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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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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1answer
47 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
188 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
72 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. ...
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1answer
126 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
955 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
34 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
121 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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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
1k 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
56 views

Questions about null geodesic [closed]

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
48 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 ...
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1answer
189 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
149 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
90 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
47 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
80 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?
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1answer
71 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, ...
2
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2answers
90 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 ...
3
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1answer
51 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?
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0answers
24 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 ...
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2answers
378 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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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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25 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
591 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 ...
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0answers
32 views

Doubts about Chern-Simons state as a solution of the Hamiltonian constraint in quantum gravity

I've been doing some work with both Baez's Knots, gauge fields and gravity (1) and Gambini, Pullin's Loops, knots, gauge Theories and quantum gravity (2), lately. I have basically two problems: I ...
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1answer
33 views

How are the frequency and wavelength of electromagnetic waves affected within an event horizon?

I apologize if this has been asked previously or if my thinking is way off base, but I am inexperienced with relativity (and this is my first question on the site). I am wondering; as one (not ...
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0answers
35 views

Interpreting meaning of coordinates given a metric

I was working problem 3.6 in Carroll's GR textbook and was given the following metric, which is a good approximation to the metric outside the surface of the Earth. $ds^2=-(1+2 \Phi(r))dt^2 + ...
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0answers
36 views

The derivation of the Mass-Energy(including mechanical energy) equivalence principle [duplicate]

(Not duplication! I couldn't find the answer for the general case, instead of the special case that I've already seen in Youtube I hyperlinked.) I will fully satisfy with not only a mathematically ...
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0answers
23 views

The mass-energy equivalence is a principle which can not be derived from anything? [duplicate]

Not duplication) I couldn't find the answer for the general case, instead of the special case that I already seen in Youtube I hyperlinked. I will fully satisfy with not only a mathematically ...
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1answer
83 views

Simulation of relativistic probe passing through an external solar system

I recently read about the Breakthrough Initiative to launch "StarShot", a nano-probe that is designed to travel to Alpha Centauri at $0.2c$. One of the challenges to be solved involves the precise ...
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2answers
53 views

Does the constancy of the speed of light in vacuum hold for any observer in GR as well?

From SR, we know that the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. But in GR, does it still hold for all observers? I mean the constancy ...
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26 views

Non equilibrium black hole radiating away energy and angular momentum, with total energy and angular momentum conserved

The question refers to whether mass (i.e., energy) and angular momentum can be considered to have been carried away by the gravitational radiation in the hole settling down. And whether those entities ...
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2answers
108 views

A spin zero graviton?

Why can the graviton not be a spin 0 particle? On a similar note why can it not be a spin 4, spin 6 particle?
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396 views

Pressure and density using a general Lagrangian

Given a lagrangian of a form: \begin{equation}\mathcal{L}=f(\phi,\partial_{\mu}\phi\partial^{\mu}\phi)\end{equation} where $f$ is a function, I need to derive pressure and density in a FLRW universe ...
12
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2answers
510 views

Doesn't the Schwarzschild metric combined with Hawking radiation imply that nothing ever gets past the event horizon of a black hole?

According to the General Theory of Relativity, the coordinate time distance per spacetime distance traveled by a particle freely falling into a black hole gets closer and closer to $0$ as the particle ...
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0answers
31 views

Geodesic tangent vector in a Riemannian 4-space

I am doing a question in Lewis Ryder's introduction to General relativity. I am very close to the answer but not quite there. The question is: A Riemannian 4-space has metric $$ds^2 = ...
4
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4answers
206 views

Binary black hole merger viewed from inside the event horizon

How did the metric evolve inside the event horizons of the black holes whose merger caused the GW150914 signal? In principle the Schwarzchild metric of a non-rotating black hole is known inside the ...
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1answer
64 views

On the proof of the existence of geodesics coordinates [closed]

From "Introducing Einstein’s Relativity" by Ray D’Inverno page 77-78 In my calculation, the process is $$\frac{\partial{x^{'a}}}{\partial{x^d}}=\frac{\partial{x^{a}}}{\partial{x^d}}+\frac{1}{2} ...
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2answers
128 views

Is this analogy of Hawking Radiation correct?

Through reading of textbooks and other research papers, I have settled on the analogy of hawking radiation below (Written completely by myself) Within the ergosphere of the black hole, virtual ...
4
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3answers
877 views

What is / are the primary criticism(s) against Einstein-Cartan-Evans field theory?

What is / are the primary criticism(s) against Einstein-Cartan-Evans (ECE) field theory? On Wikipedia the references provided were: arXiv:physics/0607186, MR2372785 (2008j:83049b), MR2218579 ...
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1answer
447 views

Variation of the metric with respect to the metric

For a variation of the metric $g^{\mu\nu}$ with respect to $g^{\alpha\beta}$ you might expect the result (at least I did): \begin{equation} \frac{\delta g^{\mu\nu}}{\delta g^{\alpha\beta}}= ...
1
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1answer
34 views

Eddington-Finkelstein coordinate

The Eddington-Finkelstein coordinates in case of Schwarzschild metric are defined as \begin{align} u&=t-r^*\\ v&=t+r^* \end{align} where $$r^*=r+2GM\ln\left|\frac{r}{2GM}-1\right|$$ The ...
3
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1answer
50 views

Is this equation $\nabla_a\sqrt{-g}=0$ correct? [duplicate]

Is the equation $$\nabla_a\sqrt{-g}=0$$ correct? Here $\nabla_a$ is the Levi-Civita connection, and $g$ is the determinant of metric $g_{ab}$. Apparently, we have $\nabla_ag_{bc}=0$, but I am not sure ...
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228 views

Bending of light - photon's inertia instead of mass

Using classical mechanics, the formula for gravitational attraction is $$F = G\frac{m_1m_2}{r^2}.$$ This formula does not work for photons, and we need to use Einstein's theory of gravity to ...
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43 views

Dark matter from general relativity? [duplicate]

We know that there is dark matter due to the observational orbital velocities and mass to light ratio not matching that of expected ones. However the expected orbital velocities of stars in the Milky ...
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0answers
26 views

what is the metric of N-sheeted $AdS_3$?

Suppose the AdS$_3$ metric is given by $$ ds^2 =d\rho^2+cosh^2\rho d\psi^2 +sinh^2 \rho d\phi^2 $$ what is the n-sheeted space of it? Can the n-sheeted BTZ be constructed from it by identifications ...
53
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4answers
3k views

GR and my journey to the centre of the Earth

[General Relativity] basically says that the reason you are sticking to the floor right now is that the shortest distance between today and tomorrow is through the center of the Earth. ...