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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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 ...
3
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2answers
375 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
911 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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883 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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1answer
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) ...
10
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1answer
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 ...
3
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3answers
486 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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2answers
503 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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3answers
229 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 ...
1
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1answer
274 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) = ...
2
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1answer
320 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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0answers
318 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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1answer
2k views

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 ...
5
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1answer
165 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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1answer
70 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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0answers
83 views

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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2answers
232 views

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' ...
5
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1answer
236 views

Kaluza-Klein Christoffel Symbols

I have a question regarding the connection coefficients as they pertain to the following paper: http://www.weylmann.com/kaluza.pdf . When I try to calculate the 4D Christoffel symbols from the 4D part ...
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1answer
166 views

Are group representations possible when the solution space is not a vector space?

As far as I understand, the motivation for using representation theory in high energy physics is as follows. Assume that a theory has some (internal or external) symmetry group which acts on a vector ...
4
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3answers
579 views

Why do clocks measure arc-length?

Apologies in advance for the long question. My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
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0answers
54 views

Why does the local inertial compass coincide with the stellar compass?

I found this physics paper via a non-duality site and I wished that I could understand it. Could someone please either read it and explain it to me or else point me to pages that would help me ...
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2answers
611 views

Expression for distance of closest approach in Schwarzschild Geodesics

The Wikipedia article Two-body problem in General Relativity uses two length-scale variables, $a$ and $b$, to simplify the math. For some information about these, consider these statements from the ...
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2answers
417 views

What is the Riemann curvature tensor contracted with the metric tensor?

Can the Ricci curvature tensor be obtained by a 'double contraction' of the Riemann curvature tensor? For example $R_{\mu\nu}=g^{\sigma\rho}R_{\sigma\mu\rho\nu}$.
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3answers
349 views

Setting up a local-coordinate system in space-time using only a single clock and light beams

I have a question to ask about the operationalist view of space-time. I am a mathematician who happens to be interested in physics, so if anyone thinks that my question is a silly or vague one, please ...
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0answers
59 views

The definition of $f_{NL}$ and transfer function

To me there seems to be quite a few different definitions of $f_{NL}$ in cosmology and I would like to know if or how they are equivalent. Let me cite at least 3 such, One can see the equation 6.71 ...
5
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2answers
200 views

Order = Energy = Mass?

Here is a following problem I encountered when chatting about physics with my friend: Let us imagine a classical example of ordered state of matter in thermodynamic sense: let's take a cylinder ...
3
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1answer
295 views

Propagating degrees of freedom of graviton

What is the best way to see that the number of propagating degrees of freedom or gravitons in 3 dimensions is $0$ ? By graviton I mean the metric and NOT some topologically massive graviton that one ...
2
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4answers
270 views

Equivalence principle question

I understand the equivalence principle as "The physics in a freely-falling small laboratory is that of special relativity (SR)." But I'm not quite sure why this is equivalent to "One cannot tell ...
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4answers
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Can spacetime exist in the absence of matter and energy?

I'm pretty sure Ernst Mach would have said that spacetime cannot exist without matter in it. But I'm also pretty sure that a black hole can be described as a self-sustaining gravitational field, ...
3
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1answer
140 views

Does spacetime have momentum?

In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?
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2answers
192 views

Could an ultra-relativistic particle tunnel directly through a stellar mass black hole?

It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of ...
4
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2answers
894 views

Graviton and photons interaction

If one believes in the theory of gravitons then by viewing a black hole you see gravitons affect photons. This in turn leads to the conclusion that force carrier's mass equivalences allow them to be ...
5
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1answer
112 views

Help with the understanding of boundary conditions on $AdS_3$

So I am trying to reproduce results in this article, precisely the 3rd chapter 'Virasoro algebra for AdS$_3$'. I have the metric in this form: ...
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3answers
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What is the capture cross-section of a black hole region for ultra-relativistic particles?

What is the capture cross-section of a black hole region for ultra-relativistic particles? I have read that it is $$\sigma ~=~ \frac{27}{4}\pi R^{2}_{s}$$ for a Schwarzschild BH in the geometric ...
9
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1answer
478 views

How to thoroughly distinguish a coordinate singularity and a physical singularity

In a course on general relativity I am following at the moment, it was shown that the singularity $r=2M$ in the Schwarzschild solution is a consequence of the choice of coordinates. Introducing ...
21
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3answers
7k views

How does faster than light travel violate causality?

Let's say I have two planets that are one hundred thousand lightyears away from each other. I and my immortal friend on the other planet want to communicate, with a strong laser and a tachyon ...
10
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3answers
652 views

Since there are gravitational lenses, are there gravitational mirrors?

Gravitational lensing is an observed phenomenon. Can one have a gravitational mirror? A slightly unrelated question: Can gravitational waves be reflected?
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2answers
10k views

Newtonian gravity vs. general relativity: exactly how wrong is Newton?

Is there a simple function I can use to describe the difference between simple Newtonian dynamics and the actual observed motion? Or maybe some ratios for common examples of, say, the motion of stars ...
6
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1answer
2k views

Physical significance of Killing vector field along geodesic

Let us denote by $X^i=(1,\vec 0)$ the Killing vector field and by $u^i(s)$ a tangent vector field of a geodesic, where $s$ is some affine parameter. What physical significance do the scalar quantity ...
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4answers
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The bigger the mass, the more time slows down. Why is this?

If I were to stand by a pyramid, which weighs about 20 million tons, I would slow down by a trillion million million million of second. Don't know if that's exactly right, but you get the point. Also, ...
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0answers
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Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
3
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79 views

Gravitational effects and metric spaces

Could somebody please explain something regarding the Nordstrom metric? In particular, I am referring to the last part of question 3 on this sheet -- about the freely falling massive bodies. My ...
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3answers
447 views

where the proper time is invariant why $d\tau$ is not zero?

where the proper time is invariant why change (differential) in proper time $d\tau$ is not zero? $\Delta \tau=\tau_f-\tau_i$ as i know. $d(invariant)=0$ note to comment: action $S=-m_oc^2\int_C d\tau$ ...
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1answer
132 views

Can the zeroth-component of a 4-velocity be negative?

Is it allowed to have the zeroth-component of a four-velocity be negative? I presume the answer is yes, but I just want to make sure. Many thanks. This is referring to $V^0$ for a curved space ...
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1answer
341 views

Homogeneous gravitational field and the geodesic deviation

In General Relativity (GR), we have the geodesic deviation equation (GDE) ...
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2answers
1k views

How can mass affect spacetime?

In General Relativity Theory, mass can warp spacetime. However, in my view interaction only occurs between pieces of matter. Spacetime is not matter; how can it be affected by matter?