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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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
419 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 ...
3
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1answer
268 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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1answer
177 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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1answer
443 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
307 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
90 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
266 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
87 views

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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2answers
237 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
192 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 ...
2
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1answer
476 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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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 ...
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1answer
134 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
188 views

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
341 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 ...
6
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2answers
538 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
500 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
1k 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
239 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
844 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
680 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
117 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
394 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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0answers
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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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1answer
259 views

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 ...
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1answer
68 views

Why is it suffice to show Tensorial identity on a tensor composed of two vectors?

I've encounter many proves of Tensorail identity that begin with assuming our tensor can be written in form of: $T^{\alpha\beta}=u^{\alpha}v^{\beta}$ . As helpful is it might be, I'm not sure if its ...
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1answer
133 views

Query in Carroll Section 5.2 Birkhoff's Theorem

This is regarding the proof of Birkhoff's theorem. A part of the proof requires one to show that the most general spherically symmetric metric can be written in the form $$ ds^2 = -e^{2\alpha(t,r)} ...
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1answer
185 views

Is a singularity a real thing?

I've heard the work a few times now, the most recent in the star trek film. Is a singularity a real thing? If so what is it?
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1answer
105 views

Maximum aging and path of rock

When a rock falls from a ledge, why does it head to the surface and not up to where time runs faster? If a rock, free from forces, follows a worldline of maximum aging, why would that rock approach ...
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0answers
91 views

Would a closed field of gravity neccesarily lead to paradoxes?

I've asked wether artificial gravity, as seen in some SF-Movies, would violate known laws of physics. To recap, my idea of an Artificial Gravity (AG) system was like this: A Device that creates an ...
0
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1answer
85 views

What physical sense has following transformation?

Let's have an interval expression for Friedmann Universe with 3-metric of a sphere, $$ ds^{2} = c^{2}dt^{2} - c^{2}\frac{ch^{2}(Ht)}{H^{2}}\left( d\rho^{2} + sin^{2}(\rho )(d\theta^{2} + ...
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697 views

Equation of motion of a photon in a given metric

I have this metric: $$ds^2=-dt^2+e^tdx^2$$ and I want to find the equation of motion (of x). for that i thought I have two options: using E.L. with the Lagrangian: $L=-\dot t ^2+e^t\dot x ^2 $. ...
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1answer
484 views

Gravitational field strength and Horizon in Rindler coordinates

I came across the following statements in 't Hooft's black holes notes, but not being able to justify them. The metric in the Rindler coordinates $x=\tilde{x}, y=\tilde{y}, z= \rho \cosh{\tau}, t= ...
6
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1answer
243 views

Einstein action as a functional of the tetrad (first order formulation of gravity)

Let the Einstein-Hilbert action be rewritten as a functional of the tetrad $e$ (units shall be set to $1$) such that $S_{EH}(e)=\int \frac{1}{2}\epsilon_{IJKL}~e^I\wedge e^J\wedge F^{KL}(\omega(e))$, ...
2
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1answer
264 views

Angular momentum for the Kerr solution of a rotating blackhole

I am reading 't Hooft's noted on Black holes, where he quotes the Kerr metric for a black hole rotating about the z-axis as follows: He later says: "The parameter a can be identified with the ...
2
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1answer
249 views

Do physicists believe the singularity theorems to be accurate?

This question is largely based on the last post by reddit user RobotRollCall who gave some fantastic explanations of phenomena in relativity on a layman's level. About a year ago, she said: The ...
0
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1answer
158 views

the higher you go the slower is ageing [duplicate]

as per to einstein as we go far from the earth the TIME tends to slow down , so it means when I am one metre above the earth's surface , the time has slow down for me as per ...
11
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3answers
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Can we disprove Artificial Gravity (like in the movies) with a thought experiment?

Suppose you have a Device that creates an 'artificial gravity' (AG) inside a Box, with these properties: the system does not use inertial forces (like centrifugal force) or a huge mass to create AG ...
2
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2answers
205 views

How much faster would a Clock without gravity run?

Pardon the misleading title. It is to my understanding that moving/heavy clocks run slow. The Earth itself is under gravitational influence from many sources, and is moving. Is there a way to know ...
7
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1answer
847 views

Counting degrees of freedom for gravitational waves as a gauge field

Sean Carroll has a new popularization about the Higgs, The Particle at the End of the Universe. Carroll is a relativist, and I enjoyed seeing how he presented the four forces of nature synoptically, ...
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2answers
676 views

Effect of space time relativity on the age of the universe?

So we all heard about the twins paradox to explain einstein's time space relativity. Wikipedia Quote :" In physics, the twin paradox is a thought experiment in special relativity involving identical ...
4
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1answer
175 views

What is a set of minimal assumptions needed to interpret general relativity?

Next semester, I am going to lecture about (the mathematics of) general relativity and I am still thinking hard how to organize and even more importantly how to motivate all the stuff. I am wondering ...
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0answers
61 views

Photon detection time in NMR rotating frame

I think of an NMR experiment, but with a single spin half nucleus initially set to the excited state. When the nucleus finally returns to its ground state, it will emit a photon. An observer in the ...
7
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1answer
782 views

Why is the stress-energy tensor symmetric?

The relativistic stress-energy tensor $T$ is important in both special and general relativity. Why is it symmetric, with $T_{\mu\nu}=T_{\nu\mu}$? As a secondary question, how does this relate to the ...
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2answers
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Evidence for expansion of space [duplicate]

If I understand correctly, Einstein's theory of General Relativity predicted the expansion of space itself, and Hubble confirmed this prediction by observing the red shift of receding galaxies. I ...
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150 views

Singularity and Black Hole Complementarity

When looking at a (eternal) Schwarzschild Black Hole, we may identify two worlds. The region $R_1$ (right) - our world -, and the region $R_2$ (left) - an other world. The "black hole interior" ...
2
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1answer
383 views

Solving Klein-Gordon equation in the Rindler coordinates - the Unruh effect

I am reading 't Hooft's notes on Black Holes. I want to find the solutions of the Klein-Gordon equation $(\tilde{x},\tilde{y}, \rho, \tau)$ in the Rindler coordinates which are $$x=\tilde{x}\,\,\,\,\ ...
6
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1answer
235 views

QFT in curvilinear coordinates

I have a question that I believe is confusing me more than it should. We all know the path integral in the usual $(t,\vec{x})$ coordinates. For example, consider a simple $U(1)$ gauge theory. The ...