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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7
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7answers
4k views

Gravitation is not force?

Einstein said that gravity can be looked at as curvature in space- time and not as a force that is acting between bodies. (Actually what Einstein said was that gravity was curvature in space-time and ...
4
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4answers
457 views
2
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4answers
54 views

Resource Recommendations: General relativity, local tetrads and particle physics

I'm still self-learning general relativity. I have been a huge fan of Andrew Hamilton's amazing lecture notes on GR, black holes and cosmology. He goes through GR in pretty much full tetrad formalism. ...
1
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1answer
49 views

If I spin around why do the stars not dissappear?

Galaxies at the far limit of the visible universe are moving away from us near the speed of light. There may be some beyond that that are moving away from us faster, so the universe appears to have an ...
0
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1answer
35 views

If I spin around do the stars move faster than light?

In fact I don't even need to spin around, just being on the spinning earth is good enough. Suppose I look out into space at the nearest star, Alpha Centauri, approximately 4 light years away. ...
0
votes
1answer
106 views

The equivalence principle and identifying free-fall as a locally inertial frame

As far as I understand it the equivalence principle in general relativity is the statement that a frame at rest in a uniform gravitational field is equivalent (indistinguishable) to an accelerated (...
1
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0answers
17 views

Linearly accelerated charge experiment feasibility

Wikipedia states: Though maybe it is surprising, there is no experiment that measures directly if an uniformly accelerated charge radiates in an inertial frame. Classic electromagnetic theory says ...
0
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0answers
126 views

What is the mass and density distribution of a Schwarzchild black hole in the viewpoint of distant observer?

According to Schwarzschild metric the density element $$ \frac{\mathrm dm}{\mathrm dV} $$ becomes infinite on the event horizon if there is mass $$ \mathrm dm > 0 $$very near at the outside of ...
-1
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1answer
47 views

Should any matter form a singularity before crossing the event horizon?

I guess the destiny of any object that falling into a black hole will depend on its size and the density of the black hole it falling in. And from distant observer it should looks different. A small,...
4
votes
1answer
257 views

Closed timelike curves in the spin-2 gravity formalism

Let's say we take some topologically trivial CTC spacetime, like the Gödel metric: $$ds^2 = -dt^2 - 2e^{\sqrt{2}\Omega y} dt dx - \frac{1}{2}e^{\sqrt{2}\Omega y} dx^2 + dy^2 + dz^2$$ And then I ...
0
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1answer
49 views

Scalar fields and general coordinate transformations

In classical mechanics, a scalar field is characterised by the fact that its value at a particular point must be invariant under rotations and reflections of coordinates. That is, one requires that $\...
1
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0answers
52 views

What are the different definitions of torsion-free connections in GR? [on hold]

What are the different definitions of torsion-free connections in GR? I am summarizng torsion-less condition in various context, if you know anything about it please let me know. One typical ...
3
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0answers
22 views

Is there an analog of the Komar mass for conformal Killing Fields?

Is there an analog of the Komar mass for conformal timelike Killing vector Fields? For a stationary spacetime M, the Komar mass may be given as: $$M=\oint_{\partial M}\sqrt{g_{00}}(2T_{\mu\nu}-g_{\...
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2answers
87 views

Origin of time or origin of space-time? [on hold]

Are there alternate theories or models that contradicts the idea that big bang is the origin of time ?
1
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0answers
35 views

Experimental tests of electric and magnetic fields in a gravity field

Has anyone experimentally verified that the measured values of the electric and magnetic fields do not change due to gravity, that there is no post-Newtonian effect on the strength of either $E$ or $B$...
7
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0answers
109 views
+50

Zeno effect in quantum gravity?

Given that "the quantum zeno effect can "freeze" the evolution of the system by measuring it frequently enough in its known initial state." Is there any equivalent/similar Zeno effect in quantum ...
10
votes
3answers
2k views

Is energy conserved when things fall into a black hole?

We all know in physics, the law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy can neither be created nor ...
1
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0answers
28 views

Poisson brackets among derivatives in the constraints of the Hamiltonian formulation of General Relativity

The issue I have is from the Hamiltonian formulation of General Relativity (GR) and concerns calculation of certain Poisson brackets. In this formulation, we have the 3-dimensional metric $h_{ij}(x)$ ...
2
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2answers
83 views

Source of Dark Energy.

In accelerated expansion dark energy play a crucial role because of negative pressure, but during expansion Dark Energy(DE) do not dilute. DE density is independent of scale factor unlike matter and ...
1
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1answer
58 views

In what way has GPS had an impact on our understanding of physics?

I've been reading about the effects GPS has had on our society with the February launch of a IIF Satellite and I was wondering if launching GPS satellites and the actual GPS satellites have lead to ...
3
votes
1answer
90 views

A question about Kaluza-Klein mechanism

We know that there is a kind of compactification mechanism named Kaluza-Klein theory which states that the extra dimensions can be compacted dimensions such as $T^n$ or $S^n$ and so on. To make the ...
2
votes
2answers
67 views

Can we exit the event horizon of merging black holes?

I have an intuitive scenario. Consider we have a spaceship just below the event horizon of a BH, which is merging with another black hole. Finally, the singularities merge and we have a single black ...
0
votes
0answers
62 views

Stress-Energy tensor of a static, spherically symmetric, perfect fluid [on hold]

I am trying to derive the equation for the interior mass of a spherically symmetric, static, perfect fluid in general relativity, $$\frac{\mathop{dM}}{\mathop{dr}} = 4\pi r^2 \rho(r).$$ This question ...
2
votes
1answer
149 views

What is the metric of a constant electromagnetic (pure electric or pure magnetic) field?

For example, imagine a magnetic field $B_x$ directing in $\hat{x}$ direction filling all the space. What is its associated metric field? I can construct the electromagnetic stress-energy tensor for ...
3
votes
1answer
153 views

Distance between two galaxies of different redshift

Let $Q_1$ and $Q_2$ two different objects in the Universe (we can think to two galaxies or quasars), that we observe from the Earth at different angular position $(\alpha_1,\delta_1)$, $(\alpha_2,\...
0
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0answers
28 views

Explanation of galaxy rotation curves by space-time drag

I expect, that known effect of rotating body (made of galaxy stellar mass) it too small to explain galaxy rotation curves. By how small is it comparing to required value? What if introduce ...
4
votes
1answer
176 views

Derivation of Christoffel Symbols

So I am reading a book on relativity & differential geometry and in the text, they gave the Christoffel symbols in terms of the metric and its derivatives, but I wanted to derive it myself. ...
3
votes
2answers
56 views

Does the charge of a black hole affect its space-time geometry?

Does a black-hole of a given mass and angular momentum have the same space-time geometry regardless of its charge? I'm pretty sure that an electric field can accelerate a charged particle but doesn't ...
18
votes
1answer
204 views

Curvature Invariants in General Relativity and Singularities

Suppose that I want to check if a given metric is singular or not. I'm interested in curvature singularities, not coordinate singularities, so I can look to scalars made with Ricci, Riemann and Weyl ...
4
votes
0answers
64 views

Can this relativistic hack allow one to see beyond an event horizon, in principle, else why not? [duplicate]

Consider a lone photon. As its frequency increases, its energy increases. Taken to the limit, a sufficiently-high-frequency photon could be a black hole unto itself. But the frequency of a photon is ...
5
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2answers
2k views

What role does electrical charge play in black holes?

Not having studied General Relativity, I have sometimes been puzzled by references to the behaviour for "classic" black holes — as they are popularly portrayed — as being true for black ...
0
votes
2answers
152 views

Gravitational Time Dilation vs Acceleration Time Dilation

I might be a little dense to this subject, but I would like to ask a question relating to this one ( Is gravitational time dilation different from other forms of time dilation? ) but asking if this ...
4
votes
1answer
26 views

Interpretation of components of energy-momentum flux near a null surface

Let $k^a$ be the normal to a null surface and $l^a$ be the auxiliary null vector satisfying $l^a k_a=-1$ (see, for instance, the textbook A Relativist's Toolkit by Poisson). I wanted to understand ...
-1
votes
1answer
52 views

Why does one particle in Hawking radiation have negative energy? [duplicate]

So as I understand it, Hawking radiation occurs when virtual antiparticle-particle pair are created near the event horizon of a black hole due to vacuum fluctuations because of Heisenberg uncertainty ...
-1
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0answers
26 views

Black Hole mass

Where is the material that has past the event horizon of a black hole stored/kept? Does it become pure energy once it passes the event horizon? Does the singularity at the center of the black hole ...
-4
votes
0answers
37 views

Parenthetical tensor notation [on hold]

Just out of curiosity, what does it mean to be a type $(n,m)$ tensor? For instance in the context of special and general relativity, the Minkowski metric $\eta$ is considered a type $(0,2)$ tensor. I ...
3
votes
1answer
180 views

Does mass compress space-time?

My understanding of relativity explains that the presence of mass warps space-time so that light travelling through the warp follows at straight line but the warp itself is curved and therefore the ...
1
vote
2answers
57 views

Riemann Tensor and Covariant Derivative in Carroll's Spacetime

In Spacetime and Geometry, Sean Carrol defines the Riemann Tensor in terms of the commutator of covariant derivatives: $R^\rho_{\sigma\mu\nu}V^\sigma = [\nabla_\mu, \nabla_\nu]V^\rho + T^\lambda_{\...
4
votes
3answers
778 views

Space-Time Curvature Depends on Relative Speed

When the mass of a planet causes the curvature of space-time we see that an approaching free-falling object deviates its path towards the planet. We also see the amount of that deviation depends on it'...
1
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0answers
25 views

Black Hole Scattering of Low-Frequency Light

What is the far-field interference pattern for low-frequency (i.e., the wavelength is much larger than the Schwarzschild radius) electromagnetic plane wave radiation about a point mass? I envision a ...
0
votes
1answer
50 views

Can revolving movement also generate gravitational waves? [closed]

If an object revolves around a circular path at the speed of light could it still generate gravitational waves and what would be the simulation in inner area?
1
vote
3answers
76 views

Ricci scalar for Black Hole

What is the value of Ricci scalar at $r=0$ inside Black Hole? Since $R_{\mu \nu}=0$ is vacuum solution and valid outside event Horizon of black hole where there is no mass energy density. But inside ...
0
votes
1answer
46 views

Does gravity cause the gravity of another mass to curve?

For example say star 1 is at position x, however star 2 causes gravitational lensing on star 1's light that is traveling toward you and you now see star 1 at position y. Will star 1's gravity move you ...
24
votes
1answer
2k views

Is spacetime flat inside a spherical shell?

In a perfectly symmetrical spherical hollow shell, there is a null net gravitational force according to Newton, since in his theory the force is exactly inversely proportional to the square of the ...
2
votes
2answers
271 views

Coordinate Singularity in Metric

Suppose I have some metric $$ds^2=g(t)dt^2+\frac{1}{r}dr^2$$ which has a singularity at $r=0$. However, if I make the coordinate transformation $u=\frac{1}{r}$, then I get: $$ds^2=g(t)dt^2+r^3 du^...
-3
votes
1answer
61 views

In relativity theory could we talk energy rather than frames of reference? [closed]

In relativity theory, the space geometry, of space and time, is no longer absolute, if one observer is accelerating compared to the other. Could I say in other words that space geometry is changed if,...
3
votes
2answers
115 views

Using $\sqrt{-g}$ in integrals of proper volume

I am a little confused over integration using proper volume element. When do we use $\sqrt{-g}$ in calculations? For example, in many calculations involving stars, say when using TOV equation, this ...
11
votes
2answers
3k views

Why is light described by a null geodesic?

I'm trying to wrap my head around how geodesics describe trajectories at the moment. I get that for events to be causally connected, they must be connected by a timelike curve, so free objects must ...
0
votes
1answer
63 views

Is there energy output when mass moves between two spacetimes [closed]

Is there energy output when mass $m$ moves between two spacetimes? Say, it starts in a flat spacetime and then falls into a black hole (other examples don't come to mind, but this doesn't mean they ...
3
votes
1answer
225 views

Deriving the Poisson bracket relation of the Ashtekar variables

I'm trying to figure out how to calculate the orthogonality of Ashtekar variables with respect to the ADM hypersurface metric and conjugate momentum. $$\{{A_a}^i(x), {E^b}_j(y)\} = 8 \pi \beta \delta^...