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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Better explanation of the common general relativity illustration (stretched sheet of fabric)

I've seen many science popularisation documentaries and read few books (obviously not being scientist myself). I am able to process and understand basic ideas behind most of these. However for general ...
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40 views

Hubble's law for the Kasner solution

I'm puzzled with the following question: find an analog of the Hubble's law for the Kasner solution. Kasner metric is a solution to the vacuum Einstein equations ...
0
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2answers
149 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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72 views

Relativistic Black Hole? [duplicate]

So recently, looking at high energy particles through the lens of General and Special Relativity has peaked my interest. One thing I was considering, using the electron as the first example, is as ...
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1answer
74 views

Is there a minimum mass is required for light to be noticeably bent?

The sun bends the trajectory of light slightly. And a black hole will bend the trajectory entirely. This is all dependent on the proximity to the source of gravity. For a given angle, is there some ...
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1answer
135 views

Specify the Stress Energy Tensor and Calculate the Curvature

I have a simple question about general relativity and the Einstein field equations, I wonder if you can specify the stress energy tensor, i.e. specify some mass distribution in space and then ...
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1answer
71 views

Why we can set variations for the metric and its derivatives to zero at infinity?

This question is the continuation of the following one. I still don't understand why $(1)$ may be set to zero. This refers to the zero value variations of metric and its derivatives on the infinitely ...
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1answer
145 views

Are there any good references on the “gravitational” curvature of spacetime of a moving mass being distorted due to special relativity?

In this Wikipedia paragraph suggesting an explanation for the phenomenon of inertia, it claims: Another physicist, Vern Smalley, has derived the Lorentz transformation for mass by assuming that ...
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1answer
210 views

Einstein action and the second derivatives

I have naive question about Einstein action for field-free case: $$ S = -\frac{1}{16 \pi G}\int \sqrt{-g} d^{4}x g^{\mu \nu}R_{\mu \nu}. $$ It contains the second derivatives of metric. When we want ...
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114 views

How do we derive force/acceleration vectors from Einstein's field equations?

I'm new here and I don't have any formal experience in physics beyond A-level. I've been exploring an idea for a space sim game someone else is developing in which propulsion of a spacecraft is ...
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1answer
172 views

Relation between symmetries and Killing vectors by Weinberg

In his book, "Gravity and Cosmology", Weinberg talks about relations between homogeneous metric spaces and Klling vectors. First he says about infinitesimal isometrics $$ x^{\alpha}{'} = x^{\alpha} + ...
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3answers
135 views

Is light slower when traveling inside a gravity field?

This question is not about phase velocity changed which causes refraction, but about the real time itself being slower by the gravity of any object (from general relativity). If so, would this mean ...
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2answers
132 views

Proof that higher genus surface admits a metric of negative Ricci scalar everywhere

In the Green, Schwarz and Witten Superstring Theory textbook, the paragraph below equation 3.3.15 says, For genus greater than one, it can be shown that the surface admits a metric of everywhere ...
5
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1answer
312 views

6 independent Einstein field equations?

I can't understand the comment on page 409, Gravitation, by Misner, Thorne, Wheeler It follows that the ten components $G_{\alpha\beta} =8\pi T_{\alpha\beta}$ of the field equation must not ...
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76 views

Weak gravitational lensing multispectral, multibackground correlations

My understanding of weak gravitational lensing is that it assumes random alignment distribution of galaxies in order to estimate statistical shear and convergences, which are used to estimate matter ...
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2answers
164 views

A complicated question about $E=mc^2$

I know this is a little outside the normal question and there may not be a direct answer, but it is an interesting thought experiment. Starting with a supermassive black hole, if you were able to ...
3
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2answers
432 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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2answers
46 views

Are high redshift masses corrected for relativistic mass dilation? They would appear more massive right?

A distant quasar would be less massive in its frame of reference than our observations would suggest. Are such highly red-shifted objects corrected for relativistic mass dilation?
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20 views

Method of determining peculiar speed of the galaxy which moves on celestial sphere and emits the light

This question is the continuation of this one. I came up with solution, but I'm not sure that it is correct. Can someone check it? Let's introduce transverse (to the observer) proper speed ...
3
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1answer
120 views

Gravitational waves as information carriers

Is it possible to utilize gravitational waves as a delivery system for information between two observers straddling the event horizon of a black hole? And why ?
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44 views

How to find proper speed (relate to homogeneous cosmic background) of the galaxy by given redshift z and observing angular velocity?

The galaxy moves of the celestial sphere. It is given that proper speed is transverse to the observer and it must to find this speed in the moment of light emission. The motion is in the FLRW ...
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1answer
63 views

A simple derivation

During the study of a paper I see that its author defines $$\frac{dh^{ab}}{d\tau}:=h^{am}h^{bn}\frac{dh_{mn}}{d\tau}$$ and from this concludes that ...
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43 views

Differential equation for speed relate to the homogeneous cosmological background in FLRW metric

How to derive DE for the speed (which relate to the homogeneous cosmological background) of the observer which moves with constant proper acceleration in spatially flat FLRW universe?
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70 views

What are the current experimental restrictions of the possible speeds of gravitation?

Somewhere I read that the Hulse-taylor binary pulsar can not differentiate between competing theories assuming different speeds of gravity. Is it mathematically true in general, that the orbital decay ...
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1answer
255 views

Non-linear Dirac equation in Einstein Cartan theory

Can someone explain this Wikipedia article, specifically the section on Einstein-Cartan theory? I have no idea how the equation ...
6
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1answer
230 views

Dirac Lagrangian density in curved spacetime

I'm trying to derive this form of the Dirac Lagrangian density in curved space-time: $$ \mathcal{L}~=~\det\left(e\right)\bar{\Psi}\Bigg ...
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82 views

On the Geroch's argument

During the study of Geroch's argument to prove positive mass theorem, I faced a problem explained below: Suppose $(M,g_{\mu \nu})$ is a four dimensional Lorentzian Manifold and $\Sigma$ is a ...
2
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2answers
325 views

First integral of relativistic Euler-Lagrange equations

Connsider a pseudo-Riemannian ($4$-dimensional) manifold $M$ with a pseudometric $g_{ab}$. The Lagrangian of a free particle in $M$ (in analogy to the flat case) is $$\mathcal ...
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1answer
415 views

Lie derivative of Riemann tensor along killing vector ( = 0 )

I'm currently learning the mathematical framework for General Relativity, and I'm trying to prove that the Lie derivative of the Riemann curvature tensor is zero along a killing vector. With the ...
5
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1answer
131 views

Lower limit of the size of the Universe? (WMAP)

The measurement of the WMAP satellite resulted a planar geometry of the universe with a 0.4% uncertainity (http://en.wikipedia.org/wiki/Shape_of_the_universe). If there is a little deviation from the ...
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1answer
88 views

What does it mean for a metric to be regular?

A problem in Carroll (a general relativity textbook) asks if a certain metric is regular. What does it mean for a metric to be regular?
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2answers
145 views

How is Space-Time curved?

How does space-time curved by mass/energy if there's nothing to be curved? I haven't seen any satisfying answer.
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2answers
266 views

Einstein equation and scalar field stress-energy tensor

Let's have interaction between gravitational and scalar real fields. For an action of gravitational field in vacuum I add term $S_{m} = \int d^{4}x\sqrt{-g}L_{m}$, where $$ L_{m} = \frac{1}{2}g^{\mu ...
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1answer
113 views

Combined speed of Earth in Space is 1.5 million mph - how much slower is time for Earthlings as a result?

Theres a problem for intergalactic astronauts which is finding their way back to Earth. Combining all the rotational speeds, we are spinning and orbiting the sun, in our solar system which is spinning ...
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1answer
355 views

How does one measure space-like geodesics? Or: What is the physical interpretation of space-like geodesics?

In general relativity, time-like geodesics are the trajectories of free-falling test particles, parametrized by proper time. Thus, they are easy to interpret in physical terms and are easy to measure ...
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328 views

How to show that every Killing vector field is a matter collineation?

Various texts make this claim, but no proof is given. Explicitly, let $L$ denote the Lie derivative. Suppose $L_X g_{ab} = 0$ for some vector field $X$, called a Killing vector field. Suppose that ...
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59 views

One more time about the connection of Weyl tensor and gravitational waves

There is differential identity with Weyl tensor and energy-momentum tensor: $$ D^{\lambda}C_{\lambda \alpha \sigma \beta} = 4 \pi G \left(D_{\sigma}T_{\alpha \beta} - D_{\beta}T_{\alpha \sigma} + ...
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2answers
186 views

Exterior (covariant) derivatives and electromagnetism

I'm porting Maxwell's equations to curved spacetime and am having trouble reconciling the tensor and forms treatments. I think the problem boils down to a misunderstanding on my part concerning the ...
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1answer
135 views

How to make a black hole?

Many Physics discussions I have often conclude with: Well you will then form a black hole... My questions are: Is there a general recipe for making a black hole? If not, then can you list the ...
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1answer
111 views

How to show that value is conserved along geodesics?

Let's have the motion of charged particle in a field of Reissner-type black hole. The equation of motion looks like $$ \frac{d^{2}x^{\mu}}{d \tau^{2}} + \Gamma^{\mu}_{\nu \lambda}\frac{dx^{\nu}}{d ...
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4answers
223 views

Is there a distinguished reference system, after all?

The equivalence principle, being the main postulate upon which the general relativity theory rests, basically states that all reference systems are equivalent, because pseudo forces can (locally) be ...
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1answer
71 views

Why must the final state be stationary?

I faced the following sentences: We consider a gravitational collapse taking place in this spacetime. The singularity theorems assure us that a singularity will form. The assumption that the ...
2
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2answers
174 views

How does the Einstein Equivalence Principle imply a spacetime with a metric (and a connection)?

I have at hand the book by Clifford Will, "Theory and Experiments in Gravitational Physics", and the following Living Reviews in Relativity article. He quotes the Einstein Equivalence Principle (EEP) ...
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23 views

If the absolute horizon were exclusionary of matter, what supernova behaviors would that predict?

Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.415, Box 12.1: ... The absolute horizon is just a point when created, but it then expands smoothly, like a balloon being blown up, ...
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3answers
294 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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0answers
27 views

What is the total mass of the accelerated viewpoint particle atmosphere of a black hole?

Kip S Thorne's "Black Holes & Time Warps", 1994 paperback, p.443, just above Figure 12.5: Surprisingly, from the accelerated viewpoint, the vacuum fluctuations consist not of virtual particles ...
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1answer
109 views

If charged particles always attach to black hole event horizons, how can ordinary matter fall in?

(A friend at work kindly loaned me loaned me his copy of Kip S Thorne's "Black Holes & Time Warps". This may have been ill-advised... :) BH&TW 1994 paperback p.410 Figure 11.5: ... all ...
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2answers
150 views

On the singularity $r=0$ of the Schwarzschild metric

I faced following sentences: Unlike the co-ordinate singularity at $r = 2M$, the origin of the Schwarzschild metric $r = 0$ has a true curvature singularity. It was first believed that this ...
3
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1answer
239 views

What's the importance of conformal transformations in general relativity?

I tried to understand the importance of conformal transformations in general relativity, but I failed. I didn't see that conformal transformations help to simplify the metrics, and also I didn't see ...
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1answer
151 views

Effective mass of a black hole?

Suppose a black hole forms from a given mass of particles such as the core of a star going supernova. The black hole formed will have an effective mass due to the curvature of space time induced. Such ...