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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Two Robertson-Walker observers, at what time will a light signal be received?

Here is a question I have that is inspired by this question here. The spacetime metric of a radiation-filled, spatially flat ($k = 0$) Robertson-Walker universe is given by$$ds^2 = - dT^2 + T[dx^2 + ...
6
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1answer
311 views

Null geodesics in uniform gravitational field metric

I'm trying to understand the null geodesics in the metric: $$\mathrm{d}s^2 = -(1+gz)^2 \mathrm{d}t^2 + \mathrm{d}z^2 + \mathrm{d}x^2$$ In particular I'm wondering if the following intuition is valid:...
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2answers
103 views

Flat space Solution of Einstein Field Equation

Does a trace-free energy-momentum tensor $T_{\mu}^{\mu} = 0$ ensure that the Einstein's field equations have a flat space solution?
16
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2answers
932 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 (...
4
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2answers
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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2answers
66 views

Two Black Holes held stationary by EM forces

If two black holes with large enough mass (so that the tidal forces are minimal and the intersection is large) that are held apart by like charges (saddle point stability). Imagine the black holes in ...
3
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1answer
59 views

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 (...
9
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3answers
969 views

Could a ship equipped with Alcubierre drive theoretically escape from a black hole?

Could a ship equipped with Alcubierre drive theoretically escape from a black hole? Also, could it reach parts of the universe that are receding faster than the speed of light from us?
13
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2answers
833 views

How can we recover the Newtonian gravitational potential from the metric of general relativity?

The Newtonian description of gravity can be formulated in terms of a potential function $\phi$ whose partial derivatives give the acceleration: $$\frac{d^2\vec{x}}{dt^2}=\vec{g}=-\vec{\nabla}\phi(x)=\...
111
votes
5answers
15k views

Did the Big Bang happen at a point?

TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen?
3
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1answer
83 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 ...
3
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1answer
61 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 ...
0
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1answer
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 ...
1
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0answers
29 views

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 ...
1
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1answer
60 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 ...
5
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1answer
97 views

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 ...
247
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15answers
22k views

How does gravity escape a black hole?

My understanding is that light can not escape from within a black hole (within the event horizon). I've also heard that information cannot propagate faster than the speed of light. It would seem to ...
4
votes
3answers
198 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 ...
1
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0answers
15 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 ...
4
votes
1answer
56 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\...
2
votes
3answers
112 views

How can geometrized units have more than one constant equal to 1?

I can understand how you could manipulate units to make a certain constant equal to $1$, like $c$ or $G$, et cetera. But how can you make it so two constants (in this case $c$ and $G$) are equal to $1$...
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0answers
46 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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1answer
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 ...
0
votes
1answer
48 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 ...
7
votes
1answer
290 views

Does frame dragging apply to linear motion?

Firstly I will admit I do not understand the real cause of rotational frame dragging and some of the math heavy explanations are too complicated for me. To me frame dragging looks like unsubstantiated ...
4
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2answers
109 views

For a giving metric in GR, how do we learn which observer the metric refer to?

For example, I have been told the Schwarzschild observer is far away from blackhole and events,(namely, I think, the observer is static at infinity of the coordinate.) And the second example,the ...
4
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0answers
57 views

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 ...
1
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1answer
93 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 ...
0
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0answers
24 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, ...
1
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1answer
68 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)?
5
votes
4answers
668 views

Theory that gets rid of dark matter/energy

Is there any physics theory that either groups together gravity and dark energy/dark matter or eliminates dark energy/dark matter by modifying standard understanding of gravity or any force? If so, is ...
4
votes
1answer
94 views

Indicating that indices are equal in Einstein notation

tl;dr: I have an expression like this: (dramatization) $$ R_{\mu\nu} = \begin{pmatrix} B^{00}C_{00} & 0 & 0 & 0 \\ 0 & B^{11}C_{10} & 0 & 0 \\ 0 & 0 & B^{22}C_{20} &...
0
votes
0answers
20 views

Event horizon at moments of formation of black hole [duplicate]

As I understand it, the event horizon of a black hole body, has a diameter depending on the mass. So, if an existing black hole grows through infalling matter the event horizon radius increases. I'm ...
20
votes
4answers
871 views

How Come gravity doesn't affect itself?

If gravity is this "unexplainable force" that pulls everything to the center of a planet or stellar remnant you stand upon, why doesn't gravity pull itself? If gravity affects anything with energy, ...
1
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2answers
130 views

Relativity and Galaxy Rotation Speed

If time travels slower nearer gravity wells, why can't the galaxy rotation speeds being faster on the outer edges than the inner areas be explained by relativity? What necessitates dark matter?
4
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1answer
61 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\ \...
-4
votes
1answer
60 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)? ...
0
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0answers
17 views

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-...
0
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2answers
76 views

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}...
1
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1answer
111 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, ...
0
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0answers
54 views

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?
4
votes
1answer
63 views

For gravitational wave from twin stars, how was the tidal effect counted?

As the primary indirect evidence, the work on calculating the rotational slow down earned the 1993 Nobel prize. However, I cannot find any where mention how the work deal with the tidal effect. Are ...
2
votes
1answer
64 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 ...
0
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0answers
51 views

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 ...
1
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2answers
82 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:...
4
votes
2answers
83 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\...
11
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1answer
1k views

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 ...
1
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1answer
79 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 ...
4
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1answer
93 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 ...
1
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1answer
205 views

Time dilation triplet paradox

Here is the twin paradox with a twist. Scenario 1: An observer (A) leaves from the equator of the earth and travels with an acceleration of $9.8\,\mathrm{m/s^2}$ in a north direction ( i.e. in the ...