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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19 views

Can one shed light on the velocity of the photon through the fourth dimension x4 using limits? [duplicate]

THIS QUESTION IS COMPLETELY DIFFERENT!! IT DISCUSSES LIMITS!! To begin with, please study the mathematics from Brian Greene’s book An Elegant Universe. The upshot is that the faster an object moves ...
0
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1answer
18 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
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0answers
20 views

Stress-Energy tensor of a static, spherically symmetric, perfect fluid

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
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1answer
148 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
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1answer
152 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,\...
1
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0answers
40 views

A question about Kaluza-Klein mechanism

We know that there is a kind of compactification mechanism named Kaluza-Klein which states that the extra dimensions can be compacted dimensions such as $T^n$ or $S^n$ and so on. To make the extra ...
0
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0answers
21 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
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1answer
171 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. ...
-1
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2answers
52 views

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

This might be a mere theoretical concept and I might even get down voted for asking this. I read in several sources that winding back general relativity equations leads to $t=0$, origin of time. ...
3
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2answers
53 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
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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
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0answers
63 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 ...
3
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0answers
49 views

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 ...
0
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2answers
150 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
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1answer
25 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
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1answer
50 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 ...
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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
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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
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1answer
177 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 ...
0
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0answers
117 views

What is the mass density distribution of a Schwarzchild black hole?

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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2answers
54 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
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3answers
763 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'...
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24 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
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1answer
49 views

Can revolving movement also generate gravitational waves? [on hold]

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
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3answers
72 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
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1answer
42 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
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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
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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^...
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1answer
59 views

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

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
114 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
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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
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1answer
61 views

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

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
224 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^...
7
votes
3answers
124 views

How much additional light does Earth receive from the Sun due to Earth's gravitational field?

I was reading about how gravity affects light, and that got me wondering how much additional light is collected by the Sun due to the Earth's gravitational field. Is it a significant amount of light (...
0
votes
1answer
43 views

Relativity, and Lenz's law with respect to the Lorentz force acting on a wire?

For this system: It's simple for me to predict the induced EMF, and if the wire were connected to a complete circuit(for current $I$ to flow), the opposing Lorentz force($-F$): However, if the ...
1
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2answers
102 views

Stationary v/s Static

Blau, in his GR book, says that a stationary and spherically symmetric metric is automatically static. He says this easily follows from the fact that for a stationary metric, and in spherical symmetry,...
2
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0answers
55 views

Solving the Friedmann Equation [closed]

Through substituting for values of $\rho$ and $k$, I have: $$H^2=\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi G C}{3a^4} + \frac{\Lambda c^2}{3}$$ $a=a(t)$, and $a(t=0)=0$. Note that $C$ is a ...
12
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1answer
429 views

How long can a particle survive inside of the horizon of a black hole?

By examining the causal structure of a Schwarzschild black hole, one can see that a particle in region II is unable to escape to $r=\infty$. Such diagrams do not show, however, how long a particle ...
19
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2answers
1k views

Chasing someone who has fallen into a black hole

Assume that my friend and I decided to explore a black hole. I parked the spaceship in a circular orbit safely away from the horizon. He puts on his spacesuit with a jet pack and carefully travels ...
2
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1answer
63 views

How can the size of the universe change over time when time is part of the universe?

Bit of an awkward way to phrase it, but basically: Time in relativity is just one of four dimensions of space-time. Nothing really special about it. Yet the universe was once smaller than it is now ...
0
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1answer
51 views

Trace of a Tensor

What is the significance of defining the trace of a tensor as $g^{\alpha\beta} R_{\alpha\beta}$ instead of $R_{\alpha\alpha}$ on a Riemannian manifold?
11
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2answers
2k views

How do wormholes work?

Firstly, I understand that we have no observational evidence for 'wormholes'. They are theorised solutions to general relativity equations. That said, if macroscopic wormholes do exist---how do they ...
0
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0answers
31 views

Does the general theory of relativity imply time dilation across the whole universe? [duplicate]

If not, why is my idea below not possible? The general theory of relativity tells us that time is slowed down by gravitational fields. We bounced radar signals off planets further from the sun, and ...
0
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0answers
25 views

Studying relativity from Landau [duplicate]

I'd like to have an advice from you. I was thinking about studying for the exam of general relativity from Landau II: theory of fields. I already studied mechanics and fluid dynamics from Landau and I ...
3
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1answer
53 views

Stress-energy tensor for Dirac fields, and its dependence on connection

In the stress-energy tensor (SET) for free scalar and vector fields, any references to the connection $\Gamma^\lambda_{\mu\nu}$ in the kinetic terms appear to either be absent ($\nabla_\mu \phi = \...
0
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1answer
136 views

Does time and time dilation exist in a black hole?

Since being near stronger gravitational fields causes time dilation, can this be generalized to the region beyond the event horizon? i.e , is it meaningful to say that someone outside the black hole ...
2
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1answer
82 views

GR says that time and space are aspects of the same thing, yet there is no observable for time in QM

I understand that the topic of a time operator in quantum mechanics has come up more than a few times so forgive me if this is a repeat question but I couldn't find anything specific to my question. ...
6
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2answers
854 views

Stress-energy tensor for a fermionic Lagrangian in curved spacetime - which one appears in the EFE?

So, suppose I have an action of the type: $$ S =\int \text{d}^4 x\sqrt{-g}( \frac{i}{2} (\bar{\psi} \gamma_\mu \nabla^\mu\psi - \nabla^\mu\bar{\psi} \gamma_\mu \psi) +\alpha \bar{\psi} \gamma_\mu \...