A theory that describes how matter produces and responds to 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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2answers
356 views

Seeing one's back on the event horizon

If we would hypothetically be exactly on the event horizon, we should see our own back, because of the circular motion of photons on the event horizon, right? But what would be the image size, or $-$ ...
2
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1answer
62 views

Black holes and Time Dilation at the horizon

What is the difference between proper time and the observer time? Whilst thinking about Black holes, when we see the Schwarzschild metric $$c^2\tau ^2 = \left ( 1 - \frac{r_{s}}{r} \right )c^2t^2 - ...
2
votes
1answer
54 views

Measuring proper distance using a light beam

I wonder if someone can help me with the following problem. I send a light beam to a distant galaxy which then bounces back to me. I measure the travel time of the lightbeam using say a light clock ...
10
votes
6answers
889 views

Why must a singularity form inside a black hole? [duplicate]

What is the exact reason that normal matter can not exist within an event horizon? I can understand how a super-dense object like a neutron star could accrete mass until its physical radius is less ...
11
votes
1answer
180 views

Gravitational collapse of a photon cloud

The Schwarzschild solution shows that a spherically symmetric, static fluid will undergo gravitational collapse if too much mass-energy is concentrated together (i.e. if the fluid's radius is less ...
6
votes
2answers
202 views

Inertial mass and gravitational mass of 5 dimensional stars

Consider the following metric which is 5 dimensional (2-parameter) spherically symmetric Kaluza-Klein solution ...
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0answers
35 views

How to prove this auxiliary lemma to Hawking's singularity theorem?

This theorem is number 44 of chapter 14 in Barret O'Neil's book "Semi-Riemannian Geometry (with applications to relativity)". The proof given, in particular the use of another theorem to justify the ...
2
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1answer
63 views

The Einstein-Hilbert Action On-Shell

If one consider the Maxwell action as $$S=-\int \mathrm{d^{4}}x\! \ \frac{1}{4}F_{ab}F^{ab} \,$$ one find the usual Maxwell equation $$\partial_{a}F^{ab}=0$$ Then one can simply arrive the following ...
4
votes
1answer
84 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 ...
4
votes
4answers
159 views

What makes a coordinate curved?

Bear with me while I try to explain exactly what the question is. The question Can a curvature in time (and not space) cause acceleration? is imagining a coordinate system in which the curvature is ...
2
votes
1answer
49 views

Conformal compatification of Minkowski and AdS

How do I show that the compactification of Minkowski is given by the quadric $$uv-\eta_{ij}x^{i}x^{j}=0$$ with an overall scale equivalence in the coordinates.I get that for $v \neq 0$, the surface ...
9
votes
1answer
122 views

Why are anti-de Sitter spaces so interesting when we believe the universe is expansionary?

Perhaps this is a naive question, but in my recent (admittedly limited) readings about AdS spaces, I keep wondering why they seem to be such a hotbed for theoretical research (AdS/CFT correspondence, ...
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0answers
20 views

Angular diameter distance in an inhomogeneous universe?

Computing the angular diameter distance $D_{A}$ is a well known academic exercise in an homogeneous Universe. But now suppose that we are in an inhomogeneous Universe and that I am interested in ...
1
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1answer
47 views

power counting and (superficial) non-renormalizability

Comment: This stuff is new to me so it doesn't entirely make sense (yet). Question: As I understand from Peskin and Schroeder chap 10 if you have a theory with interaction terms $\lambda \phi^n$ in ...
3
votes
2answers
152 views

Can a curvature in time (and not space) cause acceleration?

I realize that the curvature of space-time causes acceleration (gravity). Is it possible to have a curvature only of space, or a curvature only of time? If so, would a curvature only of space, or a ...
2
votes
1answer
52 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 ...
4
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0answers
53 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
votes
0answers
23 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?
1
vote
2answers
78 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
61 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
votes
2answers
96 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 ...
-1
votes
1answer
53 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 ...
4
votes
4answers
468 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
votes
1answer
138 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
votes
4answers
132 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 ...
0
votes
0answers
35 views

Are particles with gravitomagnetic charge possible or excluded? [duplicate]

Are particles with a sole gravitomagnetic charge (gravitomagnetic monopoles) possible? Does the theory exclude this possibility? Were there attempts to find such particles, similar to the search for ...
8
votes
2answers
124 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. ...
3
votes
1answer
53 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 ...
3
votes
4answers
143 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
votes
1answer
71 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?
0
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4answers
84 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
votes
0answers
72 views

Is general covariance a symmetry?

Is general covariance a symmetry? If it is ,what is its symmetry group and corresponding generator?
1
vote
1answer
80 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
votes
1answer
72 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?
0
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1answer
108 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 ...
6
votes
2answers
148 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
votes
1answer
38 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
votes
3answers
445 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
votes
0answers
29 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) ...
2
votes
1answer
71 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 + ...
2
votes
1answer
141 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 ...
11
votes
8answers
3k 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 ...
2
votes
2answers
116 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 ...
0
votes
1answer
66 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 ...
-3
votes
1answer
110 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.
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vote
0answers
34 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
186 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} ...
9
votes
1answer
128 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
80 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
71 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 ...