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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Geodesic devation on a two sphere

So the geodesic deviation equation gives the relative acceleration between two geodesics in motion. But given a pair of geodesic (let's say on the two sphere) that start at the equator, separated by ...
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Could dark energy make a large black hole less black?

Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying ...
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Why does weak equivalence principle say gravity is equivalent to acceleration?

I am told that the weak equivalent principle, that $m_i=m_g$ (inertial and gravitational masses are equivalent) is equivalent to the statement that in a small system you can't tell whether you are in ...
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What are the local covariant tensors one can form from the metric?

Normally in differential geometry, we assume that the only way to produce a tensorial quantity by differentiation is to (1) start with a tensor, and then (2) apply a covariant derivative (not a plain ...
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Changing vector basis in AdS_3

I have AdS${}_3$ given as a surface embedded in a 4 dimensional pseudo-Riemannian space $$x^2+y^2-u^2-y^2=-l^2$$ With metric: $$ds^2=dx^2+dy^2-du^2-dv^2$$ I have Killing vectors of that space ...
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What is the entropy of the universe today?

What's the entropy of the universe today? How does one go about calculating this? I've heard the statement that black holes account for the bulk of the entropy in the universe today, but don't know ...
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174 views

Do gravitational waves cause time dilatation?

The effect of gravitational waves in transverse traceless gauge on matter is represented by the expansion and contraction of a ring of test particles in the direction of polarization of the wave. ...
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Surely space-time Curvature does not explain gravity, it just describe its effects?

In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ...
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velocity in inertial and nontial frames

I got confused about the difference between the last term of both pictures. In the first one, we have w x r, but in the second we have w x r underlined. Does anyone have a better explanation? They ...
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46 views

Riemann curvature tensor in first order perturbation theory as a Lie derivative of Riemann curvature tensor in zero order

I am having a difficulty solving my homework so I was hoping I could get some help, so here it is. It is about gravitational waves and first order gravitational perturbation theory, I have to prove ...
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4answers
145 views

Can we think of gravity as space itself moving?

So if you move through space with a constant acceleration you experience longer time dilation than when you're at rest, but you also experience the same time dilation when you're under the effect of ...
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Field equations in extended EH-GHY action. Is Schwarzschild a solution?

When taking the EH action, $$S_{EH} = \frac{1}{16\pi G}\int_M d^4x \sqrt{-g}R$$ and making a small variation in the metric while ignoring boundary terms, we obtain $$\delta S_{EH} = \frac{1}{16\pi ...
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Does the universal expansion affect the gravitational constant?

If the universe was not expanding, would gravity be stronger? since the expansion happens everywhere and can overcome gravity at long distances? If not, then are there any changes that would happen to ...
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45 views

Can a magnet or a magnetic field push gravity? [closed]

I have been asking around at my school and at the high school and at EWU but no one can answer this question: can a magnet or a magnetic field push gravity?
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41 views

SPEED of LIGHT as photons reach black holes [duplicate]

As photons reach a black hole and begin fall in - is their speed increased as they go down (like a vacuum cleaner does to dust).
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38 views

General covariance and global Poincaré algebras

Reading an article (page 7) I read this: Just as ordinary general covariance may be regarded as the local gauge symmetry corresponding to the global Poincare algebra and local gauge invariance ...
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Hilbert action's invariance under general coordinate changes

In an article, when considering invariance of the Hilbert action under a general coordinate change this formula appears for how the metric changes ...
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Is the Hilbert-Felber model of repulsive gravity correct?

This theory states that at relative velocities exceeding 3^-0.5 c, gravitational repulsion ensues. The relevant papers are on arXiv by Franklin Felber. Here's one of them ...
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Speed of light originating from a star with gravitational pull close to black-hole strength?

Imagine you have a star which is on the brink of turning into a black hole. Lets say it is infinitely close to become a black hole, but not there yet. Since there is no event horizon, but a great ...
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Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics?

In classical mechanics, we had Newton's law of gravity $F \propto \frac{Mm}{r^2}$. Because of this, all laws of classical electrostatics applied to classical gravity if we assumed that all charges ...
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Geometric interpretation of Electromagnetism

For gravity, we have General Relativity, which is a geometric theory for gravitation. Is there a similar analog for Electromagnetism?
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132 views

Do electromagnetic fields gravitate?

It's well known that electromagnetic fields contains energy but do they gravitate ? When we talk about the composition of the universe it's now accepted that the 74 % is dark energy , the 22 % is ...
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41 views

Poincaré symmetry and linearized gravity

When working with linearized gravity, is Poincaré symetry assumed to be the symmetry of space-time?
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271 views

How to obtain the field equations in Brans-Dicke theory from the action?

The action for the Brans-Dicke-Jordan theory of gravity is $$ \\S =\int d^4x\sqrt{-g} \; \left(\frac{\phi R - \omega\frac{\partial_a\phi\partial^a\phi}{\phi}}{16\pi} + \mathcal{L}_\mathrm{M}\right). ...
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That 10km/day error predicted if GPS satellite clocks not corrected for relativity

Some authorities have stated publicly and without explanation that if the theories of Special and General Relativity were not taken into account in the design of the GPS (by building the satellite ...
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Local Lorentz invariance or local Poincaré invariance?

Fast question. I know that the group of all the isometries in Minkowski's space-time is the Poincaré group that is just Lorentz's group (rotations and boosts) and translations in space-time. Now, ...
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At which point of the universe $R_{\mu \nu}=0$ if there is a source of gravitation (point mass)

Schwarschild found his solution to Einstein's field equations for vacuum ($T_{\mu \nu}=0$) by placing a point-mass in the center of origin. Since the Ricci tensor $R_{\mu \nu}$ and the Einstein ...
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Null Geodesics in Einstein Universe

I am currently taking a course in General Relativity, and I've hit a bit of a roadblock with a homework assignment. We are given the metric for Einstein's universe to be (forgive me, this is meant to ...
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188 views

Is the flatness of space a measure of entropy?

This is a bit quirky: For a very long time I've found Stephen Hawking's evaporating small black holes a lot more reasonable and intuitive than large black holes. The main reason is that gravity is ...
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6answers
396 views

Physical meaning of non-trivial solutions of vacuum Einstein's field equations

According to Einstein, the space-time is curved and the origin of the curvature is the presence of matter i.e. the presence of the energy-momentum tensor $T_{ab}$ in Einstein's field equations. If our ...
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82 views

The source of gravitation in a spacetime without matter

In a discussion concerning: Physical meaning of non-trivial solutions of vacuum Einstein's field equations there were a number of answers claiming that the flatness of the Ricci space (Rµv=0) ...
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1answer
35 views

Would gravity on the surface of a planet which is being consumed by a black hole change?

Assuming that the black hole starts grow in the exact center of the planet and that the general structure of the planet does not degrade as it is eaten from the inside, would the gravity on the ...
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What if UV behaviour of gravity was perturbative?

I understand that the UV behaviour of gravity ought to be dominated by black hole production and that graviton-graviton scattering ought to blow up above the Planck scale. Suppose, however, that ...
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Are there 'special' cases for when special relativity can be applied for accelerating bodies?

I have the following theoretical situation: A space station modeled as a ring in free space is rotating about its centre point at a high speed. I am trying to work out where time flows slower. From ...
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Total energy of the Universe

In popular science books and articles, I keep running into the claim that the total energy of the Universe is zero, "because the positive energy of matter is cancelled out by the negative energy of ...
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1answer
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How does a black hole slow time? [duplicate]

I've been reading about black holes, and I keep coming across the fact that time runs slower near a them. My questions are: Does this mean that if you left Earth at age 30 and spent 30 years near the ...
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6answers
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How exactly does time slow down near a black hole?

How exactly does time slow down near a black hole? I have heard this as a possible way of time traveling, and I do understand that it is due in some way to the massive gravity around a black hole, but ...
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What transformation is the metric of general relativity invariant under?

My limited understanding of metrics comes from Cartan. From there, I understand that a metric is something invariant under certain transformations, e.g. Lorentz in special relativity. But with the ...
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Wave equation for de Sitter invariant Green's functions

In several papers on QFT in de Sitter space (curvature set to $1$) it is asserted that the Klein-Gordon equation obeyed by the two point function of the free fields: $$(\square-m^2)G(x_1,x_2)=0 $$ can ...
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Geodesic distance in de Sitter space

Consider $N$ dimensional de Sitter space embedded in $N+1$ dimensional Minkowski space: $$\eta_{\mu\nu}X^\mu X^\nu=1, \hspace{1cm}\eta_{\mu\nu}=\text{diag}(-1,1,\dots,1)$$ where I set $H=1$ for ...
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Is the interpretation of BICEP2 data being due to “graviational waves” concerning considering the negative results of the LIGO's experiments? [closed]

Gravitational waves are a yet unproven idea... The lack of positive results from LIGO indicates these are still theoretical constructs not yet supported by experimental data. Is not the explanation of ...
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1answer
54 views

Where is Strong Equivalence Principle stronger than Weak Equivalence Principle

In my note, the two equivalence principles are stated as follows Weak Equivalence Principle: Gravitational and inertial masses are equal. Strong Equivalence Principle: There is no observable ...
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Does a charged particle accelerating in a gravitational field radiate?

A charged particle undergoing an acceleration radiates photons. Let's consider a charge in a freely falling frame of reference. In such a frame, the local gravitational field is necessarily zero, ...
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Direction of future time cone inside Schwarzschild horizon

Following is the picture copied from enter link description here, illustrating the future time cone inside the Schwarzschild horizon. My question is, on the left side of $r=2M$, why must the time ...
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Is it theoretically possible to shield gravitational fields or waves?

Electromagnetic waves can be shielded by a perfect conductor. What about gravitational fields or waves?
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239 views

Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
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Metric to describe an expanding spacetime from coordinates reflecting the perspective of a local observer

The FLRW metric describes the metric expansion of spacetime from the perspective of comoving coordinates. Given the way this metric is usually formulated, comoving distances stay constant, and the ...
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Definition of a spinor and applications to GR

I understand the construction of the Clifford algebra $C(r,s)$ and in turn the corresponding $Pin$ and $Spin$ groups. I would like first to clarify that $Spin(r,s)^e$ is the universal covering group ...
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Can relativistic momentum (photons) be used as propulsion for 'free' after the initial generation?

In discussing this question about propelling a spacecraft with photons and their relativistic momentum, the author asked that I restate my comment as another question. If photons can really be used ...
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Is gravity just relative rotational velocity?

Einsteins law of relativity states that velocity is relative. so when object $A$ passes object $B$ at $v$ kph, object $B$ also passes object $A$ at $v$ kph. Maybe gravity is the universes way of ...