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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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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79 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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4answers
233 views

Equivalence principle and acceleration vs a gravitational field

I picked this up on the net: Einstein came to realize the principle of equivalence, and it states that an accelerated system is completely physically equivalent to a system inside a gravitational ...
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3answers
1k views

Why gravity is an attractive force? [duplicate]

Why gravity is an attractive force? One may say that it is because of space time curvature but General Relativity is built on this law: $\displaystyle G \frac{m_1 \times m_2}{r^2}$ (To be more ...
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266 views

Retarded potential in gravitational field?

Is there a retarded potential concept in gravitational field similar to electromagnetic radiation?
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341 views

Negative potential energy of gravity

Does the negative potential energy in the gravitational field have to be considered in calculating the total mass of the system in question (because of $E=mc^2$)? If so it seems to me that the ...
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654 views

How to calculate Riemann and Ricci tensors for a sphere? [closed]

Let's have the metric for a sphere: $$ dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right). $$ I tried to calculate Riemann or Ricci tensor's ...
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465 views

What is the curvature of an empty universe?

My calculations tell me an empty universe has hyperbolic curvature. Is this correct? If it is, can anyone help me understand why this is intuitively?
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247 views

Ricci scalars for space and spacetime, local and global curvature

If Ricci scalar describes the full spacetime curvature, then what do we mean by $k=0,+1,-1$ being flat, positive and negative curved space? Is $k$ special version of a constant "3d-Ricci" scalar? ...
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196 views

How to find a curvature of the space-time by having $g^{\alpha \beta}$ in the following case without cumbersome calculations?

The metric tensor for Fock-Lorentz space-time, $$ \mathbf r_{||}{'} = \frac{\gamma (u)(\mathbf r_{||} - \mathbf u t)}{\lambda \gamma (u) (\mathbf u \cdot \mathbf r) + \lambda c^{2} (1 - \gamma (u))t + ...
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265 views

about the 1D singularity of black hole

I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the ...
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53 views

Can a black hole actually grow, from the point of view of a distant observer? [duplicate]

Possible Duplicate: Black hole formation as seen by a distant observer I've read in several places that from the PoV of a distant observer it will take an infinite amount of time for new ...
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173 views

How do black holes accrete mass?

Thanks to time dilation, a distant observer watching a man fall in to a black hole will only see him asymptotically approach the event horizon. So how do black holes ever get bigger?
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1answer
494 views

Do atoms expand with universe? [duplicate]

Possible Duplicate: Why space expansion affects matter? Why does space expansion not expand matter? As we know, the universe is expanding, galaxies are away from each other. But what ...
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3answers
588 views

The vacuum light speed: Is it really constant, i.e., independent of location in space-time?

I am by no means an expert in this field, however something puzzles me about the speed of light and the relativity of time and space (space-time). Is is universally acknowledged that the speed of ...
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325 views

Could gravity hold electron charge together?

Could the gravitational force be what holds the charge of the electron together? It seems to be the only obvious possibility; what other ideas have been proposed besides side-stepping the issue and ...
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172 views

How do we resolve a flat spacetime and the cosmological principle?

As I've said elsewhere, I've not had the opportunity to take a class in general relativity. Nonetheless, I understand that two major aspects of the standard cosmological model are the cosmological ...
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111 views

Knowledge needed to study and understand general and special relativity theory [duplicate]

Possible Duplicate: What are the prerequisites to studying general relativity? I'am 27 now and i have a burning desire to study math and physics from the ground up and I strongly prefer ...
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431 views

Expansion of the space-time metric [duplicate]

If the space-time metric is expanding with the expansion of the universe, if I could travel back in time, would I be less dense than the matter in that previous era?
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86 views

Carroll's derivation of the geodesic equations [duplicate]

In Carroll's derivation of the geodesic equations (page 69, http://preposterousuniverse.com/grnotes/grnotes-three.pdf), he starts with ...
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28 views

Seeking a coordinate-free expression of the orbital period for uniform circular motion around a non-rotating point-like mass

Consider a point-like (non-rotating, uncharged) mass $M$ and five separate participants (uncharged and of masses negligible in comparison to $M$) where participants $\mathsf A$, $\mathsf B$, ...
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39 views

Charged black hole

It is known that there is solution of Einstein's equations for charged black hole. Reissner–Nordström metric in case of non-rotating charged black hole and for rotating charged black hole is a ...
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2answers
63 views

Proving a relation with Four-velocity tensor [duplicate]

I'm trying to show that: $U^a_{\space\space;b}U^bU_a = 0$ (Where U is four-velocity) and I'm stuck on how to go about it. I tried expanding it out into the Christoffel symbols, but that didn't seem ...
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54 views

Duality and 1 forms

If a Killing vector is equal to: $$X= -\frac{1}{\sqrt{2}}\partial _t + \frac{\alpha}{\sqrt{2}}\partial_1.$$ But as far as I know is that the dual of a vector is a 1-form, so can I represent that ...
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107 views

Are a black hole really connecting 2 parallel universe?

What is beyond the point of singularity in a black hole and universe expands in all the 3 $x$, $y$ and $z$ axis? So how can one thing be on top of another when we don't know where the end point of ...
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3answers
173 views

Why does time slow down the closer you are to a mass?

When ever i look this up all I get is sites saying how its because general relativity says "-" why does it do it though? it is because there is more motion near gravity than further away? Or is it ...
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Given two events such that either one of them is 'on the light cone' of the other, do they constitute a 'null interval'?

One basic part of determining a metric (or applicable generalization) of a given set $\cal S$ of events (up to an arbitrary non-zero constant) is to determine to which pairs among those events, ...
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65 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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2answers
200 views

What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
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2answers
535 views

Is the tide on Earth caused by curvature of spacetime

The tide on Earth appears absolutely whenever the moon is overhead. Is that tide caused by spacetime, re-curvature in space or attraction gravity?
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88 views

Changing the scalar curvature (k = 0,+1,-1) with coordinate transformations?

I would like to prove that I can (or can't) change curvature of space, k = 0,+1,-1, via general coordinate transformations, which in principle can mix space and time coordinates together.
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112 views

Is weak lensing the statistical effect of microlensing?

I am looking into the effects of gravitational lensing of gravitational waves. I know that gravitons travel along null geodesics, just as photons, and so they will suffer the same deflection angle by ...
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1answer
1k views

Metric tensor under coordinate transformation x to y(x)

Say I have a metric representation $g_{\mu\nu}$ in a coordinate system $x$ and I want to find the representation of the metric in a new set of coordinates $y = y(x)$. I know how to do this if you are ...
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119 views

If it is given which intervals are spacelike, can be determined which intervals are lightlike?

Provided that the notion of "$\mbox{spacelike}$"-ness (of an interval) is symmetric: $$\text{spacelike}( \, x - y \, ) \Longleftrightarrow \text{spacelike}( \, y - x \, ),$$ then for any set $X$ (of ...
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87 views

Can anything come out from the big bang?

If any configuration of matter can fall into a black hole and hit the singularity, and ditto for the big crunch, and there is time reversal CPT invariance, does it mean anything can pop out of the ...
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1answer
139 views

Can we develop in the future a technology that can send a message to the past? [duplicate]

Possible Duplicate: Is it possible to go back in time? I believe that everything is possible in this world. If that can be done then why aren't we receiving any message from the future.
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2answers
254 views

How can we model intrinsic curvature?

Can it only be done in Euclidean space? Doesn't Euclidean space only model extrinsic curvature?
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Deflection of light by the Sun

Can you give details of a recent experiment of deflection of light by the Sun? What is the distance from the surface of the Sun and what is the exact value of the angle of deflection?
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80 views

More about gravitation as the source of redshift of light beams [closed]

In the realm of physics there is no knowledge, the justification of which does not depend either upon experience or upon reason. In the light of the findings of the preconditions of knowledge made in ...
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3answers
238 views

Can the Cosmological Constant explain an accelerated expansion?

From what I've learned so far, it appears that all models that attempt to explain the expansion of the universe are either based on Lambda-CDM or quintessence. The former support a big bang with ...
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2answers
365 views

General Relativity & Kepler's law [duplicate]

According to Kepler's law of planetary motion, the earth revolves around the sun in an elliptical path with sun at one of its focus. However, according to general theory of relativity, the earth ...
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1answer
136 views

2 + 1 dimensional gravity as an exactly soluble system [closed]

In Gomez's article (Higher spin part 2)http://arXiv:1307.3200, I face to gauge algebras. Gomez says we have some algebras for ISO(2,1)and SO(2,2),SO(3,1). and he tells us only ISO(d-1,1) and only ...
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2answers
320 views

Local Charts in General Relativity

We may consider a "local" region in curved spacetime (local in respect of the spatial and the temporal coordinates). A "local inertial frame" may be constructed by some transformation that produces ...