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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Why Hausdorff and Paracompact manifold in GR?

What can we say about the transition map if the manifold is a Hausdorff space? Why do we need the manifolds to be Hausdorff and paracompact in General Relativity?
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4answers
530 views

How to measure the curvature of the space-time?

I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ...
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71 views

Building a wormhole

We regularly get questions about wormholes on this site. See for example Negative Energy and Wormholes and How would you connect a destination to a wormhole from your starting point to travel through ...
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2answers
46 views

Why does gravitational lensing bend light rather than absorbing it?

I've read that gravitational lensing bends the light; I am a little confused about black holes and why lensing produces different results. Black holes absorb light whereas lensing should have also ...
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2answers
59 views

Photons emitted at the event horizon?

While looking through the questions, a came across a section about black holes. I immediately though; what would happen if an atom is orbiting a black hole and emitted a photon perpendicular to the ...
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2answers
117 views

Is energy conserved in general relativity? Does $\nabla_aT^{ab}=0$ represent the conservation of energy and momentum?

For example, the radiation dominated cosmology, the energy density of radiation is propotional to $a^{-4}$ and the volume is propotional to $a^3$, where $a$ is the scale factor. So the total energy ...
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26 views

2 Event Horizons come into contact [duplicate]

Just a question out of curiosity, what would happen if the event horizons of 2 black holes of the same mass were to come into contact? Would both gravitational accelerations be canceled where the ...
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2answers
62 views

Mass of a black hole

I know that if a star collapses into a volume with radius less or equal to the Schwarzschild radius $r_s=\frac{2GM}{c^2}$ then a black hole is created and it has the same mass of the star that gave it ...
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1answer
48 views

What is the energy of a black hole?

This might be a stupid question but given Einstein's general theory of relativity $E = m c^{2} $ what is the energy of a black hole? Isn't the mass of a black hole infinite? Wouldn't that be infinity ...
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27 views

'hypersurface orthogonal' component of covariant derivative of normal vector

I believe that answer to my question is rather trivial but I can't seem to get my head around it. In context of ADM formulation of gravity (or any other differential geometry context, I guess) the ...
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0answers
26 views

Gregory-Laflamme Instability

Certain solutions to the low energy effective action of string theory, namely black strings and branes, were shown to exhibit an instability via perturbation theory. Specifically, the metric is ...
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22 views

How to find solutions to the gravitational potential metric h

I'm working on a problem in which a star of mass M1, radius R1 is surrounded by a shell of mass M2, , radius R2. I want to find the solutions to the gravitational potential h in the regions in between ...
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1answer
81 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, ...
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80 views

How come that an Infinite universe will collapse under gravity?

In this PSE post the issue is about the stability of an infinite universe under Newtonian gravity. Here I'will drop the Newtonian constraint because we know of the finite speed of interactions and I ...
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2answers
91 views

What is the meaning of space-time curvature?

What is the difference between the Space-time curvature and Space curvature?
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what are wormholes made of and how do they function?

what are wormholes made of and how do they function ? Also, what is the relation between black holes and wormhole ?
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2answers
289 views

Does GR really allow superluminal movement?

In this video, Michio Kaku says "...general theory of relativity, where it is possible, we think, that you might be able to go faster than the speed of light..." Does GR really allow ...
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0answers
39 views

Ricci tensor of direct product of manifolds

Imagine I have a (Lorentzian) manifold with a metric $\left[ {\begin{array}{cc} g_{\mu\nu} &0\\ 0&g_{mn}\\ \end{array} } \right]$ Will the Ricci tensor be also block diagonal ...
3
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2answers
120 views

Cosmological constant doubts

I have read about cosmological constant given by einstein in universe in nutshell as well as in general and special relativity. But still I am not able to understand the aim to use it or to introduce ...
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1answer
53 views

Can weakness of gravity explore new dimensions

Since gravitational force is weakest force out of the four fundamental fources at the microscopic level. Is it possible that gravitational force is strong in a particular direction at a new ...
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0answers
61 views

Why is the Ricci tensor diagonal for isotropic spacetime?

I'm reading Zee's Einstein Gravity in a Nutshell and while calculating the Ricci tensor for FRW spacetime he claims that because the spacelike slices of constant $t$ are rotationally invariant, the ...
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2answers
50 views

Would an Object Near a Pre-Blackhole Star Experience the Same Gravity as Post-Blackhole?

My question was inspired by this question, which got me thinking. According to Newton's Law of Gravitation, $$F = G\frac{m_1m_2}{r^2},$$ the gravity of an object is inversely proportional to the ...
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0answers
38 views

How to derive the schwarzchild metric?

I'm having trouble differentiating the following when making a change of co-ordinates to determine the Schwarzchild metric. $$r'^{2}=r^{2}C(r)$$ Then taking the total derivative of both sides, the ...
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1answer
73 views

The Spin Connection

Why do we need to introduce the spin connection coefficients $\omega_{\mu \space \space b}^{\space \space a} $ in General Relativity? To me, they just look (mathematically) like the Christoffel ...
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Rigid rectangle in Schwarzschild

Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial ...
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1answer
37 views

How to calculate the gravity level at the boundaries of a black hole? [closed]

Imagine that a body is attracted to a black hole and it has a mass $M$, if the body is moving with $v=.99c$, will its speed and mass affect the gravity relation between the body and the black hole? or ...
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1answer
68 views

Metric for infinite straight cosmic string

A string theory question on my general relativity problem set: Metric is given as $$\mathrm{d}s^2 = -A(r)\mathrm{d}t^2 + B(r)\mathrm{d}r^2 + r^2 \mathrm{d}\theta^2.$$ a) Solve the vacuum equations ...
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2answers
100 views

What is the notion of a spatial angle in general relativity?

Is there a notion of spatial angles in general relativity? Example: The world line of a photon is given by $x^{\mu}(\lambda)$. Suppose it flies into my lab where I have a mirror. I align the mirror ...
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0answers
58 views

The difference between The Dilaton and The Radion?

I have read this question on the Dilaton, but I am a little confused with the distinction between the Dilaton and the Radion. I definitely have the feeling that these two scalar fields are different ...
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3answers
1k views

Wouldn't angular momentum of a binary star system decrease?

Consider a binary star system, as these stars go around one another they would emit gravitational waves. Since, the graviton is a spin 2 particle. Wouldn't the angular momentum of the stars decrease? ...
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44 views

Non-commuting vector multiplication in GR

If the tensors of GR were composed of non-commuting vector multiplications, this would at least in spirit bring GR closer to QM. Has this approach been attempted?
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2answers
404 views

Why gravity is a spin-2 field? How can I read the spin from Einstein-Hilbert action?

I have often heard that the gravitational field has spin $2$. How can I read the spin of the field from the Einstein-Hilbert action $$S=\int \! \mathrm{d}^4x \,\sqrt{|g|} \, \mathcal{R} \, \, \, ?$$
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18 views

Instabilities in the CDMT

Could anyone explain or refer to references on why the CDMT f(R) gravity model suffers from Instabilities any why the sign of ${\mu}^{4}$ matters.
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1answer
50 views

How to calculate spatial distance in space-time?

Pinning two test particles at two different points in space, how can I calculate their spatial distance, when the geometry is given by the Schwarzschild metric? Let's say particle 1 is pinned at ...
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2answers
78 views

Stress-energy-momentum tensor

In Wald's General Relativity, he writes on pg 61 For an observer with 4-velocity $v^a$, the component $T_{ab}v^a v^b$ is interpreted as the energy density, i.e. the mass-energy per unit volume, as ...
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0answers
45 views

Does non-matter energy curve spacetime? [duplicate]

I know that matter (mass) curves spacetime, but do other forms of energy do the same? I.e. is matter the only form of energy that curves spacetime?
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1answer
26 views

Calculating Hubble Radius using relativistic effects

I am trying to calculate the Hubble Radius, or the distance from which an object will recede from an observer at the speed of light. I initially tried using $v=H_0d$ which gives $d=1.424\times10^{26}$ ...
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1answer
53 views

Covariant derivative of a vanishing tensor component [closed]

Is the covariant derivative of a vanishing tensor component necessarily zero?
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4answers
95 views

A question about moving and time dilation

I was thinking that if you are in empty space with another person (with no other objects around), and from a distance you see that the other person is approaching you a constant speed, you wouldn't ...
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1answer
78 views

Geodesic devation on a two sphere

So the geodesic deviation equation gives the relative acceleration between two geodesics in motion. But given a pair of geodesic (let's say on the two sphere) that start at the equator, separated by ...
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1answer
48 views

velocity in inertial and nontial frames

I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They ...
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1answer
64 views

Riemann curvature tensor in first order perturbation theory as a Lie derivative of Riemann curvature tensor in zero order

I am having a difficulty solving my homework so I was hoping I could get some help, so here it is. It is about gravitational waves and first order gravitational perturbation theory, I have to prove ...
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1answer
32 views

Does the universal expansion affect the gravitational constant?

If the universe was not expanding, would gravity be stronger? since the expansion happens everywhere and can overcome gravity at long distances? If not, then are there any changes that would happen to ...
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0answers
46 views

Can a magnet or a magnetic field push gravity? [closed]

I have been asking around at my school and at the high school and at EWU but no one can answer this question: can a magnet or a magnetic field push gravity?
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4answers
147 views

Can we think of gravity as space itself moving?

So if you move through space with a constant acceleration you experience longer time dilation than when you're at rest, but you also experience the same time dilation when you're under the effect of ...
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0answers
42 views

SPEED of LIGHT as photons reach black holes [duplicate]

As photons reach a black hole and begin fall in - is their speed increased as they go down (like a vacuum cleaner does to dust).
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0answers
38 views

General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
3
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1answer
56 views

Field equations in extended EH-GHY action. Is Schwarzschild a solution?

When taking the EH action, $$S_{EH} = \frac{1}{16\pi G}\int_M d^4x \sqrt{-g}R$$ and making a small variation in the metric while ignoring boundary terms, we obtain $$\delta S_{EH} = \frac{1}{16\pi ...
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1answer
76 views

Is the Hilbert-Felber model of repulsive gravity correct?

This theory states that at relative velocities exceeding 3^-0.5 c, gravitational repulsion ensues. The relevant papers are on arXiv by Franklin Felber. Here's one of them ...
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1answer
42 views

Poincaré symmetry and linearized gravity

When working with linearized gravity, is Poincaré symetry assumed to be the symmetry of space-time?