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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2
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39 views

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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0answers
24 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 ...
1
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1answer
78 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. ...
4
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5answers
267 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 ...
9
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1answer
3k views

Explicit Variation of Gibbons-Hawking-York Boundary Term

Are there any references that present the explicit variation of the Hilbert-Einstein action plus the Hawking-Gibbons-York boundary term, and demonstrate the cancellation of the normal derivatives of ...
0
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0answers
21 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
123 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 ...
21
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0answers
837 views

A dictionary of string - standard physics correspondences

Motivated by the (for me very useful) remark ''Standard model generations in string theory are the Euler number of the Calabi Yau, and it is actually reasonably doable to get 4,6,8, or 3 ...
22
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1answer
1k views

Is general relativity holonomic?

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the ...
2
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2answers
143 views

Can we add two singularities and make a single singularity?

My question is if we have two black hole and they will merge into each other, then where will be the singularity?
5
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3answers
226 views

Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?

The definition of the SI unit "second" is stated as The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground ...
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0answers
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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0answers
30 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 ...
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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2answers
54 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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0answers
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 ...
2
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1answer
148 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
3
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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 ...
3
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1answer
209 views

Wave Packet in Curved Spacetime

It is known that the classical equation of motion for a scalar field wave packet on a curved spacetime background gives the geodesic trajectory (the e.o.m. is $(\nabla_\mu \nabla^\mu + m^2) \Phi=0$). ...
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0answers
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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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 ...
3
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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 ...
2
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3answers
129 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
104 views
+100

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, ...
2
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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 ...
2
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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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8answers
1k views

Is it foolish to distinguish between covariant and contravariant vectors?

A vector space is a set whose elements satisfy certain axioms. Now there are physical entities that satisfy these properties, which may not be arrows. A co-ordinate transformation is linear map from a ...
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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 ...
0
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1answer
41 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. ...
3
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5answers
259 views

Does coordinate time have physical meaning?

I have always been a little confused by the meaning of the "$t$" which appears in spacetime intervals or metrics in general relativity. I concluded that $t$ was just a mathematical thing which allow ...
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1answer
64 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 ...
0
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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 ...
0
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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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3answers
1k views

Is the speed of sound almost as high as the speed of light in neutron stars?

Have you ever wondered about the elastic properties of neutron stars? Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...
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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 ...
5
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2answers
215 views

Kerr Metric in Orthogonal form

I've seen the Kerr metric usually presented in the Boyer-Lindquist coordinates where there is a cross term in the $d\phi$ and $dt$ term. I've done a good bit of searching and cannot find any ...
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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 ...
1
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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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10answers
17k views

How exactly does curved space-time describe the force of gravity?

I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or ...
0
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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, ...
1
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1answer
110 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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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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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 ...
0
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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\ ...
1
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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 ...
0
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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 ...
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 ...
5
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2answers
412 views

Asymmetric Schwarzschild solution - unequal mass on each side

Look at any Kruskal–Szekeres coordinate plot of the Schwarzschild solution. It shows the same mass everywhere. Yet the two sides cannot talk to each other, in that no information, particles, etc can ...
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0answers
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 $u_{\alpha}u^{\alpha} = -1$?