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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Can bending spacetime produce electromagnetic fields?

Let's say that we can somehow bent spacetime, can this produce electromagnetic fields? or EMF can only be emitted from charged particles of matter?
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1answer
17 views

Stress-Energy Content

I think that the Einstein Field Equation relates the pseudo metric to the the distribution of matter-energy as represented by the stress-energy tensor. Are the stress entries in the stress-energy ...
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0answers
9 views

Is the distortion of spacetime caused by frame dragging continuously changing, or fixed?

Consider a very heavy star and let´s take a look at the distorted spacetime accompanying the star. Does the spacetime gets increasingly wind up, or is it stationary? If it´s not stationary, then we ...
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1answer
183 views

If a point r lies in the boundary of the chronological future of another point p, why does the chronological future of r belong to that of p?

I am studying the global causality of the spacetime. Here, I come across a problem. Suppose a point $r\in \partial I^+(p)$. $I^+(p)$ is the chronological future of a different point $p$ in ...
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1answer
88 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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0answers
29 views

Black Holes and dimensions [on hold]

In a mental experiment, I was pondering the paradox of the event horizon of a black hole and the use of multiple dimensions. I have seen the question before. If gravity increases infinitely as you ...
2
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2answers
216 views

Timelike Boundary

I was reading in a paper (see 1st paragraph of introduction section in http://arxiv.org/pdf/1510.00709.pdf) that in AdS space, waves can reach the boundary in finite time and, since said boundary is ...
2
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0answers
27 views

Is there high ring-down frequencies in LIGO's recent discovery?

This question is from Physics overflow: question in physicsoverflow. I am reading LIGO's new discovery of gravitational waves by black hole merger. During the merger, two phases are not hard to ...
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2answers
125 views

Why would a modern smartphone not work if the theory of general relativity hadn't been discoverd? [on hold]

My teacher told me that todays smartphones wouldn't work if the theory of relativity hadn't been discovered, but he didn't explained why.
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3answers
210 views

What does general relativity predict for spacetime without energy?

I am kind of new to GR but I have been familiar with the concepts for a long time, I am getting used to the mathematics just now. My question is, what would GR predict if we would have an empty ...
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0answers
35 views

How does an observer at the center of a black hole collapse explains the singularity? [on hold]

Suppose an observer at the center of a cloud of mass. Imagine that the cloud collapses with the observer at the center and forming a crust with an almost empty core and forms a black hole. So, from ...
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0answers
45 views

(Causal) Set notation round brackets vs square brackets? [on hold]

In many (quite old) papers & books I have been reading recently in the causal theory of general relativity (e.g. On the structure of causal spaces, Kronheimer & Penrose, 1967) I find sets ...
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15answers
29k views

Getting started self-studying general relativity

What are some good books, videos, websites for getting started with general relativity? I would prefer mathematically rigorous sources.
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2answers
102 views

Is this video's notion of general relativity correct? [duplicate]

In this video it explains the path of the apple in the general relativity version of gravity as being a straight line on a curved surface. Is this valid? Edit: this isn't a duplicate of the supposed ...
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1answer
57 views

Can there exist an observer able to observe a collapse of a star into a black hole?

We know that an observer at infinity cannot see a star forming into a black hole as the matter will take progressively longer and longer time to compress (from this observer's point of view). Is ...
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1answer
52 views

Cosmic Rest Frame

Cosmic Rest Frame is defined in the paper "Adventures in Friedmann cosmology :A detailed expansion of cosmological Friedmann equations" by R Nemiroff and B Patla as the frame at a point where average ...
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1answer
59 views

Gravitational wave equations worked out

Is there a website where gravitational wave equations are worked out numerically? I would like to experiment with mass configurations but can't find examples.
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0answers
16 views

Newman-Janis algorithm (Schwarzschild to Kerr metric) [on hold]

my question is how to find the null tetrad for the Schwarzschild metric in Eddington-Finkelstein coordinate? pic 1: I only get the last two values but not able to find the first two tetrad values ...
2
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1answer
39 views

An example of a theory that respects the Weak Equivalence Principle but violates the Einstein Equivalence Principle

The Weak Equivalence Principle has any one of the following forms: the inertial mass is equal to the gravitational mass there exists a preferred class of trajectories through spacetime, known as ...
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2answers
178 views

What manifold is spacetime?

In General Relativity, spacetime is a $4$-dimensional manifold with one Lorentzian metric tensor defined on it. In the Special Relativity case what manifold is spacetime is quite clear: it is ...
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1answer
20 views

Two Robertson-Walker observers, at what time will a light signal be received?

Here is a question I have that is inspired by this question here. The spacetime metric of a radiation-filled, spatially flat ($k = 0$) Robertson-Walker universe is given by$$ds^2 = - dT^2 + T[dx^2 + ...
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1answer
68 views

When and where to check the formal definition of a manifold

In most texts on GR we are first introduced to a formal and rigorous definition of a manifold. We then learn the point that in GR "any coordinate system" might be used for the 4D spacetime metric. ...
3
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1answer
111 views

Diffeomorphism invariance and geodesic action

I'm trying to understand the role of diffeomorphism and isometry invariance in the geodesic action in GR: $$ S = \int_{\tau_1}^{\tau_2} \! d\tau~ g_{ab}(x(\tau)) \frac{dx^a}{d\tau} \frac{dx^a}{d\tau} ...
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3answers
944 views

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start?

Are quantum mechanics and general relativity predictions of string theory, or were they built into the theory from the start? If the former, why aren't tests of GR and QM considered simultaneous tests ...
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0answers
27 views

How does Einstein's curved space time produce acceleration in a free falling object? [duplicate]

I never really thought much about all of this before so I'm definitely a newbie. Please excuse my ignorance. If I understand what I have read so far: if spacetime is curved time would click by at a ...
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1answer
114 views

Torsion-free, symmetric connection and non-coordinate basis

The torsion tensor is defined as (Hawking p.34) \begin{equation} \mathbf{T}(\mathbf{X},\mathbf{Y}) = \nabla_{\mathbf{X}}\mathbf{Y} - \nabla_{\mathbf{Y}}\mathbf{X} - [\mathbf{X},\mathbf{Y}]. ...
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2answers
219 views

Confusion about gravity

I understand the “rubber sheet” model of Relativistic gravity is just an illustration, and beyond the initial issues of mixing three dimensional objects with a two dimensional representation of 3D ...
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4answers
953 views

Lagrangian for relativistic massless point particle

For relativistic massive particle, the action is $$S ~=~ -m_0 \int ds ~=~ -m_0 \int d\lambda ~\sqrt{ g_{\mu\nu} \dot{x}^{\mu}\dot{x}^{\nu}} ~=~ \int d\lambda \ L,$$ where $ds$ is the proper time of ...
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1answer
124 views

Can we embed 2+1 space-time of GR in a 3 Dimensional Euclidean space? [on hold]

Wikipedia says that inflation is the exponential expansion of space in the early universe.I'm trying to have a physical picture of this.Given that I can't visualize 3+1 pseudoriemannian manifolds,I'm ...
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1answer
52 views

Questions about null geodesic [on hold]

Show for the null geodesic in 3D flat spacetime using polar coordinates so the line element is $ds^2=-dt^2+dr^2+r^2d\phi^2$. Do light rays move on straight lines? My question is that I only learned ...
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1answer
42 views

About periodicity of coordinates given a metric

If I am given a metric how do I decide which coordinate is periodic? Eg. can I look at metric in plane polar coordinates and tell that θ direction is periodic. Also How do I calculate the period of ...
5
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1answer
188 views

Rotation of Spacetime $\Rightarrow$ Change in orbit/path

Along the idea of frame-dragging; Will the rotation of a black hole, which has some velocity v and angular momentum, influence its path in 3D space? I've seen the fact that depending on the ...
3
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2answers
147 views

Does all of spacetime exist?

In Brian Greene’s 2004 book, The Fabric of the Cosmos, he quotes Einstein on the meaning of time, …the distinction between past, present and future is only an illusion, however persistent. ...
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2answers
88 views

Could there be a “massive gravity” theory?

If we talk about a "quantum theory" of General Relativity, we know that the particle that mediates the gravitational force would be the so called Graviton, a massless particle with spin $2$. I ...
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1answer
39 views

Energy conservation around a black hole

In the Schwarzschild black hole, the Killing vector "time translation" $k^a$, so that the following quantity is conserved along a geodesic: $$E = -g_{ab}k^au^b = (1 - ...
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2answers
76 views

What is more fundamental: Geometry and Topology or physical matter? [closed]

Since, there is always an interplay between gravity and the fabric of spacetime. I wonder which is more fundamental: Geometry and Topology or physical matter?
2
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0answers
41 views

Indicating that indices are equal in Einstein notation

tl;dr: I have an expression like this: (dramatization) $$ R_{\mu\nu} = \begin{pmatrix} B^{00}C_{00} & 0 & 0 & 0 \\ 0 & B^{11}C_{10} & 0 & 0 \\ 0 & 0 & B^{22}C_{20} ...
3
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1answer
61 views

What happens if I slowly lower a dangling object into a black hole?

I could've sworn I've seen this question before, but I couldn't find it. Suppose I have an object on the end of a really long string. I can slowly lower it near the event horizon of a black hole, ...
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2answers
78 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 ...
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0answers
32 views

Difference in time for clock in attic vs clock in cellar [closed]

This question is regarding relativity: Two clocks are stationed in a house, one in the cellar and one it the attic. Which one of the following statements is true? A : The clocks tick at the ...
3
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1answer
47 views

Difference between Fermi and Riemann normal coordinates

What is the difference between Fermi normal coordinates and Riemann normal coordinates? Which one of them is related to the vanishing of the Christoffel symbols?
4
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5answers
518 views

What is the significance of Planck force?

I have been curious to find what could be the significance of Planck force? It is calculated by the formula $c^4/G = 1.21031359\times 10^{44} \, \mathrm{N}$, where $c$ is the speed of light and $G$ is ...
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0answers
23 views

Does a black hole ever fully form to an outside observer? [duplicate]

According to general relativity, I had understood that time appears to slow down when looking into high gravitational fields from afar, so that as a black hole forms, the light from a collapsing star ...
1
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2answers
366 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' ...
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0answers
44 views

Interpretation of black-hole infalling and apparent geometry of the event horizons

Consider a citizen of the cosmos crosses the event horizons of a black hole. For sake of discussion let's suppose is a Kerr black hole, so that his fate is not sealed the moment he crosses. Does at ...
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3answers
1k views

Equivalence of definitions of ADM Mass

ADM Mass is a useful measure of a system. It is often defined (Wald 293) $$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$ Where $s_r$ is two ...
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0answers
23 views

Relative motion in particle measurements

I was thinking about measurement of particles at almost-zero energies/temperatures and the movement associated with it. Compared to an observer next to the particle who sees the particle moving at ...
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4answers
553 views

Another layman blackhole question, pulling one end of a string out from behind the event horizon

No long explanation is needed, What would happen if I were to allow one end of a rope to fall past the event horizon of a black hole while I held the other end? Would I be able to pull it out? Would ...
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1answer
209 views

Equilibrium for a rope hanging in a Schwarzschild spacetime

Update: Trimok and MBN helped me solve most of my confusion. However, there is still an extra term $-(2/r)T$ in the final result. Brown doesn't write this term, and it seems physically wrong. Update ...
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1answer
54 views

What will happen to Earth if it's tied to a black hole thru a really strong string?

Imagine a very strong string (with infinity as as its breaking point) attached to earth very strongly and the other end is put inside a black hole, What will happen to Earth? And the string? Will ...