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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Are electrons moving? If so relative to whom? and why is there no magnetic field?

electrons on earth moving with us, due to rotation of earth, revolution of earth, sun and our galaxy right? Then, why is there no magnetic field around a piece of copper wire?
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167 views

Gravitational distortion of an object's diameter, at a distance,

Does the curvature of space-time cause objects to look smaller than they really are? What is the relationship between the optical distortion and the mass of the objects?
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67 views

does a rotating moving body in “flat” space curve its path because of frame dragging?

I am not a physicist. let's say we have a space with an object in it, where all other gravitational bodies are so far away that their affect on the shape of the space is negligible. let's say the ...
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575 views

Fermi Walker vs. Fermi transport

A vector field $f^\mu$ is said to be Fermi-Walker transported along a curve $\gamma$ parametrized with $\tau$ if the following holds $$\frac{\mathrm{D}}{\mathrm{d}\tau}f^\mu = -(a^\mu v^\nu - a^\nu ...
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443 views

Can negative energy explain black holes?

I think black holes are peculiar and I want to know if there is a relation to negative energy. Does negative energy have positive mass and therefore can explain the nature of black holes? IS there any ...
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118 views

General Relativity Paradox - Different local times of two frames a constant distance apart

Suppose there is a habitable star with a significantly large mass, and thus a huge gravitation field. It has a clock on it that ticks each local second. And it also has a mirror. This is Star A. ...
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170 views

Going through a ring of black holes

Mathematician here with a speculative physical question -- feel free to boot me if the level isn't right. Suppose one finds, or builds, a constellation of several black holes arranged in a circle. ...
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62 views

Trying to speak correctly of spacetime intervals and how to compare them

Is it correct to speak of "magnitude of a spacetime interval"? For instance, considering a pair of (distinct) events, $A$ and $B$, which are lightlike separated, is it correct to say that "the ...
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2answers
643 views

The Uncertainty Principle and Black Holes

What are the consequences of applying the uncertainty principle to black holes? Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
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Did Hilbert publish general relativity field equation before Einstein?

Did Hilbert publish general relativity field equation before Einstein?
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471 views

Calculating Riemann Tensor Using Tetrad Formalism

I was trying to calculate the Riemann Tensor for a spherically symmetric metric: $ds^2=e^{2a(r)}dt^2-[e^{2b(r)}dr^2+r^2d\Omega^2]$ I chose the to use the tetrad basis: $u^t=e^{a(r)}dt;\, ...
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77 views

Regarding Electromagnetic Plane and Maxwell equations

I asked this on the math.stackechange but I was told that it might be a good idea to ask here too since my problem is physics/math! Here is the question: Hello everybody I am kind of struggling with ...
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209 views

Does the curvature of space-time cause objects to look smaller than they really are?

What's the difference between looking at a star from a black hole and looking at it from empty space? My guess is that the curvature of space-time distorts the wavelength of light thus changing the ...
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139 views

Falling into a black hole emitter vs observer

Let's say we are working with the Schwarzschild metric and we have an emitter of light falling into a Schwarzschild black hole. Suppose we define the quantity $$u=t- v$$ where $$dv/dr= ...
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146 views

Understanding how the rate of time changes

The rate at which time passes is relative depending on speed and the gravity as predicted in general relativity. This theory has been tested by scientists by comparing two identical atomic clocks, one ...
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126 views

Einstein +Maxwell 's tensor

Why is it true that we can deduce that Einstein's GR equations coupled with Maxwell's EM equations may be written in the form $$R_{ij}=C(F_{ik}F_j^{\,\,k}-{1\over 4}g_{ij}F_{mn}F^{mn})$$ without ...
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321 views

Liouville's theorem and gravitationally deflected lightpaths

It is customary in gravitational lensing problems, to project both the background source and the deflecting mass (e.g. a background quasar, and a foreground galaxy acting as a lens) in a plane. Then, ...
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150 views

Spacelike slicing of Schwarzschild geometry

I am having trouble understanding how to obtain a spacelike slicing of the Schwarchild black hole. I understand there is not a globally well defined timelike killing vector, so we can define t=cte ...
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3answers
603 views

Relation between the determinants of metric tensors

Recently I have started to study the classical theory of gravity. In Landau, Classical Theory of Field, paragraph 84 ("Distances and time intervals") , it is written We also state that the ...
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179 views

Why can certain functions be absorbed into the Schwarzschild metric, while others can't?

Another question about the Schwarzschild solution of General Relativity: In the derivation (shown below) of the Schwarzschild metric from the vacuum Einstein Equation, at the step marked "HERE," we ...
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Gravitational Redshift around a Schwarzschild Black Hole

Let's say that I'm hovering in a rocket at constant spatial coordinates outside a Schwarzschild black hole. I drop a bulb into the black hole, and it emits some light at a distance of $r_e$ from the ...
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675 views

Einstein Field Equations and Electromagnetic Stress-Energy Tensor

My question is: if we write Einstein field equations in this form: $$R_{\mu\nu} - \dfrac{1}{2}g_{\mu\nu}R=8\pi \dfrac{G}{c^4}T_{\mu\nu}$$ Then the left hand side is one statement about the geometry ...
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185 views

General Relativity Equivalence

Is Einsteins Equivalence theorem in General Relativity correct? It seems to me that it neglects the fact that gravitational acceleration depends upon separation distance squared, thus neglecting the ...
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1answer
159 views

How to choose a solution from all possible solutions of general relativity

So there are so many solutions for general relativity - then how does one "choose" the solution that is right one? By checking with observation? (though I also know that it is currently unknown which ...
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2answers
149 views

Does the distance to the cosmic horizon Lorentz-contract? Does the universe Lorentz-contract?

Our universe has a finite size. It is often called the "radius of the universe", or "distance of the cosmic horizon". If we would fly with relativistic speed at the position of our Earth, would this ...
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196 views

Vacuum-ether and spacetime

in the past you could not give an explanation for various phenomena in which was an action at a distance like magnetism or gravity that occurred in a vacuum; For this reason, it was hypothesized ether ...
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355 views

Is the curvature of spacetime invariant? Could it be characterized as the ether?

I'm writing a paper for a Philosophy of Science course about GR/SR and I'm wondering if I can (1) characterize the curvature of spacetime as invariant and (2) argue that this is what Einstein referred ...
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327 views

Is the quantization of gravity necessary for a quantum theory of gravity? Part II

(At the suggestion of the user markovchain, I have decided to take a very large edit/addition to the original question, and ask it as a separate question altogether.) Here it is: I have since ...
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1answer
218 views

Relationship between a formal vector derivative and time evolution of an operator

I'm an undergraduate in physics, with all the lack of knowledge inherent in that. In two of my classes, my professors introduced two equations which look eerily similar. The first, from general ...
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1answer
238 views

Jacobi's matric formulation for tensors

Hi I am trying to derive the E field equation and am stuck using the Jacobi formula, is this correct: $$\delta \det g_{\mu \nu} = Tr(ADJ(g_{\mu\nu}\delta ...
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1answer
388 views

Hawking Radiation: how does a particle ever cross the event horizon?

The heuristic argument for Hawking Radiation is, that a virtual pair-production happens just at the event horizon. One particle goes into the black hole, while the other can be observed as radiation. ...
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1answer
274 views

Material strain from spacetime curvature

Let's say that you moved an object made of rigid materials into a place with extreme tidal forces. Materials have a modulus of elasticity and a yield strength. Does the corresponding 3D geometric ...
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1answer
124 views

Strings on a curved spacetime

Suppose we are interested in in string on a specific metric G, is it necessary to include a Dilaton field on back ground in order to preserve the Weyl invariance? suppose the spacetime is not empty, ...
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Similarity between the Coulomb force and Newton's gravitational force

Coulomb force and gravitational force has the same governing equation. So they should be same in nature. A moving electric charge creates magnetic field, so a moving mass should create some force ...
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Surely space-time Curvature does not explain gravity, it just describe its effects?

In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ...
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1answer
466 views

Lagrangian definition of stress energy tensor

Can anyone explain why $T_{\mu \nu} = \frac{2}{\sqrt{-g}} \frac{\delta \mathcal{L}_M}{\delta g^{\mu \nu}} $, other than justifying it from the Einstein field equations?
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231 views

Boundary conditions of relativistic wave solutions?

If you take Einstein's field equations, \begin{equation} R_{\mu\nu}-\tfrac{1}{2}g_{\mu\nu}R = -\kappa T_{\mu\nu}, \end{equation} and you insert the metric \begin{equation} g_{\mu\nu} = \eta_{\mu\nu} ...
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1answer
70 views

Constraint on a metric

Given a metric of the form $$ds^2=dr^2+a^2\tanh^2(r/b)d\theta^2$$ why does it follow that $a=b$? I can't quite spot a constraint condition...
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236 views

about the 1D singularity of black hole

I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the ...
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586 views

Does gravitational redshift imply gravitation time dilation?

The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in ...
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2answers
364 views

Is light affected by gravity? Why?

I would like to know if light is affected by gravity, also, I would like to know what is the correct definition of gravity: "A force that attracts bodies with mass" or "a force that attracts bodies ...
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374 views

If matter creates space, shouldn't there be experimentally detectable consequences?

Ernst Mach, a man to who influenced Albert Einstein significantly in his approach to relativity, did not quite seem to believe in space as a self-existing entity. I'm pretty sure it would be correct ...
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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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1answer
904 views

How is the second-order covariant derivative of a scalar computed?

What is second-order covariant derivative $$\nabla_i\nabla_jf(r)$$ in terms of $r,\theta, g(r)$ and partial derivative, given that the metric takes the form $$ds^2=dr^2+g(r)d\theta^2$$ and $f$ is a ...
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1answer
146 views

Flat space metrics

This question concerns the metric of a flat space: $$ds^2=dr^2+cr^2\,\,d\theta^2$$ where $c$ is a constant. Why is it necessary to set $c=1$ to avoid singularities and to restrict $r\ge 0$? Thanks.
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2answers
880 views

Question about proper time in general relativity

I think I may have some fundamental misunderstanding about what $dt, dx$ are in general relativity. As I understand it, in special relativity, $ds^2=dt^2-dx^2$, we call this the length because it is ...
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1answer
620 views

Does local physics depend on global topology?

Motivating Example In standard treatments of AdS/CFT (MAGOO for example), one defines $\mathrm{AdS}_{p+2}$ as a particular embedded submanifold of $\mathbb R^{2,p+1}$ which gives it topology ...
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1answer
129 views

An infalling object in a black hole looks “paused” for a far away observer, for how long?

As I understand, to an observer well outside a black hole, anything going towards it will appear to slow down, and eventually come to a halt, never even touching the event horizon. What happens if ...
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540 views

In what limit does string theory reproduce general relativity? [duplicate]

In quantum mechanical systems which have classical counterparts, we can typically recover classical mechanics by letting $\hbar \rightarrow 0$. Is recovering Einstein's field equations (conceptually) ...
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247 views

Equation of state of cosmic strings and branes

I'm sure these are basic ideas covered in string cosmology or advanced GR, but I've done very little string theory, so I hope you will forgive some elementary questions. I'm just trying to fit some ...