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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Precession of Mercury (Python simulation)

I was trying to simulate the precession of Mercury based on the perturbed solution, and my questions about its implementation in python can be seen here: ...
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14 views

Cosmological Constant on the LHS of Einstein's Field Equation

The cosmological constant seems to be normally described as an energy (repulsive force, Dark Energy) of Space-Time. I was just wondering, if we were to interpret the cosmological constant as being ...
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1answer
63 views

Obtaining a copy of Hawking's Ph.D thesis - Properties of Expanding Universes

Due to its popularity, I am interested to know the 4 chapter titles and topics covered in S.W. Hawking Ph.D, Properties of Expanding Universes. I also ask this because that thesis is hardly available. ...
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20 views

First fundamental form in the Gibbons-Hawking-York boundary term

Let me expose my problem, I am trying to perform the explicit variation of the Gibbons-Hawking-York boundary term, $$S_{GH}=\int_{\partial M} d^{n-1}x\sqrt{\left|h\right|}K$$ The problem I have is ...
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2answers
121 views

Are photon energies conserved in general relativity?

As I understand it, both Maxwell's wave equation and the null geodesics of general relativity are scale invariant. Thus an electromagnetic wave can be shifted along a null geodesic without changing ...
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31 views

Entropy of the boundary and stress-energy tensor in the bulk

The importance of this result cannot be understated: Positivity, monotonicity and convexity of relative entropy in the boundary is implied by the positivity of the stress-energy density tensor in the ...
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28 views

Posibility of time travel/multiple realities/time phase shifting [on hold]

Sounds odd and unlikely, but let me explain the situation. Going on the de ja vue ideal, which we probably have all experienced, I believe things of such a matter are possible. Just today when I ...
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2answers
53 views

if singularities can be observed from the rest of spacetime, causality may break down

if singularities can be observed from the rest of space-time, causality may break down, and physics may lose its predictive power,i don't understand how it will happen?we don't have any idea what will ...
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5answers
263 views

Resolving General relativity and Newtonian mechanics to a computer [on hold]

I know this is considered an old subject long ridiculed by many as the folly of layman. But I work in the field of computer simulation, specifically in producing fully functional 3D interactive ...
2
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2answers
77 views

If you fall in a black hole, when do you go past the event horizon? [duplicate]

Say I fall into the event horizon of a black hole. As I cross the black hole, I would appear to outside onlookers to freeze in time, and would never move from that point again. In my perspective, time ...
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31 views

Would the asymmetric collapse of a star produce a naked singularity?

If this is a duplicate, I will remove it. A few years ago SciAm ran an article based around possible variants of stellar collapse. My apologies, I can't remember much more than their main point, that ...
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0answers
24 views

Yamabe flow, Metric times Scalar curvature? [migrated]

I was watching a lecture on differential geometry on Ricci flow, when someone asked a question about "Scalar curvature being multiplied by metric" to my understanding this shall be written as ...
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29 views

Is there any matter inside an event horison? [duplicate]

Consider a feeding, growing black hole. We never observe any matter to cross the event horizon, because time stops there. All matter would be "stuck" in a sphere around the event horizon, slowly ...
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1answer
94 views

If the effects of gravity cannot travel faster than the “c”, does this mean we are only gravitationally bound by masses in our observable universe?

I'm 17 and fascinated by the differences and omissions Newton made in his equations of motion. However it makes sense that gravity can't travel faster than light because of the force-carrying ...
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1answer
47 views

Using metric tensor to contract

Can the metric tensor also contract the indices in the $$\epsilon^{\tau\lambda\mu\nu}~?$$ For example, if we have ...
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1answer
40 views

Influence of spacetime curvature on electromagnetic wave propagation [duplicate]

Classical physics assumes that spacetime is evenly distributed in the sense that Coulomb's Law predicts that a charged particle will create a spherically symmetric electric field around its location. ...
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2answers
108 views

Do clocks measure conformal time (new argument)?

Assuming the spatially flat FRW metric for simplicity: $$ds^2=c^2dt^2-a(t)^2(dx^2+dy^2+dz^2)$$ where $t$ is cosmological time, $a(t)$ is the scaling factor and $x,y,z$ are co-moving spatial Cartesian ...
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2answers
86 views

Is an event horizon absolute to all observers?

Recently I had discussion whether the event horizon of a black hole is absolute or relative to different (outside) observers. Does someone just 1m above the horizon (disregarding effects of tidal ...
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1answer
31 views

The significance of the pressure term within the momentum-energy tensor [duplicate]

EDIT: this question is based around my notion regarding the possible role of potential energy in the momentum energy tensor T$_{\mu\nu}$, The answer below resolves the question and I have deleted ...
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1answer
62 views

Suggestions for GR solved problems books

Study Topic: General Relativity I'm looking for a recommendation for either a dedicated problems and solved solutions book or, failing that, a textbook with a separate comprehensive solutions ...
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0answers
46 views

Contraction of Kronecker delta = 4 [duplicate]

This suggests, as a shortcut notation, the concept of lowering indices; from any vector we can construct a (0, 1) tensor defined by contraction with the metric: $$A_\nu ≡ g_{\mu\nu}A^\mu$$ so that ...
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1answer
63 views

Confusion about two forms of connection coefficients

I am new to GR. In one book I found that the connection coefficient expression is given by $$ \Gamma^\mu_{\nu\lambda} = -\frac{1}{2} g^{\mu\rho} (\partial_\nu g_{\lambda\rho} + \partial_\lambda ...
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2answers
67 views

“Shortest” path in general relativity

My professor in mechanics course sneakily teach us some basic idea of general relativity. Which one of the basic assumption is particle walks in shortest world line. I understand shortest path in ...
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1answer
49 views

How much is time slowed down inside a planet or star?

An answer to What would be the rate of acceleration from gravity in a hollow sphere? states "that according to General Relativity time passes more slowly inside a hollow massive sphere than it does ...
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0answers
26 views

1. How is Newtonian calculations compatible with curved spacetime? and 2. multiple competing reference frames for gravity [duplicate]

Since spacetime is curved, and since the measurement of distance on a curve is along a geodesic, how is it that Newtonian (non-curved) physics can be successfully deployed to calculate distances, ...
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0answers
25 views

Vector fields corresponding to null geodesic congruences in general relativity

I'm working in Minkowski space, and I'm considering some 2D surface, $S$. On each point of the surface, I've computed a null vector, $k^a$, which is orthogonal to it. There will be a unique null ...
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1answer
88 views

Can Bosons couple to gravity? Why do we need vielbein?

It is said that In theories such as Supergravity where there are fermions coupled to gravity, one must use an auxiliary quantity, the frame field (vielbein). In supergravity, can a boson be coupled ...
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3answers
128 views

In GR, why should the spacetime manifold be differentiable?

In general relativity (GR), spacetime is viewed as a differentiable manifold of dimension $D$ with a metric of Lorentzian signature $(-,+,+,...,+)$. My question is why differentiable?
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1answer
103 views
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Spinning micro blackholes power conversion

In the context of energy extraction of spinning black holes, there are two known mechanisms: the Penrose process and the Blandford-Znajek process. The former relies on fragmentation of accreting flow, ...
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3answers
156 views

How does warped space actually look (visually)?

Recently, I was reading about space warping due to extreme gravity and at speeds approaching c, but in books, they always show space in 2D and depth to show space distortion. I was wondering how ...
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1answer
50 views

Can't derive FRW Christoffel symbol [on hold]

I'm trying to confirm that the $\Gamma^1_{01}$ Christoffel symbol of the FRW metric is $\dot{a}/a$. I have the FRW metric: $$ds^2=-dt^2+a(t)^2\left[\frac{dr^2}{1-kr^2}+r^2(d\theta^2+\sin^2\theta\ ...
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0answers
21 views

Does fixing a metric component have anything to do with diffeomorphism invariance?

It is well known that in general relativity, the metrics $g_{\mu \nu}$ and $g_{\mu \nu} + \epsilon L_\xi g_{\mu \nu}$ are physically equivalent, where $L_\xi g_{\mu \nu}$ is the Lie derivative of the ...
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1answer
52 views

Uncertainty principle within a neutron star or black hole

Take the time-energy uncertainty relation, $\Delta$$E$$\Delta$$T$$\ge$$\hbar/2$. My question is based on my confusion about the effect this relation may have within the interior of a highly ...
3
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1answer
51 views

Does Birkhoff's theorem apply to rotating collapsing stars?

Birkhoff's theorem states that every spherically symmetric vacuum solution to $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time ...
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15 views

A Relativity question about radial acceleration? [duplicate]

How do you calculate the radial acceleration of a stationary observer in the Schwarzschild coordinates? I have calculated the 4-velocity and 4-acceleration but not sure how to proceed?
2
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2answers
163 views

Relativity question about 4-velocity

Given a 4-velocity $u^0$, how do you find $u_0$? Do you use $u_{\alpha}u^{\alpha} = -1$?
2
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1answer
33 views

When does light reach a shell observer in Schwarzschild metric?

I am trying to simulate the trajectory of light in the Schwarzschild metric (as seen by a far away observer) with fixed $\theta = \pi/2$. According to my source (Chapter 18, section 18.5) the ...
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0answers
25 views

Tangent Vector Field from Metric

Question: Starting from an arbitrary spacetime metric, how does one obtain a tangent vector field? (We might need to assume certain geodesic congruences but my understanding is very limited.) Build ...
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0answers
40 views

Question about wormholes with ends moving relative to one another [duplicate]

Let's say the two ends A and B of a wormhole are moving relative to one another. If I stick a starship halfway into end A of the wormhole, does the part of the starship that sticks out of end B move ...
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1answer
40 views

Do we weigh more when standing near massive buildings?

I'm very new to the concepts of SR/GR and curvature of spacetime. My understanding is that the bending of spacetime is the causation of gravity, and that matter is the causation of the bending of ...
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1answer
56 views

A general relativity question about the Einstein equations?

Assuming a Robertson-Walker metric to describe homogeneous and isotropic cosmological models, Einstein equations with cosmological constant reduce to these 3 non-linear ordinary differential equations ...
11
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4answers
1k views

Does General Relativity imply loops in space?

Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. The analogy with a rubber sheet is popular. In ...
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0answers
54 views

A General Relativity question? [closed]

The line element for the outside of a spherical star\black hole is given by the Schwarzchild line element : $$-c^{2}d\tau^{2} = ds^{2} = -\left(1-\frac{2m}{r}\right)c^{2}dt^{2} + ...
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2answers
82 views

Is the time “direction” in General Relativity equivalent to a spatial volume [on hold]

Most G.R.textbooks introduce time as an extra dimension, i.e. -ict. (see EDIT below for clarification). So although I can not mentally imagine this, I think of it as an extra line, "orthogonal" to the ...
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0answers
21 views

Killing vectors of AdS space with the metric given in Poincaré coordinate [closed]

I am trying to solve this problem: Find the Killing vector correspond to the symmetry of the scale invariant for the AdS(n+1) $$ (t,{\bf x}) \rightarrow (at, a{\bf x}) $$ when the metric of the AdS ...
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0answers
20 views

DGP brane world model

Can we think of interaction between dark energy and dark matter within the brane in DGP model like in case of GR?
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1answer
65 views

What are Einstein constraint equations?

Yesterday, I met Einstein constraint equations in a thesis? I failed to understand them. Do they have physical meaning? And what do they "constrain"?
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42 views

Momentum conservation in FRW spacetime

The spatially flat FRW metric in Cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it, since the metric does not depend on the spatial co-moving ...
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1answer
46 views

Seeing in shell reference frame in general relativity

I'm trying to understand how an observer in a shell reference frame sees an object (star) near a black hole. I'm specifically trying to understand the equation: $$\tan \theta_{shell} = ...
2
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2answers
61 views

Schwarzschild metric: motivations and applications in physics

I have a mathematical background and I have just derived the expression of the Schwarzschild metric. Now I was wondering what were the motivations and applications in physics of this metric. Any info ...