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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Torsion in kerr black holes

In General Relativity, we generally assume that the derivative operator is torsion-free, i.e., second covariant derivatives commute on functions. However, in Kerr black holes, spacetime is dragged (...
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37 views

Do the energies of cosmic rays approach infinite at the event horizon of a black hole?

Let's assume an observer orbits close to a black hole, he is not alone, massive cosmic rays, like electrons and protons and other kind of space dust comes from the outer space and may hit him. Since ...
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Going to the Einstein frame in f(R) theories

First of all thank you for your time! I have a question that I can't solve. In every review that I read, I find that when you want to go to the Einstein frame in a $f(R)$ theory what you have to do ...
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Schwarzschild metric, speed of ball as measured by observer who catches the ball, just before ball is caught? [closed]

Inspired by this question here. The Schwarzschild metric, describing the exterior gravitational field of a planet of mass $M$ and radius $R$, is given by$$ds^2 = -(1 - 2M/r)\,dt^2 + (1 - 2M/r)^{-1}\,...
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69 views

Schwarzschild metric black hole

Schwarzschild metric solution presents two singularities. An apparent one at $r=2GM$ and a real one at $r=0$. It is known that everything freezes at the event horizon from an outside observer point of ...
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84 views

Metric that is Minkowski plus sum of null vectors

In GR exercises I've often seen metrics of the form $g_{ab} = \eta_{ab} + k_ak_b$ where $k_a$ is null with respect to $g$ (or equivalently $\eta$). I'm happy doing calculations with such metrics, but ...
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61 views

Is it contradictory with any theory or experimental result to have a negative gravitational force mass?

I am aware that there are many similar questions here about this in this site, but most answers concentrate on negative inertial and gravitational energy. My question is more specific. QM together ...
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139 views

$C^\infty$, nonvanishing parallel vector field along geodesic, orthogonal to tangent

The following question(s) showed up in my admittedly basic undergraduate research in general relativity/cosmology, and I was wondering if anybody could me with it. Let $(X, g)$ be a $n$-dimensional ...
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17 views

Lapse Function and Shift Vector in Minkowski and de Sitter

I'd like to find the lapse function and shift vector in 1+1 Minkowski as well as 1+1 de Sitter (flat foliation) for a region foliated this way: The $y$-axis represents time while the x-axis ...
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262 views

Killing tensor and Riemann tensor identity

I know that if we have a Killing vector then it's straightforward to show the identity: $$\nabla_a \nabla_b K_c = R_{cba}^k K_d$$ I'm now trying to show the following identity for a $(0,2)$ Killing ...
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Trying to understand Newtonian limit of GR

First ever post - please be kind. I'm trying to understand how General Relativity becomes equivalent to Newton's laws of motion, plus Newton's law of gravitational attraction in the limiting case of ...
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133 views

When is stress-energy tensor defined as variation of action with respect to metric conserved?

In General Relativity Einstein's equation implies that stress-energy tensor on its RHS is conserved (has vanishing divergence), due to the Bianchi identity. Considering variational principles leading ...
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119 views

Covariant derivative of a covariant derivative

I'm trying to find the covariant derivative of a covariant derivative, i.e. $\nabla_a (\nabla_b V_c)$. This is something I've taken for granted a lot in calculations, namely I though that by the ...
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199 views

If an astronaut had stationed in International Space Station for the duration of mission, 17 years, would he be older?

Today the NASA International Space Station started the 100000 orbit after 17 years in the space. I just wonder if there were a team of astronauts which were in the Lab for all the duration of last 17 ...
5
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58 views

Schwarzschild metric, acceleration of ball before it's dropped [duplicate]

The Schwarzschild metric, describing the exterior gravitational field of a planet of mass $M$ and radius $R$, is given by$$ds^2 = -(1 - 2M/r)\,dt^2 + (1 - 2M/r)^{-1}\,dr^2 + r^2(d\theta^2 + \sin^2\...
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47 views

Showing classical spin tensor is time independent for free particle

Reading through Weinberg's gravitation book, the following definition is given for the spin tensor (Pauli-Lubanski psuedovector): $$ S_\alpha = \frac{1}{2}\epsilon_{\alpha\beta\gamma\delta} J^{\beta\...
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52 views

Wald's Equation 3.3.6

I have an issue with Eq. 3.3.6 of Wald's General Relativity. There he would like to prove that for Gaussian normal coordinates, the geodesic tangent field remains orthogonal to all coordinate basis ...
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25 views

Why is it that light bends towards gravity when it has no mass at all? [duplicate]

Why is it that light bends towards gravity when it has no mass at all? Is it because of how gravity behaves as mentioned in general relativity? As far as I know, light cannot escape from black holes, ...
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72 views

Does Newton's third law remain totally unchanged even in Einstein's theory?

Why Newton's third law remain unchanged still now in relativity theory (as for example that is why we feel weight due to equal but opposite reaction of the Earth's surface)?
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44 views

What relative effects be for object with near light speed velocity in compactified dimensions?

What relative effects be for an object with near light speed velocity in compactified dimensions? Does gravity increase the same as for an object with near light speed velocity in usual spacial ...
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1answer
63 views

How can you tell if spherical-like coordinates are locally flat across the origin?

In general relativity, with spherical-like coordinates in a radial gauge, I have a metric that looks like: $$-g_{tt}\mathrm{d}t^2 + g_{rr}\mathrm{d}r^2 + r^2(\mathrm{d}\theta^2 + \sin^2\theta\ \...
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65 views

How energy would be consumed for bending spacetime?

If we could assume that relativity theory is correct about spacetime bending. Can we calculate energy used for moving 1 kg of object in 1 meter by changing the shape of spacetime (simulate gravity)? ...
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About the use of Newtonian Relations for the movement of stars in the Galaxy [duplicate]

From a General Relativity point of view Gravity is given as the result of spacetime curvature interacting with energy-mass density. To get to the Newtonian limit one needs to take a) Non-...
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1answer
95 views

How does the Einstein summation convention apply to the following equation?

This is the equation is in the "mathematical form" section of the following wikipedia article: http://en.wikipedia.org/wiki/Geodesics_in_general_relativity More specifically, the "Full geodesic ...
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Deriving $A^{\mu}_{;\nu}$ from $A_{\mu ; \nu}$

We have a covariant derivative of a covariant tensor: $$ A_{\mu ; \nu} = A_{\mu , \nu} - \Gamma^{\alpha}_{\mu \nu} A_{\alpha} $$ The covariant derivative of a contravariant tensor is: $$ A^{\mu}_{;\nu}...
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Why Newton's gravitational constant remains unchanged in relativity though gravity is not a force?

I know that Einstein described gravity as a curvature of spacetime. So, It is not a "force" but why Einstein had to accept Newton's gravitational force constant?
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Can black holes grow via accretion of dark matter particles?

I'm assuming that the answer to the question in the title is a resounding yes. Since Baryonic matter and dark matter interact via gravitational forces. If this is the case how is information not lost ...
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54 views

Why is the Einstein Static Universe represented as an infinite cylinder when it seems like only half a cylinder?

The Einstein static universe metric is $$ds^2=-dt^2 + d\chi^2 + \sin(\chi)^2d\Omega^2$$ where $-\infty<t<\infty$ , $0<\chi<\pi$ and $d\Omega^2$ is the metric on a $S^2$. It describes the ...
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What is basic tensor algebra in teleparallel equivalent of general relativity?

Teleparallel gravity represents a viable alternative to general relativity where gravitation comes from torsion rather that curvature. The theory is based on a new modified connection, and the ...
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1answer
65 views

Gravitational waves and it's interaction with matter

I have been reading an article on gravitational waves here. There, it is written that the gravitational wave, unlike the electromagnetic waves, interact very weakly with matter. The principle of LIGO ...
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86 views

Total derivatives in GR

Without gravity we can easily switch between terms in a Lagrangian, such as $\partial\phi\partial\bar{\phi}$ and $\phi\Box\bar{\phi}$, since total derivative vanishes. But in GR we have additional $e\...
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112 views

'Hovering' light rays on the edge of a black hole

According to Prof. Hawking, light rays will 'hover' on the edge of a black hole. If this is true, and the light 'stops' on the edge, how can the electric/magnetic fields which, constitute the light, ...
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How much energy can be extracted by lowering something into a black hole? [duplicate]

If an object is in orbit around a star, the object has gravitational potential energy that could possibly be extracted. For example, when we perform gravitational slingshots around Jupiter, our ...
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41 views

Unknown functions in Schwartzchild Metric

I was reading through MTW and they made a big deal about how we were able to make an astute choice of coordinates to eliminate unknown functions from the most general form of the metric for a ...
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1answer
124 views

What happens to objects sucked into a black hole after the black hole evaporates away?

Suppose an object falls into a black hole that's so massive that it wouldn't get torn apart at the event horizon. What happens to it after the black hole evaporates away? According to the theory ...
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80 views

At a center of Gödel's universe

A few quick questions clarifying a picture about Gödel's universe, they bug me badly! Taken from here. So Gödel's universe is made out of dust particles. All of them have angular velocity. Do this ...
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Energy of a particle as measured by an observer at infinity

I'm wondering if it is possible to make a definition for the energy of a particle as measured by an observer at infinity. I've looked through Wald for this but wasn't able to find anything - I may be ...
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1answer
35 views

About relativity [duplicate]

We know that the curvature of spacetime is gravity itself and it is not a force.so,why do we feel our weight in a curve spacetime but not in a straight(I mean not curve) space time like zero gravity ...
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56 views

Testing General Relativity using radioactivity on the Moon

I was reading a question involving an ultracentrifuge to test General Relativity. Instead of using an atomic clock the asker posited using radioactive decay as the metric to evaluate time dilation ...
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Negative Mass's Effect on Gravitational Time Dilation [duplicate]

When I was playing around with the equations for Gravitational Time Dilation, I discovered that when a negative value was plugged in for $M$, the equation gave the exact same answer, and it would ...
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176 views

Do gravitational waves propagate backwards in time?

Gravitational waves are spacetime waves, which stretch and squeeze both space and time. Since relativity puts space and time (almost) on an equal footing, it seems to me that since gravitational waves ...
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1answer
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Is there such thing as imaginary time dilation?

When I was doing research on General Relativity, I found Einstein's equation for Gravitational Time Dilation. I discovered that when you plugged in a large enough value for $M$ (around $10^{19}$ ...
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66 views

how are the infinitesimal generators of translation related to the lagrangian?

In studying analytical mechanics (or it's quantum analog), one will come across statements such as: $$f(x^{i}+\delta x^{i})=f(x^{i})+\delta f(x^{i})=f(x^{i})+\frac{\partial f(x^{i})}{\delta x^{i}}\...
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87 views

Straight line null geodesics in Minkowski, De Sitter and Schwarzschild

I'm trying to understand which part of the following metric determines whether photons travel on a "straight" line (thinking of $(t,r,\theta,\phi)$ as a flat background), the metric I'm considering is:...
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25 views

Gravitational lensing and cosmic strings

Say we have a straight cosmic string lying along the $z$-axis, with energy-momentum tensor $$T_{\mu\nu}=\mu\delta(x)\delta(y)\operatorname{diag}(1,0,0,-1)\tag{1}\label{1}$$ for some small positive ...
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Can redshift occur from relative velocity or just from expanding space

With sound the Doppler effect is caused by the wavelength of the sound being affected by the relative velocity between the observer and emitter, eg. If they are moving toward each other the observed ...
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64 views

Why does two masses with energy attract each other?

I have heard that every mass attract another mass with a force directly proportional to the multiplication of their masses and inversely proportional to the square of distance between them, but newton ...
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Gravity and circular logic [closed]

My research into gravity indicates that warped spacetime, with time as the major influence, is gravity. It also indicates gravity causes time dilation. Why is this not a circular argument. It is ...
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How does one derive Christodoulou Memory Effect?

There is a non-linear effect associated to the permanent displacement of test masses when a gravitational wave interact with them. This is called the Christodoulou memory effect. How does one obtain ...
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Traveling slower by traveling in opposite direction as the Earth rotates

I know that if I were to travel fast, the time would pass by fast for me. But if I were to travel fast in the opposite direction of the earths rotation while I'm still on earth, would the time pass by ...