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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Does the definition of the SI unit “second” require that possible perturbation of primary frequency standards should be measured?

The definition of the SI unit "second" is stated as The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground ...
3
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0answers
45 views

Confinement of charged tachyons in AdS spacetime

It is well known that the negative cosmological constant of AdS spacetime can act like a confining potential. That is, in contrast to asymptotically flat spacetime, in an asymptotically AdS spacetime ...
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27 views

freedom of choice of 1-form in canonical representation of generic local field corresponds to gauge choice?

So it is a question in Gravitation Wheeler, Thorne and Misner 4.2 Exercise. Given F=$dp_{i}\wedge dq^{i}$. Using canonical transformation from p to $\bar{p}$ and q to $\bar{q}$, one gets ...
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1answer
57 views

A question on 1 form [closed]

If $d\,\sigma=0$ and $\sigma$ is non trivially with basis' coefficient 0, then $\sigma$ is a exterior derivative of a scalar function. I knew $d^{2} =0$. So it seems that all I am quoting is that ...
3
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1answer
73 views

How do I choose my constants?

When solutions to Einstein's equations are found (in coordinates $t,r,\theta,\phi$), such as Schwarzschild, Kerr etc. the way they are found seems to be by starting with a generalised metric in terms ...
3
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3answers
264 views

Link between Special relativity and Newtons gravitational law

If I make the two statements: General relativity is an extension of special relativity that accounts for gravity. Newton's law of gravitation is a special case of general relativity for when the ...
2
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0answers
51 views

Local symmetry and General Relativity

First I want to consider an example of 1D motion. Lagrange equation: $$ \frac{d}{dt} \frac{\partial L}{\partial \dot x} - \frac{\partial L}{\partial x} = 0 $$ If we transform $ L \rightarrow L+a $ ...
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2answers
318 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 $-$ ...
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1answer
58 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
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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
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6answers
866 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
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1answer
172 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 ...
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2answers
194 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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33 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
56 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 ...
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1answer
75 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 ...
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4answers
149 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
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1answer
46 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 ...
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1answer
113 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
15 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 ...
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1answer
40 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
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2answers
145 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
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1answer
51 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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50 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 ...
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0answers
21 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
74 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 ...
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0answers
59 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 ...
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2answers
91 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
52 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
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4answers
461 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
123 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
124 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 ...
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0answers
33 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 ...
7
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1answer
98 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. ...
2
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1answer
38 views

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

If non-zero cosmological constant interpreted as a repulsive filed, 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
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4answers
138 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
68 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
78 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 ...
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0answers
69 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
77 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
71 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
103 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
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2answers
145 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
34 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
443 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
25 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) ...
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0answers
48 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
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1answer
135 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 ...
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8answers
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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
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2answers
103 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 ...