of the earth? It seems it does not because the Thirring expression¹ for the force of a spherical shell—of mass $M$, radius $R$, ...
3
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2answers
2k views

Geodesic equation from Euler - Lagrange

There are several ways to derive the geodesic equation. One of which is the variational method which I seemed to understand it because it was written in great details. Then it was mentioned that the ...
5
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2answers
234 views

Could Dust Equation of State have some negative pressure?

Traditionally the cosmological equation of state of cold matter (so-called dust) is simply: $$p = 0.$$ But, in Newtonian terms, each particle is gravitationally attracting every other particle. ...
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149 views

How strong is the force of space expansion?

There are many questions about space expansion, its cause, or its effects. But I have the feeling we never get straight and simple answers. I do not expect answers to be simple in general, but I ...
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862 views

Do gravitational fields exist in vacuum region?

I was reading about "vacuum solution" in wiki, http://en.wikipedia.org/wiki/Vacuum_solution_(general_relativity). There are some words I'm confused. 1.In general relativity, a vacuum solution is a ...
3
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1answer
333 views

Black Holes can't exist?

So in this article here, Mersini-Houghton says that Black Holes can't exist. Is there any truth to this? references: http://arxiv.org/abs/arXiv:1406.1525 http://arxiv.org/abs/arXiv:1409.1837
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1answer
120 views

Gravity of the accelerated particle in General relativity?

Suppose heavy particle or body ("billiard ball") is accelerated with very thin and very rigid (not absolutely rigid) rod of infinitesimal (not zero) mass ("cue stick") Acceleration is constant in ...
120
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5answers
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Did the Big Bang happen at a point?

TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen?
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1answer
49 views

Are there any difference between gravitational potential of different types of black holes?

There are four possible types of black holes that could exist in the theory of gravitation (called general relativity). Are there any difference between the value of gravitational potential of these ...
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1answer
302 views

Is relativistic event horizon half of Newtonian event horizon?

Is Relativistic event horizon half of Newtonian event horizon? relativistic escape velocity formula (from $m\phi=E-E_0$) is $v_e=\sqrt{2\phi-(\frac{\phi}{c})^2}$ and the Newtonian version of the ...
3
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1answer
178 views

Can light produce weak gravitational waves?

I have read online that light can produce a weak gravitational field (for example antiparallel beams should, in principle, attract weakly). This made me wonder if light can produce minute ...
14
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1answer
1k views

How does the Hubble parameter change with the age of the universe?

How does the Hubble parameter change with the age of the universe? This question was posted recently, and I had almost finished writing an answer when the question was deleted. Since it's a shame to ...
2
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1answer
103 views

Can these two terms cancel out?

In trying to prove that $$\Gamma_{\mu\nu\lambda} = \eta_{ab}J^a_bJ^b_{\nu\lambda}.$$ The author canceled out while expanding the first equation $$J^a_{\mu\lambda}J^b_\nu$$ with $$J^b_{\mu\lambda}J^a_\...
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2answers
268 views

Differentiation in general relativity

If we have: $$ \frac{d\phi^a}{d\tau}= \frac{\partial \phi^a}{\partial x^\mu} \frac{dx^\mu}{d\tau} \tag{1}$$ Differentiating it, we get: $$ \frac{\partial \phi^a}{\partial x^\mu}\frac{d^2x^\mu}{d\...
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1answer
81 views

Simplifying Friedmann's Equation

So we have one of Friedmann's equation: $$\rho_c = \frac{3H^2}{8\pi G}$$ Using This website, resources where gathered for specific times in the universe. The resources being the Hubble constant at ...
4
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1answer
353 views

Boundary term in Einstein-Hilbert action

Why is the boundary term in the Einstein-Hilbert action, the Gibbons-Hawking-York term, generally "missing" in General Relativity courses, IMPORTANT from the variational viewpoint, geometrical setting ...
2
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0answers
107 views

How to prove the energy of gravity in general relativity is non-local?

Every textbook in general relativity containing the energy of gravity all says that the energy of gravity is non-local and every energy-momemtum density received is pseudo-tensor, but "having not ...
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1answer
73 views

Friedmann equations question

Friedmann equations for critical density is: $$\rho_c = \frac{3H^2}{8\pi G}$$ Is there any other way to write this equation? For example: $$\rho_c = \frac{3}{8\pi GH^2}$$ I saw the above form on ...
2
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1answer
235 views

Riemann Curvature Tensor Symmetries Proof

I am trying to expand $$\varepsilon^{{abcd}} R_{{abcd}}$$ by using four identities of the Riemann curvature tensor: Symmetry $$R_{{abcd}} = R_{{cdab}}$$ Antisymmetry first pair of indicies $$R_{{...
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0answers
50 views

problem with spin connection term

While working out Kaluza Klein compactification, I am getting the unwanted spin connection term $\omega_{c}^{ac}$ .I have tried to show that this is zero.But I am not quite sure of it. What I tried ...