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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0answers
75 views

Asymtotically flat spacetime applicable for spacetimes which are not diffeomorphic to $\mathbb{R}^4$

I wanted to investigate changes on a compact 4-manifold $M$. More specifically it is the K3-surface. I follow a paper by Asselmeyer-Maluga from 2012. The idea there was to make sure that the manifold ...
3
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0answers
34 views

Stability condition for AdS background (when gravity coupled to matter fields)

In finding the stability condition for AdS background (when gravity coupled to matter fields), why the conserved energy should be positive?
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2answers
118 views

When we look in different directions in the universe how do we know we're not seeing the same thing?

For my question assume: 1: Big bang happened at a point (I know it happened everywhere) but after that explosion universe started to expand in all directions so it maybe considered to happened ...
2
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0answers
87 views

A question on spin algebra

In scattering theory, one can form a lorentz invariant quantity by $\epsilon_{\mu 1 2\nu}P^{\mu}_{1}P^{\nu}_{2}$ which is really $1\otimes 1$ 's spin 0 state. Is there such a kind of argument to show $...
2
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2answers
142 views

Can a fundamental particle black hole with conserved charge emit Hawking radiation?

Let's says there is a fundamental particle: That is so massive that it is a black hole by itself (Compton wavelength < Schwarzschild radius) That carries a conserved quantum number (e.g. charge ...
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1answer
150 views

Does a hydrogen atom today have same mass as a hydrogen atom in the future?

Does an atom of hydrogen today have the same rest mass energy as an atom of hydrogen a billion years in the future? Standard cosmology seems to tacitly make this assumption. But surely one can only ...
5
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4answers
2k views

Light and Gravity - bending of light around a massive body [duplicate]

Well, as I have read, a massive body can cause light to bend around itself due to its gravitational attraction. What I don't understand is how, as the Newtonian formula for the force of gravitational ...
3
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1answer
475 views

Black hole thermodynamics in a time dependent metric

For a time dependent space time metric, to get the thermodynamics, does the standard procedure of Wick rotating the time, and then calculating the free energy, work ?
0
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4answers
239 views

How does gravity slow light without an equal and opposite action? [closed]

This is regarding the gravity well sort of explanation. People claim that gravity doesn't slow light by saying it curves the road by which it travels but if space is indeed without properties and ...
9
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2answers
558 views

Why does angular momentum shorten the Schwarzschild Radius of a black hole?

Angular momentum causes the event horizon of a black hole to recede. At maximum angular momentum, $J=GM^2/c$, the Schwarzschild radius is half of what it would be if the black hole wasn't spinning. ...
4
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1answer
81 views

If non-zero cosmological constant interpreted as a repulsive field, what would be the properties of this field's quanta?

If non-zero cosmological constant interpreted as a repulsive field, what would be the properties of the excitation of such field, i.e. the particle which serves as the field's quantum? What would be ...
2
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4answers
406 views

What does it mean by complex frequencies? (Quasinormal Modes)

Something I've taken for granted and not yet thought about physically, is how the frequency of quasinormal modes related to a black hole are $\textit{complex}$. I know that it's something to do with ...
4
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1answer
805 views

Are gravitational waves transverse or longitudinal waves, or do they have unique/unknown properties? [duplicate]

Gravitational waves propagate through a medium of space-time. Are they traverse waves or longitudinal waves? Or do they propagate without oscillating?
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4answers
160 views

Would infinite time elapse relative to an outside observer if an object was completely at rest?

Here's my reasoning... time dilation due to velocity: t'=t√(1-v^2) v expressed as a % of the speed of light. If you are moving through distance at the speed of light, to an observer at rest relative ...
3
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0answers
106 views

Is general covariance a symmetry?

Is general covariance a symmetry? If it is ,what is its symmetry group and corresponding generator?
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1answer
180 views

Second fundamental form

How do I calculate the integral of the trace of the second fundamental form on a surface? The formula used in the Gibbons, Hawking, York paper Action integrals and partition functions in quantum ...
0
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1answer
99 views

Naive unification of scalar QFT and GR is possible?

I am thinking on the Klein-Gordon equation with curved (non-diagonal) metrics. Is it possible? Doesn't have it some inherent contradiction? If yes, what? If no, what is this combined formula?
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1answer
157 views

Problem in Grandfather paradox

I am very confused about a paradox and a recent research on Quantum particles. I have read an article which states that time travel is possible for quantum particles. If it is possible then why does ...
7
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2answers
368 views

Killing vectors in flat FLRW metric

I have the flat FLRW metric, $$ ds^2=-dt^2+a(t)^2(dx^2+dy^2+dz^2) $$ and a geodesic $\gamma(s)=(t(s),x(s),y(s),z(s))$ with parameter $s$. Two of the Killing vectors of the metric are $ \partial_x$ ...
2
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1answer
247 views

Lorentz transformation via light clocks in parallel direction

In order to derive the Lorentz transformation one can use the picture of a light clock. A Photons bounces back and forth between two mirrors. This is then observed in two different inertial systems. ...
4
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3answers
645 views

Slowing of time under gravity

I am not calling this gravitational time dilation because that is a relativistic effect due to the equivalence principle. Now imagine two light clocks (a clock that ticks due to light) are placed ...
2
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0answers
116 views

Observers in (Schwarzschild-) de Sitter spacetime

In (pure) de Sitter spacetime, the cosmological horizon is said to be ‘observer dependent’. I imagine that as the observer always being in the center of that horizon. Another (spacelike separated) ...
4
votes
1answer
158 views

The relationship between Lorentz Lie algebra and curvature

Here I transfered the question from the comment The relationship between spin and spinor curvature How $\mathcal{R}_{ab} = \frac{1}{4}R_{abst}\gamma^s \gamma^t$ is from $\Psi \mapsto \Psi + \frac{1}{...
2
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1answer
369 views

Two definitions of Riemann curvature tensor

I am relatively used to the coordinate free expression of the Riemann tensor: $$ R(X, Y)Z=\nabla_X\nabla_Y Z - \nabla_Y\nabla_X Z - \nabla_{[X, Y]} Z, $$ where $\nabla$ is the Levi-Civita connection ...
13
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8answers
12k views

Is gravity just electromagnetic attraction?

Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the ...
3
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2answers
833 views

Time-like Killing vector in FRW metric?

The spatially flat FRW metric in cartesian co-ordinates is given by: $$ds^2 = -dt^2 + a^2(t)(dx^2 + dy^2 + dz^2)$$ As I understand it there are Killing vectors in the $x$, $y$, $z$ directions implying ...
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1answer
89 views

What happens when some asteroid comes in the way of warp drive?

Recently Harold white, NASA scientist shared his knowledge and the things he is working on. That is Warp drive for interstellar navigation. This spaceship compresses the space in front of it and ...
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votes
1answer
473 views

Does time really exist? [duplicate]

Does time really exist? or is it a human invention and convention? What is the truth? are there time particles? please remember, I'm looking for constructive answers, not condescending and void ones.
2
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0answers
95 views

Infinite Redshift [closed]

My text says that the signals emitted at a physical size of horizon $l_{H}(t)$ come to an observer at time $t$ with an infinite redshift. How do I show this mathematically? My approach is as follows: ...
5
votes
2answers
199 views

Proving one field equation leads to the other [closed]

Assume that the universe is homogenous and isotropic, and the following equation holds: \begin{equation}R_{00}-\frac{1}{2}g_{00}R=8\pi GT_{00}; \space \space \nabla_{\mu}T^{\mu 0}=0.\end{equation} ...
13
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2answers
884 views

Energy-Momentum Tensor in QFT vs. GR

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
1
vote
1answer
117 views

How big or small is a reference frame in Relativity?

What exactly is a frame of reference? Does it have an objective existence and if so what is it? What's the size of a reference frame? Is a reference frame the same size for a stationary frame of ...
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0answers
237 views

Are standard and isotropic forms of Schwarzschild metric truly equivalent?

My admittedly rudimentary understanding of physical meaning of conformal flatness - as pertaining to a stationary observer exterior to a spherically symmetric static gravitating mass $M$: Locally ...
2
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4answers
611 views

Is it true that gravitational lensing only occurs for objects made of plasma?

The question concerns this video: It says that the Gravitational Lens effect is an illusion, meaning it's not caused by gravity but by change in density of a plasma atmosphere. It claims further ...
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3answers
1k views

What is space made of?

General Relativity posits that matter curves spacetime, such that geodesics point towards the object in question, hence, gravity. Now, how does matter do this? What is spacetime "made of", anyway, ...
2
votes
2answers
107 views

Does geodesics from solving full field equations are same as path from energy-momentum tensor?

As we know, if we had an energy-momentum tensor in all space-time we could obtain the metric tensor by solving field equations. Also i think if we had an energy-momentum tensor then we have ...
22
votes
5answers
4k views

How does “warp drive” not violate Special Relativity causality constraints?

I'm talking about this nonsense: http://www.washingtonpost.com/news/post-nation/wp/2014/06/11/this-is-the-amazing-design-for-nasas-star-trek-style-space-ship-the-ixs-enterprise/ Now, I'm aware that ...
2
votes
2answers
548 views

Time dilation at the Big Bang

At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time. If so, could it be that the time periods just after Big Bang which ...
0
votes
1answer
40 views

Gravitational effect of charged masses held apart by a rod?

Imagine two oppositely electrically charged masses held apart by a rigid rod of negligible mass. At some distance the gravitational field due to this system is proportional to the sum of the masses + ...
2
votes
0answers
113 views

A Subtle Connection Between Time Dilation in SR and GR - Why is this so?

I've been reading a book on General Relativity lately (Gravitation and Cosmology, Weinberg), and I was reading about the weak field approximation. It derived the time dilation in a weak gravitational ...
2
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1answer
382 views

Reconciling “The Big Crunch” with the 2nd Law of Thermodynamics

Assume "The Big Crunch" scenario (the universe will collapse to a singularity). In this case, I think of the entire universe as an isolated system; in the "Big Crunch" scenario, it seems to me gravity ...
1
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1answer
100 views

Velocity and curved spacetime

It is possible that the universe has naturally a slight curve of spacetime, even in a place where there is not a massive object, and that this curve is responsible for the perception of the relative ...
1
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2answers
129 views

Does mutual gravitational attraction imply a negative pressure?

Imagine a small ball of gravitating dust particles initially at rest at the center of a large volume $V$. Following John Baez, Einstein's field equations say (in units of $c=8 \pi G=1$): $$\frac{\...
5
votes
1answer
293 views

Non-stationary spacetime

What is an example for a spacetime that is non-stationary that is considered as a description of something in nature? So far all the spacetimes I encounted have always been stationary (Schwartzschild,...
4
votes
3answers
380 views

What exactly is charge? [duplicate]

If gravity is really the bending of space/time causing objects with mass to experience acceleration, is there a similar physical meaning to 'charge' besides 'a property of matter which causes it to ...
9
votes
1answer
749 views

Gravitational Constant in Newtonian Gravity vs. General Relativity

From my understanding, the gravitational constant $G$ is a proportionality constant used by Newton in his law of universal gravitation (which was based around Kepler's Laws), namely in the equation $F ...
4
votes
1answer
2k views

Is the scalar curvature of the Schwarzschild solution 0?

The Schwarzschild solution is meant to be a solution of the vacuum Einstein equations. That is $$R_{\mu\nu}=0.$$ So, the Ricci tensor must be null for $r>0$. Now, if the scalar curvature is ...
4
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0answers
189 views

Lie derivative of Dirac Delta

In the setting of general relativity, I came across a source term of the wave equation of the following form: $$ \frac{1}{\sqrt{q}}\,\delta^{(3)}(p-\gamma(t)) $$ where $p\in M$ is a point in our 4d ...
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2answers
132 views

Planetary motion: integration of equation of motion

I was reading Planetary Motion (page 117) in Barry Spain's Tensor calculus, and stupidly enough, I didn't understand this. The equations are : $$\frac{d^2\psi}{d\sigma^2} + \frac{2}{r}\frac{dr}{d\...
3
votes
2answers
265 views

Covariant derivative of a covariant tensor wrt superscript

Is it true that when you take the covariant derivative of a covariant tensor, do you always have to do with a subscript? What if you do it wrt a superscript?Does the first term (with the partial ...