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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Geodesic deviation on a 2-sphere - is this the right track?

Apologies if I have this completely wrong (and for the general long-windedness). I've searched online but can't find anything helpful/relevant. I'm trying to use the geodesic equation ...
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1answer
32 views

Junction conditions in GR including electromagnetism

I have recently learned about the Israel junction conditions in GR (as explained in for example Gravitation by MTW). I then tried to generalize it when including Electromagnetism, ie matching two ...
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45 views

What is the metric of Vaidya black-hole horizon?

The metric of a Vaidya black hole in outgoing/retarted null coordinates are $$ds^2=-\left(1-\frac{2m(u)}{r^2}\right)du^2-2dudr+r^2\Big(d\theta^2+\sin^2\theta d\phi^2 \Big)$$ The eveolving horizon ...
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2answers
82 views

Why do the space time get curved around a massive object?What problems do we face if we do not consider the space time to be curved? [on hold]

As far as I have the knowledge of GTR that a mass bends the space time around it.But why does this bend occur?The example from real life that when a mass is placed on a net then the net bends but it ...
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1answer
91 views

Angular momentum, what is it, is it conserved, and how do we know?

Firstly, most definitions of angular momentum assume a point about which you define angular momentum. I realize that you can consider the angular momentum about any point, and have many angular ...
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48 views

If $S$ is a closed achronal set in a spacetime, any timelike curve starting at a point in $I^+[S]$ and ending at a point in $I^-[S]$ interset $S$?

Suppose $S$ is an achronal set in a spacetime $M$. And $S$ is closed. At the same time, any null geodesic of $M$ intersects $S$. Then, why does any timelike curve from $I^+[S]$ to $I^-[S]$ intersect ...
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60 views

Is there a general stress-energy tensor for vector fields?

I've been reading about scalar fields in the context of general relativity, and I found this page: https://en.wikipedia.org/wiki/Stress-energy_tensor#Scalar_field. It says that the stress-energy ...
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1answer
41 views

Christoffel symbol

For two nearby points in General Theory of Relativity. The change in the vector components when parallel transported is given by Now, since the parallel transport change must depend on the path ...
3
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1answer
48 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 ...
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1answer
67 views

Why does the second Weyl scalar describe electromagnetic radiation?

I've been reading about the null tetrad, the Weyl tensor, and the Newman-Penrose identities, and so I found out about the Weyl scalars. While the zeroth, first, third, and fourth scalars describe ...
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43 views

geodesic conjugate points

I was reading "Nature of space and time" by Penrose and Hawking, pg.13, If $\rho=\rho_0$ at $\nu=\nu_0$, then the RNP equation $\frac{d\rho}{d\nu} = \rho^2 + \sigma^{ij}\sigma_{ij} + ...
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76 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 ...
4
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0answers
85 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 ...
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3answers
221 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 ...
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44 views

the path of the moon's orbit [closed]

I'd like to know the exact path of the moon's orbit around the earth. when i searched i found that it's nearly circular but i also found these two simulation ...
3
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2answers
100 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 ...
3
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42 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 ...
2
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1answer
94 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) ...
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3answers
779 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
77 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 + ...
3
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3answers
81 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 ...
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2answers
65 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: ...
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1answer
122 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 ...
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3answers
148 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 ...
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46 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 ...
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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 ...
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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, ...
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1answer
32 views

If a point r lies in the boundary of the chronological future of another point p, why does the chronological future of r belong to that of p?

I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in ...
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2answers
51 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 ...
4
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54 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
87 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 ...
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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 ...
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2answers
137 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, ...
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2answers
50 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
93 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!), ...
2
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4answers
489 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 ...
3
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1answer
128 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
36 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 ...
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1answer
29 views

Robertson-Walker metric and stable orbits

The RW metric is defined using 4 spatial dimensions, but stable planetary orbits require 3 spatial dimensions. Does this indicate a problem with the assumption of the RW metric to describe the cosmos? ...
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2answers
111 views

Energy of gravitation

EDIT: As some confusion has appeared, I want to make another clear question. If gravitational energy is meaningless in general relativity (since it is the geometry), how can one come up with the ...
3
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1answer
113 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 ...
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0answers
61 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 ...
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39 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. ...
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2answers
41 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 ...
6
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1answer
55 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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1answer
54 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 $r$? $$X^iX_i=-t^2+r^2+?$$
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3answers
82 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 ...
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1answer
41 views

Should the universe be modeled by perfect fluid or ideal gas?

In physical cosmology, the content of the Universe is modeled by the stress-energy-momentum tensor of perfect fluid, with energy density rho(t) and pressure P(t). I'm wondering, why not use ideal gas ...
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68 views

Minkowski to Euclidean

When dealing with solutions to Einstein's equations given by a 4d metric with signature $(-,+,+,+)$, we're able to move to Euclidean space using some transformation so that our signature is now ...
4
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1answer
69 views

The particle content of a given state

In Carroll's we read ...The Unruh effect teaches us the most important lesson of Quantum Field Theory (QFT) in curved spacetime, the idea that "vacuum" and "particles" are observer-dependent ...