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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Tensors in general relativity

This is a question on the nitty-gritty bits of general relativity. Would anybody mind teaching me how to work these indices? Definitions: Throughout the following, repeated indices are to be summed ...
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386 views

What are the general relativity equations for relativistic constant acceleration?

At constant acceleration in special relativity, the time differs for a stationary observer and the astronaut. see the following article for an in-depth explanation: Relativistic Rocket However, when ...
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181 views

Components of the Ricci Tensor

Is there any interpretation of what each of the components of the Ricci tensor corresponds to? For example, for the stress-energy tensor, $T_{00}$ corresponds to energy density, $T_{0i}$ is the ...
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2answers
127 views

Are orbits reversible in general relativity?

It seems if I reverse velocities then things begin orbiting backwards, at least in classical mechanics. From here: Every orbit and trajectory outside atmospheres is in principle reversible, i.e., ...
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1answer
575 views

energy momentum tensor and covariant derivative

In field theory, the energy momentum defined as the functional derivative wrt the metric $T_{\mu\nu}=\frac{2}{\sqrt{-g}}\frac{\delta S}{\delta g^{\mu\nu}}$ (up to a sign depending on ...
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1answer
52 views

Tighten rope around cylindricaly shaped space

Imagine we live on cylinder(we are 2d creature), put a rope around that cylinder and start pulling both ends of the rope against each another. Will the space get deformed? I guess it will, I have to ...
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573 views

If time stops for an object, does that object feel gravity?

As far as I understand The GTR, it is said that Mass bends space-time which causes gravity. So every Mass in this universe is flowing through space-time example earth is moving along with space-time ...
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130 views

Axial symmetry constraints on the metric

I am reading the paper on Gravitational Waves in General Relativity. VII. Waves from Axi-Symmetric Isolated Systems by H. Bondi, M. G. J. van der Burg, A. W. K. Metzner. (link) Here is a quote(s) from ...
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What would be the effect on gravity if space expanded at > $c$?

If space were to expand at > $c$ (as in inflation) would that mean gravity would no longer have any effect on the curvature of space, since gravity can only propagate at $c$?
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422 views

About an Einstein equation

This is a question about an historical theory of gravitation, studied by Einstein quite a bit before he settled on General Relativity. At that time, Einstein did not know that gravity was a ...
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1answer
76 views

Conservation of Energy and Birkhoff's theorem

I am reading the original paper by Bondi, van der Berg and Metzner (link) regarding gravitational waves in asymptotically flat axisymmetric spacetimes. In the introduction, he makes the following ...
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1answer
258 views

Asymptotic Symmetry Group of General Relativity

This question is a little vague and I hope I can put across what I am looking for without too much confusion. What is the motivation behind studying asymptotic symmetry groups in the context of ...
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3answers
158 views

Numerical relativity coordinate system displayed

In a picture or video of a numerical relativity simulation, such as a neutron star merger into a black hole, how do they set up their coordinate system? Lets take the point in a video corresponding to ...
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244 views

General relativity theory [duplicate]

As I understand general relativity theory (please correct me if I'm wrong), time becomes dilated and space becomes compressed around mass, and this is responsible for gravity. I'm struggling with ...
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0answers
42 views

Dark energy lorentz invaraince

Dark energy (or the cosmological constant) is stated as Lorentz Invariant, form websites like: http://cerncourier.com/cws/article/cern/28917 In newtonian mechanics, this is correct. But time dilation ...
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2answers
295 views

Why does $8\pi/3$ appear in the equations describing cosmological expansion?

What is the significance of $8\pi/3$ in the first Friedmann Equation, and in the question concerning the time independence of the Hubble Constant? Is it the 'same' $8\pi/3$ that appears in the total ...
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Covariant derivative of connection coefficients

Is there a meaningful way to define the covariant derivative of the connection coefficients, $\Gamma^a_{bc}$? As in, does it make sense to define the object $\nabla_d\Gamma^a_{bc}$? Since the ...
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1answer
741 views

What are the Conflicting Predictions of General Relativity & Quantum Mechanics? [duplicate]

I see a lot of questions in various sites about why the 2 theories are or aren't incompatible, I'm satisfied as to why that's the case. However it has been mentioned that both theories make ...
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3answers
7k views

Why does light always travel in a straight line?

No matter the frame light is in, it always moves in a straight line in that frame. Why is that? It doesn't seem like something to me that should necessarily be true. If some one runs forward and sends ...
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2answers
580 views

Why does the event horizon of a black hole not look like a bright sphere?

All infalling matter-energy appears to an external observer as frozen in time at the event horizon. Why then is this horizon not extremely bright due to radiation that is able to escape radially? So ...
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Gravity as a gauge theory

Currently, (classical) gravity (General Relativity) is NOT a gauge theory (at least in the sense of a Yang-Mills theory). Why should "classical" gravity be some (non-trivial or "special" or ...
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1answer
137 views

Are third derivatives of metric perturbations zero?

I'm working on a problem related to fluid perturbations of stars. I'm following this paper. They start with the Einstein equation: $$G_{\alpha \beta} = 8 \pi G T_{\alpha \beta}$$ and then perturb the ...
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1answer
90 views

Are there bounds or measurements on the derivative of acceleration (jerk)

The title says it all. Is there a physical maximum value to the 3rd derivative of position? Common Lore says that there is not and that jerk does not play any role in physics. My guess is that there ...
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How energy curves spacetime?

We know through General Relativity (GR) that matter curves spacetime (ST) like a "ball curves a trampoline" but then how energy curves spacetime? Is it just like matter curvature of ST?
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Restriction of a Lagrangian

I'm wondering if anyone could help me with the following questions. Let $M$ be the Minkowski spacetime, given $f\in C^{\infty}(M) ; f(m)=x^{0}(m)$, with $\{x^{\mu}\}$ being a global Cartesian ...
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2answers
437 views

Derivation of freely falling frame in Schwarzschild spacetime

Thinking about the equivalence principle, is there a nice, simple way to show that a local, freely falling frame in Schwarzschild spacetime is described by the Minkowski metric ...
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1answer
277 views

White hole and Schwarzschild solution

What is the relation between white hole and the Schwarzschild solution commonly found in textbooks of physics and interpreted usually as black hole?
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184 views

Can inertial mass affect gravity of the object? [duplicate]

Every time I watch this TV program that discusses about all the facts about the universe , and it came to a point where they said that as an object approaches the speed of light the mass of the object ...
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456 views

Maxwell's equations in curved spacetime

I know that we can write Maxwell's equations in the covariant form, and this covariant form can be considered as a generalization of these equations in curved spacetime if we replace ordinary ...
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1answer
317 views

What happens when I increase the density of a stellar object so that its mass surpasses the Schwarzschild limit?

We know that every object that has mass, also has a Schwarzschild radius $r_s$: $$r_s = \frac{2Gm}{c^2}$$ With $G$ being Newton's gravitational constant, $m$ the mass of the object and $c$ the speed ...
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1answer
94 views

What is *uplift* in respect to extra dimensions and their stability?

What is uplift in respect to extra dimensions and their stability? It's notoriously hard to find something on this, as all possible keyword combinations pull up plethora of unrelated Google hits.
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3answers
271 views

Basic Question About General Relativity?

I'm a layman that loves Physics. I'm also horrible at math. Having said that I have many, many questions in regards to physics and General Relativity in-particular. I will try to keep my question(s) ...
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0answers
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Preservation of a scalar along geodesic trajectory

Let $u^\mu$ be the velocity of a particle , and $\xi^\mu$ be a killing vector. would taking a contravariant derivative of to scalar product $\xi_\mu u^\mu$ , and showing that it equals to 0 shows that ...
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250 views

AdS/CFT and boundary translational invariance

I work in quantum information theory/condensed matter and have some very basic questions about AdS/CFT correspondence. For simplicity, I would like to restrict to 1+1 CFT <-> 2+1 AdS. I apologize ...
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1answer
195 views

Alcubierre Drive

I am a layman. I am aware that the Alcubierre Drive has not yet been proven to be possible, but there is something about the concept itself that I am confused about. If there is no movement within the ...
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1answer
480 views

Schwarzschild solution

I am calculating for many hours and I am really confused with this exercise. Consider a comoving observer sitting at constant spatial coordinates$(r∗,θ∗,φ*)$, around a Schwarzschild black hole of ...
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3answers
1k views

A Cosmological horizon at the Hubble radius?

I have calculated that if one extends a rigid ruler into space by a fixed proper distance $D$ then a clock at the end of the ruler, running on proper time $\tau$, will run more slowly than time $t$ at ...
2
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1answer
164 views

Thermal radiation in the Unruh Effect

The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator): $$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} ...
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1answer
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Timelike/null generic condition in general relativity

My question concerns the following definition Definition: The timelike (resp. null) generic condition in GR is fulfilled if $$u_{[\alpha} R_{\rho]\mu \nu [\sigma}u_{\beta]}u^\mu u^\nu \ne 0$$ ...
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2answers
347 views

Does general relativity fail in conditions with very large gravitational forces?

It is said in this wikipedia article (in the 7th paragraph) that where there exists huge masses and very large gravitational forces (like around binary pulsars), general relativistic effects can be ...
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2answers
553 views

The General Relativity from String Theory Point of View [duplicate]

I have a hard time understand the statement that When you only look at the classical limit or classical physics, string theory exactly agrees with general relativity Because from what I know, ...
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1answer
521 views

Can the Hubble constant be measured locally?

The Hubble constant, which roughly gauges the extent to which space is being stretched, can be determined from astronomical measurements of galactic velocities (via redshifts) and positions (via ...
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1answer
2k views

Solving the Tolman–Oppenheimer–Volkoff (TOV) equation

The Pressure of a static spherical object (say star), which has the Schwarzchild metric outside it, satisfies the following differential equation called the TOV equation. ...
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1answer
247 views

Question about Komar integral derivation in Wald

I have a question about derivation 11.2.10 in Wald (page 289). Here is a screenshot of the relevant passage: I don't get the step $$-\frac{1}{4\pi}\int _{\Sigma}R^{d}{}{}_{f}\xi^{f}\epsilon_{deab} ...
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3answers
873 views

Can we apply Schrodinger equation in Newton Gravitational potential and derive the deterministic Newton's gravitation as a special case of it

We know the solutions for wave functions of a an hydrogen atom, and the energy values as given by spectral analysis of radiation emitted by Hydrogen, confirms the possible energy states as predicted ...
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1answer
703 views

A Hollow Black Hole

I was just reading a question about the gravity inside a hollow neutron star. It was a trivial question, obviously there is no force felt. But then it got me thinking. Suppose you had a hollow sphere ...
3
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1answer
124 views

Killing vector field in terms of the tetrad basis

I have come across the following equations in Wald. For a static spherically symmetry metric $$ds^2 = -f(r)dt^2 + h(r)dr^2 + r^2 ( d{\theta^2} \sin^2{\theta}d{\phi^2})$$. If $(e_{\mu})_a$ are the ...
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1answer
403 views

Static Spherical symmetric solution of Einstein's equations with a perfect fluid

I am reading Wald for the interior solutions of a static spherical metric. Assume it to be of the form $$ds^2 = -f(r)dt^2 + h(r)dr^2 + r^2 ( d{\theta^2} \sin^2{\theta}d{\phi^2})$$ Wald states: For a ...
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Significance for LQG of Sen's result on entropy of black holes?

Sen 2013 says, ...we apply Euclidean gravity to compute logarithmic corrections to the entropy of various non-extremal black holes in different dimensions [...] For Schwarzschild black holes in ...
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The metric Tensor inside a massive shell [duplicate]

Given a fixed shell with the mass of $M$ and a radius $R$ , what would be the metric tensor for $r<R$? I do know that using Birkhoff Theorem the metric for $r>R$ should be schwarzschild. I'm ...