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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16answers
6k views

Getting started general relativity

What are some good books, videos, websites for getting started with general relativity? Mathematically rigorous preferred!
5
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1answer
55 views

Parallel Transport and covariant derivative

I have been trying to understand the notion of parallel transport and covariant derivative. I am unable to see why the change in a vector when it is parallel transported from one point to another ...
5
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3answers
236 views

A thought experiment on vision and curved spacetime

What follows is a long self-made example to deal with my conceptual issues of visualizing curved spacetime. Imagine an observer floating somewhere in space. He feels no strain on his body, ...
0
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1answer
124 views

Positive Mass Theorem

I'm currently a third year undergrad writing about Minimal Surfaces. In particular, trapped surfaces and black holes. What does the Positive Mass Theorem have to do with this? And does the theorem ...
0
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2answers
509 views

Spacetime around a Black Hole

If we consider the sun, then space-time is curve around it. My question is that what is the kind of curvature of space and time around the black hole. Is that space and time more curved around the ...
2
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0answers
78 views

Calculation of Einstein Equation

I have a 3d system with Lagrangian $$e_3^{-1} L_3 = -\frac{1}{2} R_3 + \delta_{ab} \partial_\rho q^a \partial^\rho q^b + \frac{1}{2H} V(q)$$ From this I want to calculate the Einstein equation by ...
2
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2answers
215 views

Does the total mass of an isolated object include the mass stored in its gravitational field?

Since neither the object nor its field could exist without the other, it would seem strange not to include the field energy as part of the object. But how exactly does the accounting go? How is the ...
1
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1answer
187 views

Questions about MTW's “thousand” tests of the Einstein principle

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 ...
8
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1answer
152 views

Evaluating the Einstein-Hilbert action

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

Null lines and degenerate plane

Can anyone explain me what null lines are and degenerate plane? I don't know anything about it, I don't have physics background and I am a mathematics student and please tell me if there is any good ...
3
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3answers
232 views

Is it time or duration? [closed]

Taking this post: "Is there a proof of existence of time?", as a starting point. Therein was mentioned that there is confusion between: "time" and "flow of time". There was a comment (of mine) that ...
1
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1answer
28 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 ...
3
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3answers
87 views

Does or should the metric expansion of space imply a locally observable increase in kinetic energy?

The title is the question. Here's why it seems like local kinetic energy should increase: Numerous questions and answers here and elsewhere suggest that the reason the metric expansion of space is ...
4
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0answers
96 views

Tricks for Computing Riemann Curvature Tensor with Levi-Civita connection

I am new to differential geometry, so far it seems to me that computing the Riemann tensor tends to be a rather tedious task, I wanted to know whether there are some tricks that I am missing. In ...
3
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2answers
111 views

How does the gravity well change as space expands? [duplicate]

How does the gravity well change as space expands? If we assume that the Earth's gravitational field curves flat space to create a gravity well then how does the gravity well change as space expands ...
2
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1answer
109 views

How exactly and WHY does matter affect space-time? [closed]

According to general relativity, inertial mass and gravitational mass are the same, and all accelerated reference frames (such as a uniformly rotating reference frame with its proper time dilation) ...
3
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0answers
45 views

How can one explain gravitational time dilation in non-rotating bodies? [closed]

A clock on the surface of the Earth (assuming it does not rotate) will accumulate around 0.0219 seconds less than a distant observer over a period of one year (assuming the observer is using ...
12
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3answers
786 views

Is “now” or “the present moment” properly defined in GR?

My question is about the extent to which "now" is defined in GR. In Minkowski spacetime, it's possible to define a "now" for an inertial observer by finding a spacelike 3-plane such that, in the ...
3
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1answer
53 views

Bondi-Metzner-Sachs (BMS) symmetry of asymptotically flat space-times

I started studying the BMS symmetry in connection with the paper: http://arxiv.org/abs/1312.2229 and there are a few strange things I noticed. First of all, from reading the original papers by Bondi, ...
4
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1answer
137 views

Wick Rotation in Curved space

So over time I have learned to do exhaustive searches before asking things here. Wick rotations are cool if you are trying to work in qft and make statements about the thermodynamics of some physical ...
3
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1answer
82 views

The FRW universe is NOT asymptotically flat? Its mass?

The Friedman-Robertson-Walker (FRW) metric in the comoving coordinates $(t,r,\theta,\varphi)$ which describes a homogeneous and isotropic universe is $$ ds^2\,= -dt^2+\frac{a(t)^2}{1-kr^2}\,dr^2 + ...
1
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2answers
86 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 $c=8 \pi G=1$): ...
2
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2answers
67 views

Definition of derivative operator on a manifold

I'm hoping to understand the motivation for certain parts of the definition of a derivative operator $\nabla$ on a manifold $M$. In Wald's General Relativity, two clauses of the definition are: ...
5
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3answers
158 views

What makes General Relativity conformal variant?

I have a question regarding the well known fact that General Relativity is not a conformal invariant theory or to put it in other words about the fact that it is conformal variant: What are the ...
1
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0answers
47 views

Gravity of Light [duplicate]

I'm reading Quantum field theory in a Nutshell and I find a very interesting calculation that leads to the gravitational interaction between 2 light beam. Is this kind of interaction permitted in ...
18
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4answers
1k views

How does “warp drive” not violate Special Relativity causality constraints?

I'm talking about this nonsense: http://www.washingtonpost.com/news/post-nation/wp/2014/06/11/this-is-the-amazing-design-for-nasas-star-trek-style-space-ship-the-ixs-enterprise/ Now, I'm aware that ...
2
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0answers
47 views

Deformation of light-cone

In the paper The geometry of free fall and light propagation by Ehlers and his colleagues (Gen. Relativ. Gravit. 44 no. 6, pp. 1587–1609 (2012)), when the authors introduce the differentiable ...
0
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0answers
36 views

Im a high school finisher and I want to understand Physics theories [duplicate]

I have finished my A Levels (UK high school exam) , and I have studied Further Mathematics, Mathematics, and Physics in high school. I am really interested in learning about theories of Einstein, ...
5
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2answers
144 views

Questions about the degree of freedom in General Relatity

I'm confused about the number of degrees of freedom in General Relatity. There are two ways to count it. However, they are contradictory. For simplicity, we consider vacuum solution. First, ...
0
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2answers
55 views

Tidal forces in free fall

Would a body free falling in a gravitational field which has a gradient large enough that it would affect the free falling body 'feel' the effect of the tidal forces on it. I'm curious because would ...
2
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2answers
69 views

Rectifying incomplete popular notions in cosmology

In looking at the answers to this question regarding light from distant galaxies ever being visible to us: Expansion of the Universe, will light from some galaxies never reach us? I came across a ...
4
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0answers
55 views

General relativity from helicity 2 massless field theory by using Deser's arguments

Recently I have discovered the method of constructing of GR from massless field with helicity 2 theory. It is considered here, in an article "Self-Interaction and Gauge Invariance" written by Deser S. ...
1
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1answer
92 views

Speed of light versus pull of gravity - Is $c$ really the limit? [duplicate]

The understanding I have is that the speed of light is considered to be the highest attainable speed in physics. Of course there are theories of tachyons but since those haven't been proven we'll ...
2
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4answers
493 views

Why is the Schwarzschild radius the radius of an event horizon?

I've been searching the web and many references without much success. My question is how do we know that, in the Schwarzschild black hole solution, the surface with coordinate $r=2M$ (in the geometric ...
1
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0answers
51 views

Is Gravity related to velocity? [closed]

Is the missing link of what creates gravity, the velocity that an object rotates or moves through space ? Can a small object with little mass which rotates or moves in enormous speed create a strong ...
1
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2answers
54 views

Does the mass distribution matter in (Schwarzschild) black holes?

Is it possible that from the same initial mass different black hole radius will be created due to different mass distribution during black hole creation? If mass is concentrated more on the outside ...
0
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2answers
95 views

Particles Associated With Gravitational Waves

I've been reading about linearized GR and the study of gravitational waves, and an odd thought popped into my head. According to wave-particle duality (admittedly, usually used in quantum mechanics!), ...
4
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1answer
133 views

What is the Schwarzschild metric with proper radial distance?

Reading the marvellous book "The Membrane Paradigm" I stumbled upon a suggested change of variable that I'm not able to deal with. Starting with the usual Schwarzschild metric for the spatial ...
2
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1answer
38 views

How does a spatial covariant derivative act on tensors that are not purely spatial?

I have a possibly dumb question on ADM formalism. Starting with a metric in ADM form \begin{equation} ds^2 = -N^2dt^2 + q_{ij}(dx^i + N^idt)(dx^j + N^jdt) \end{equation} where $i,j$ only run over the ...
16
votes
5answers
578 views

Are gravitomagnetic monopoles hypothesized?

My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic ...
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0answers
65 views

How to test that a flat metric represents a global three-torus geometry

When introducing Robertson-Walker metrics, Carroll's suggests that we consider our spacetime to be $R \times \Sigma$, where $R$ represents the time direction and $\Sigma$ is a maximally symmetric ...
3
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1answer
131 views

How far can something travel in a straight line?

Suppose you have an object some distance from you and moving at a velocity different to the Hubble velocity you'd expect at that point. How does the motion of this object change with time? Does it ...
1
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3answers
88 views

How can gravity affect light?

I understand that a black hole bends the fabric of space time to a point that no object can escape. I understand that light travels in a straight line along spacetime unless distorted by gravity. If ...
-1
votes
1answer
81 views

Does the formula $ \theta = \frac{v}{c} $ to find out deflection of light make sense?

I read in reliable sites that GR and classical physics calculate the angle of deflection in the same manner. The formula is almost identical: $$\theta = \frac{4GM}{c^2*r} \rightarrow \frac{4GM}{c*r} = ...
-2
votes
1answer
62 views

Length in polar coordinates

Say we are in 3 dimensions and use $(-++)$. If we have the metric $$ds^2=-dt^2+dr^2+r^2df^2(t),$$ then what is the third coordinate if the first two were $t$ and $r$? $$X^iX_i=-t^2+r^2+?$$
2
votes
2answers
45 views

How to calculate explicit form of stress energy tensor in any situation?

I know that the components of stress energy tensor are: energy density, energy flux, momentum density and momentum flux. But can I explicitly calculate the form of stress energy tensor in any ...
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0answers
41 views

In an Evolving Block Universe, does the growth rate of the universe give the value of C

In an Evolving Block Universe (http://arxiv.org/abs/0912.0808, http://arxiv.org/abs/1407.7243) the future does not exist. The present moment is the bounding edge of the universe in the time dimension. ...
6
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1answer
57 views

Dirac bracket and second class constraints in first-order gravity formalism

In the first order formulation of general relativity, the frame field $e_{\mu}^a$ and $\mathrm{SO}(3,1)$ spin connection $\omega_{\mu c}^b$ are independent variables. In the Hamiltonian formulation of ...
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2answers
263 views

Is light affected by gravity? Why?

I would like to know if light is affected by gravity, also, I would like to know what is the correct definition of gravity: "A force that attracts bodies with mass" or "a force that attracts bodies ...
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2answers
140 views

The Alcubierre drive and closed timelike curves

Under what conditions would it be possible to create closed timelike curves, assuming an Alcubierre drive could exist? Would it be possible to have the latter without the former? See here for ...