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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Gibbons-Hawking Variation

I know there already exist some questions about this and some very good answers. However, I am still having trouble understanding one part of the calculation. The GHY term is given by ...
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1answer
112 views

What is the sum of the angles of a triangle on Earth orbit?

Gauss went out and measured triangles made up of mountain peaks to show that the angles sum up to 180 degree. However, general relativity leads to non-Euclidian space and I would like to get a better ...
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31 views

Non-time orientable quotient of de Sitter space

Examples of non-time orientable spacetimes are pretty scarce, but it seems the big one is quotients of de Sitter space of the form $dS^n/\pi_1$, where $\pi_1$ is some subgroup of the isometries of de ...
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396 views

What is the general relativity explanation for why objects at the center of the Earth are weightless?

The idea that as you move through the earth you get a symmetric cancelling of gravitational acceleration which approaches zero acceleration due to gravity at the center of the earth makes a lot of ...
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73 views

Two dimensional spacetime and the Gauss Bonnet theorem

Generally two dimensional spacetimes are deemed to be static, as the Gauss Bonnet theorem implies that the Einstein Hilbert action would be a constant independent of $g$. But as far as I can tell, ...
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60 views

Which property do the word Pressure refer to in General Theory of Relativity?

In this course by MIT Alan Guth while delivering the lecture stated " Both Pressure and Energy densities can produce gravitational fields. Negative pressure creates repulsive gravity and positive ...
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5answers
229 views

Is boundary well defined if variation of metric don't vanish on the boundary?

Suppose that you want to calculate the variation $\delta S$ of an action induced by some arbitrary variation $\delta g_{\mu \nu}$ of the spacetime metric : \begin{equation} S = \int_{\Omega} ...
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1answer
211 views

An argument that massive particles don't redshift?

I start with the spatially flat FRW metric in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ This metric has the following non-zero Christoffel symbols: \begin{eqnarray} ...
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2answers
79 views

If curved paths imply that the vehicle is accelerated, how come do we assume that light gets curved whilst its speed is constant?

I don't understand how we can accept these two sentences at the same time: Light speed is constant, therefore experiences no acceleration. On the presence of a gravitation field, light path is ...
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5answers
652 views

What are some ways to justify the Einstein field equations?

Since they are a postulate of general relativity, it is not really possible to "derive" the Einstein field equations $$R_{ab} + \left(\Lambda - \frac{1}{2}R\right)g_{ab} = -8\pi T_{ab}$$ in any very ...
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96 views

Can a Set of “Maxwell's Equations” for Newtonian Gravitation be Derived from Newton's Force + Special Relativity?

When I learned about electromagnetism in my first year of undergraduate school, Maxwell's equations were derived roughly in the following way (see also here or in [1]): Gauss's law for a static ...
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5answers
159 views

Local inertial frame

In general relativity we introduce local inertial frames to be such frames where the laws of special relativity holds. Let $\xi^{\alpha}$ the coordinates in the local inertial frame, so we get ...
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2answers
79 views

Form of Spin Four-vector

The spin angular momentum of a gyro is represented, in special and general relativity, by a spin four-vector $S^{\mu}$. In the rest frame of the gyro, the spin four-vector takes the form ...
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65 views

Integral curves in null hypersurfaces [closed]

Let be $(M^{n+1},g)$ a spacetime (Lorentz manifold, connexe and time-oriented), $n\ge 2$, and $S\subset M$ a null hypersurface (codim $S=1$ and the restriction of $g$ to each tangent space $T_p S$ ...
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1answer
99 views

Thought experiment on space curvature due to gravity

Let's say you built a huge, straight rigid beam out in space, far from the sun (outside the orbit of Pluto). It is very long, say 200,000 miles long, but can be very narrow. Then you move it to the ...
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1answer
60 views

Time dilation on Satellites due to GR

I am trying to determine the time dilation onboard a satellite (say GPS @ 20,000km) w.r.t an observer on the earth. I have already determined the special relativity component using: $$ t' = ...
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10 views

DGP model, minus one dimension

Is there a name for a theory like the DGP model, but with one fewer dimension? That is, a theory whose action consists of the 4D Einstein Hilbert action at long distances, and the 3D one at small ...
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50 views

How does the expanding of null hypersurface orthogonal geodesic congruence imply a particular result?

Sorry that I do not know how to summarize my problem in the title. First, please go to the website here (free access, even though it looks otherwise) to download the paper done by R. Sashs on ...
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1answer
46 views

how is the state parameter determined?

For radiation, dark energy and dust the pressure and energy density are related, respectively, by: $p=\frac{1}{3}\rho$ $p=-\rho$ $p=0$ My question is why? How does one show that this is how ...
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32 views

Expression for the energy in the limit case of weak gravitational field

I'm trying to solve the following problem of General Relativity. Consider a particle of mass $m$ which moves following a geodesic in a space-time with metric $$ ds^2 = - ...
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0answers
70 views

Why gravitational collapse always end up in a black-hole singularity? [closed]

I know the positive energy condition and the singularity theorems by Penrose and Hawking. But still, why people didn't work on gravitational collapse to some exotic matter with an event horizon?// My ...
81
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10answers
13k views

If gravity isn't a force, then why do we learn in school that it is?

I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true, then ...
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1answer
451 views

Are some gravitational wavelengths forbidden by causality?

Consider a gravitational wave in linearized gravity $d_{\mu \nu}(X_{\eta}) = D_{\mu \nu} e^{i X_{\eta} K^{\eta}}$ with $K^{\eta} = (-\omega t, \textbf{k})$. Let $d=| \textbf{D}|$ the scalar maximum ...
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82 views

Gravity's force on space

Here is a quote from Brian Greene, The Fabric of the Cosmos: Space, Time, and the Texture of Reality, p. 273: “The early universe provided an arena in which gravity exerted its repulsive side with ...
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3answers
290 views

Is there proof gravity bends space or is it just the most convenient explanation?

I have read this sentence in an article: The theory [of general relativity] holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a ...
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Trajectories in AdS

On page 2 of this paper (http://arxiv.org/abs/1106.6073), Maldacena explains (and has a very nice picture) showing the trajectories that a timelike and null particle would take in AdS space. Of ...
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74 views

Operational Definition of Reference Frame in General Relativity

Most treatments of GR begin with the assumption that spacetime is a pseudo-Riemannian manifold (or, sometimes, that it is a more general manifold). But this entails quite a few tacit assumptions about ...
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44 views

What are the definitions and the differences between string “background” and string “vacuum”?

In cosmology one studies perturbations around FRW metric classically (pure GR, we say that we perturbe the FWR "background"). In QFT we have perturbation theory quantistically (we expand around a ...
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113 views

What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
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3answers
63 views

Suppose I apply a force to a ball that can then only be slowed down by gravity or, perhaps, relativity. What happens to the ball? What would I see? [closed]

Suppose I'm on planet Earth. I have a ball that, once set in motion, can only be slowed down or stopped by gravity. What will happen to this ball? What would I (an observer on Earth) see? Here's what ...
4
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1answer
114 views

Life of a photon in gravity?

I have a simple thought experiment and I am not sure about the answer: What would happen to a photon that is emitted by an excited hydrogen in an otherwise empty universe? Would gravity of the atom ...
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74 views

Does rest mass increase in the FRW metric?

The flat FRW metric can be written in conformal co-ordinates: $$ds^2=a^2(\eta)(d\eta^2-dx^2-dy^2-dz^2)$$ where $\eta$ is conformal time. Let us assume that $a(\eta_0)=1$ when $\eta_0$ is the present ...
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1answer
118 views

Tensor decomposition

I came across what a Physicist called "decomposing a tensor with respect to a congruence", something I simply cannot grasp. I searched a lot and I couldn't find any reference on that. I know that ...
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31 views

Black Holes should take infinite time to form with the increase in mass to form one [duplicate]

How can black hole form because as the density begins to increase gravity also start to increase and time starts to slow. wouldn't it take infinite time to form a black hole. how can anything fall ...
2
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0answers
45 views

Quasilocal stress tensor

I have been reading through the paper hep-th/9902121 and have a few questions about the first five lines of the introduction: 1) "In a generally covariant theory, it is unnatural to assign a local ...
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1answer
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1answer
152 views

Can space have angular momentum that can be transfered to/from physical objects?

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum. ...
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1answer
82 views

Variation of det metric tensor

I have the metric tensor $g_{\mu\nu}$. I want to make the variation of $\sqrt{-g}$ where $g=detg_{\mu\nu}$. Can I make this work? ...
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0answers
18 views

Traveling to the future is possible, but not to the past? [duplicate]

I understand how going to the future is possible: If you go really fast, time around you slows down for observers. But is it true that time traveling into the past isn't even theoretically possible?
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1answer
71 views

Why not all timelike world lines have infinite total length?

I don't understand this stament by Geroch(1968), when discussing the definition of singularity: We could not have required that all timelike world lines have infinite total length, for this ...
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1answer
40 views

How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity? [duplicate]

How can the speed and the mechanics of light be similar to the speed and the mechanics of gravity? Most say that light cannot escape a black hole. Then gravity cannot escape a black hole either, so ...
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1answer
41 views

How is electromagnetic binding energy introduced in the stress-energy tensor

Take the hydrogen atom. It is easy to imagine that the gravitational pull it creates is smaller than the sum of those of the proton plus the electron, because a photon of 13.6 eV was created when the ...
2
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0answers
110 views

Why can't we fix the metric and its derivatives at boundary, with the variational method?

In general relativity and for its Einstein-Hilbert action, we usually ask that the metric variations $\delta g_{\mu \nu}$ cancel on the boundary $\partial \, \Omega$ of some region $\Omega$ of the ...
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45 views

Definition of Energy in Friedmann equations?

The first Friedmann equation for a flat Universe is given by: $$\bigg(\frac{\dot{a}(t)}{a(t)}\bigg)^2 = \frac{8 \pi G}{3} \rho(t)$$ The energy density $\rho(t)$ is given by: $$\rho(t) \propto ...
5
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2answers
377 views

Gravitational waves and time

Two questions. It is said that time can only go slower in gravity fields and if you move faster. I have heard that when a gravitational wave pass earth then the space/time vibrate and time change ...
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1answer
102 views

If Alice is moving at relatavistic speeds compared to Bob, is collapse still simultaneous?

I have read some papers about experimental proof of non-locality involving a laser that goes through a beam-splitter and then each "half" goes to an observer (traditionally "Alice" and "Bob"). It has ...
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1answer
63 views

Distortion of body in Schwarzschild black hole

Suppose I toss a cloud of matter into a Schwarzschild black hole; for the sake of argument, have it be timelike dust. As we know, the dust is "spaghettified" by tidal forces: simultaneously compressed ...
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2answers
172 views

Conservation of energy and Killing-field

In general relativity we have no general conservation of energy and momentum. But if there exists a Killing-field we can show that this leads to a symmetry in spacetime and so to a conserved quantity. ...
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1answer
62 views

Is there a point at which spaghettification is highest?

I've read anything getting close to a regular black hole would experience spaghettification but not when you get close to super-massive black hole. Is there a point of "peak spaghettification" where ...
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1answer
50 views

Is there a principal difference in acceleration from an impulse and the free fall of a body in the orbit around a gravitational mass?

Especially taking in account that acceleration need a force which leads to some conversion of energy. This is not the case for orbital motion, such a acceleration does not convert energy. That seems ...