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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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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216 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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146 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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158 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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130 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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398 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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168 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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872 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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200 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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800 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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198 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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168 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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155 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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302 views

Vacuum-ether and spacetime

In the past you could not give an explanation for various phenomena in which there was an action at a distance, like magnetism or gravity, that occurred in a vacuum; For this reason, ether was ...
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391 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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356 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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235 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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257 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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498 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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309 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
131 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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5k views

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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551 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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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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71 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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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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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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485 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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506 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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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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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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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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658 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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140 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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624 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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291 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 ...
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491 views

Why is $\langle \partial_{\mu} f(x) \rangle=0$?

I'm reading page 488 of Hobson, Efstathiou & Lasenby, and I don't understand something they write... so I came here. The concept they describe is in linearised general relativity. In particular, ...
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600 views

Does Kaluza-Klein Theory Require an Additional Scalar Field?

I've seen the Kaluza-Klein metric presented in two different ways., cf. Refs. 1 and 2. In one, there is a constant as well as an additional scalar field introduced: $$\tilde{g}_{AB}=\begin{pmatrix} ...
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246 views

Black hole accretion of dark energy

Dark energy physically can be interpreted as either a fluid with positive mass but pressure the negative of its density (pressure has units of energy/volume, and energy is mass), or a property of ...
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309 views

In what way is the Riemann curvature tensor related to 'radius of curvature'?

In Misner, Thorne & Wheeler, they say, in their delightful 'word equations' that $$\left(\frac{\mathrm{radius\,\, of \,\,curvature}}{\mathrm{of\,\, spacetime}}\right) = ...
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381 views

What does it mean that Einstein's equations are hyperbolic-elliptical?

I says on Wolfram MathWorld that Einstein's field equations are a set of "16 coupled hyperbolic-elliptic nonlinear partial differential equations". What does it mean that the equations are ...
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384 views

Divergence theorem over entire space on non euclidean spaces

I'm a physics major so bear with me here on the math. This is related to a problem from the textbook General Relativity - Wald. In classical electromagnetism if we have a vector field say $V$ defined ...
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Do residents of the Hudson Bay area have more time?

Apparently there is a gravity anomaly in the Hudson Bay Area in Canada: gravity is "missing" or it is slightly less than it is in the rest of the world. Does that mean that things in the Hudson Bay ...
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185 views

How is the direction of time determined in general relativity?

In special relativity every frame has its own unique time axis, represented in Minkowski diagrams by a fan-out of time vectors that grows infinitely dense as you approach the surface of the light cone ...
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71 views

Why must the gravitational wave components be much less than unity?

We start with the metric tensor \begin{equation} g_{\mu\nu}(x) = \eta_{\mu\nu} + h_{\mu\nu}(x) \end{equation} in the linearised theory, or \begin{equation} g_{\mu\nu}(x) = \bar{g}_{\mu\nu}(x) + ...
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Is there a book that discusses General Relativity in terms of Modern Differential Geometry? [duplicate]

All of the physics books that I've seen which discuss General Relativity do so in terms of coordinates - the tensor calculus - even though the naturally relevant entities are invariant under general ...
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Hamiltonian constraint in spherical Friedmann cosmology

I'm taking a GR course, in which the instructor discussed the 'Hamiltonian constraint' of spherical Friedmann cosmology action. I'm not quite clear about the definition of 'Hamiltonian constraint' ...