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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248 views

Taking selfies while falling, would you be able to notice a horizon before hitting a singularity?

I am generally interested in the role of "pings"(0a) between participants (a.k.a. "signal roundtrips"(0b), as familiar for instance from Synge's "five point curvature detector") in the determination ...
32
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5answers
2k views

Why do we need coordinate-free descriptions?

I was reading a book on differential geometry in which it said that a problem early physicists such as Einstein faced was coordinates and they realized that physics does not obey man's coordinate ...
0
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0answers
45 views

Which is the corrispondent of the Lorentz's transformation in general relativity?

The Lorentz's transformations tell us how space and time change in a flat case? There are a more general and powerfull transformation for general relativity?
8
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3answers
736 views

Special Relativistic approximation to GR

Some time ago I was talking to a professor in college about some of the fundamental aspects and origin of General Relativity. I was surprised to learn, in fact, that a pretty good approximation to GR ...
8
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1answer
319 views

Cancelling special & general relativistic effects

We know that for a GPS we need to make a correction for both general and special relativity: general relativity predicts that clocks go slower in a higher gravitational field (the clock aboard a GPS ...
1
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1answer
59 views

Time flow difference for satellites [duplicate]

Clocks in satellites have to be adjusted due to the effects of relativity; but does time for satellites (GPS) flow slower, due to the relative motion, or faster, due to the weaker amount of ...
2
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1answer
81 views

Gravitational potential in GR

In proving that the metric will play the role of gravitational potential, there is this chain of ideas: ...
0
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2answers
68 views

The invariance vs constancy of the speed of light in vacuum

This is perhaps as much a question of semantics as of physics but it is something I have been thinking about recently and was wondering if anyone else had a perspective on this. Now, it could be that ...
0
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1answer
49 views

Spherical Symmetric Metrics

In the case where all books try to illustrate a spherical metric, the procedure goes this way: First they impose isotropy in terms of polar coordinates so that one can write: $$ds^2=-A(r)dt^2 + ...
2
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4answers
798 views

When space bends, what are the lines that are being bent?

In an electric field diagram, the lines represent the electrostatic force vector at the position. These lines are bent when you place a charge into the system. What is the equivalent description ...
5
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1answer
101 views

How is the Lagrangian defined in GR?

Reading about the Schwarzschild metric in general relativity I see that sometimes $$L=g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}$$ and sometimes $$L=\sqrt{g_{\mu\nu}\dot{x}^{\mu}\dot{x}^{\nu}}.$$ Which is ...
6
votes
3answers
636 views

Falling into a black hole

I've heard it mentioned many times that "nothing special" happens for an infalling observer who crosses the event horizon of a black hole, but I've never been completely satisfied with that statement. ...
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0answers
29 views

Zero mean curvature and maximal volume

I have a 1+1 asympotically flat spacetime system (spherical symmetry) for which I'm trying to find the hypersurface which maximizes the volume enclosed in a sphere of a given radius $r=R$. **It seems ...
1
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2answers
207 views

About Christoffel symbols in Riemann normal coordinates

According to the answer to this post, the Christoffel symbols in Riemann normal coordinates are approximated by $$\Gamma^{k}_{ij}(x)~\sim~\frac{1}{2} R^k{}_{ilj}(x_0) \xi^l \tag{5.10}$$ which came ...
7
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6answers
2k views

How to measure the curvature of the space-time?

I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ...
2
votes
1answer
82 views

The ADM Energy of Gravitational Waves?

I have been looking for books about this question for several days. However, almost all books use Landau–Lifshitz pseudotensor to calculate the energy of Gravitational Waves.And they said the result ...
16
votes
4answers
2k views

Shape of the universe?

What is the exact shape of the universe? I know of the balloon analogy, and the bread with raisins in it. These clarify some points, like how the universe can have no centre, and how it can expand ...
0
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0answers
25 views

Differential precession due to gravitational waves

To motivate the question, Andy Strominger recently put out a paper on calculating the Sagnac shift of counterrotating beams due to the angular momentum flux of a passing gravitational wave. See ...
1
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0answers
46 views

Nabla or semicolon notation for covariant derivative? [closed]

$$A_{\,;\alpha}^{\mu}=\nabla_{\alpha}A^{\mu}$$ Are there any pros and cons regarding these two notations for denoting the covariant derivative?
1
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2answers
129 views

The Big Bang theory hypothesis

Is there a simple way to state the hypotheses of the Big Bang theory? I have the impression that the Big Bang singularity is merely a consequence of Freedman equations. Could somebody clarify what ...
0
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1answer
36 views

Derivation of form of perfect fluid stress-energy tensor

Given the perfect fluid equation: $$T_{\mu\nu}=(\rho+p)U_\mu U_\nu+pg_{\mu\nu}$$ How does one derive the following form? $$T_\mu^\nu=\mbox{diag}(-\rho,p,p,p)$$ I understand one needs to raise an index ...
-5
votes
1answer
50 views

Does gravity slow entropy? [closed]

Just got to thinking about why time slows in a gravitational field. It occurred to me that, in a gravitational field, the closer you get to the source the slower time seems to travel. But also, the ...
1
vote
1answer
314 views

Questions about MTW's “thousand” tests of the Einstein principle

In Misner, Thorne, Wheeler (henceforth written as "MTW"), "Gravitation", Box 16.4, there's an experimental setup construction (or method) presented by which "Each geodesic clock is constructed and ...
1
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1answer
71 views

What is the partial differential equation expansion of the Einstein Field Equations?

I have read that the Einstein Field Equations (http://en.wikipedia.org/wiki/Einstein_field_equations) can be expressed as a series of differential equations. Some say 16, others say 10 (The disparity ...
1
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3answers
616 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 ...
2
votes
2answers
203 views

Why is the metric tensor symmetric? [duplicate]

I was reading Schutz, A First Course in General Relativity. On page 9, he argued that the metric tensor is symmetric: $$ ds^2~=~\sum_{\alpha,\beta}\eta_{\alpha\beta} ~dx^{\alpha}~dx^{\beta} $$ ...
0
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0answers
31 views

Do anyone know a good software that where I can easily find the metric from the stress-energy tensor? [duplicate]

I'm using SageMath but the obtainment of the metric from the stress-energy tensor is not trivial, i.e., it is not implemented in a predefined function. Do anyone know a good software that where I can ...
23
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3answers
6k views

Does a photon exert a gravitational pull?

I know a photon has zero rest mass, but it does have plenty of energy. Since energy and mass are equivalent does this mean that a photon (or more practically, a light beam) exerts a gravitational pull ...
1
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1answer
62 views

Difference of connections in the Killing vector equation

For the Killing vector equation, I sometimes see it written in terms of spin connection $\omega$ and other times in terms of the affine connection $\Gamma$. More clearly ...
-1
votes
1answer
34 views

modified gravitational model

In the modified gravitational model $ f(R)=R+\lambda{R_{0}}\left(\left(1+\frac{R^{2}}{R_{0}^{2}}\right)^{-n}-1\right) $ what are the units of $\lambda$ and $R_{0}$.
0
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1answer
52 views

Circular orbits in general relativity(GR)

Reading about Schwarzschild geodesics, I found that circular orbits are possible when the effective force $$ F=-\frac{dV}{dr}=-\frac{\mu{c^{2}}}{2r^{4}}\left(r_{s}r^{2}-2a^{2}r+3r_{s}a^{2}\right)=0 ...
2
votes
1answer
109 views

Problem with relativity of acceleration

In this answer http://physics.stackexchange.com/a/92833/36977 John said that acceleration is not relative in the general theory of relativity. But as we all know, accelerating charges emit ...
0
votes
2answers
157 views

why do x Schwarzschild radii equal time dilation effects of speed of light going y times faster than an object^2?

let me walk you through the math. First you start with the gravitational time dilation formula where: $$ T_1=T\sqrt{1-\frac{2GM}{rc^2}} $$ and rather than entering $r$ for the radius we replace $r$ ...
8
votes
2answers
403 views

Energy balance of closed timelike curves in Gödel's universe

I recently read Palle Yourgrau's book "A World Without Time" about Gödel's contribution to the nature of time in general relativity. Gödel published his discovery of closed timelike curves in 1949. ...
1
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2answers
96 views

Question about basic formalism of GR and the metric tensor

I really don't know much about GR, but I've come across a few rough sketches of its formalism in my DG books. I'm trying to piece it together to get a very basic intuition of what spacetime is in GR. ...
3
votes
0answers
54 views

Projector and delta function on a cycle $\Sigma$ of a manifold $\mathcal{M}_6$

In the paper ``Hierarchies from Fluxes in String Compactifications'' by Giddings, Kachru and Polchinski, the following example is considered for a localized source that may have negative tension (my ...
-3
votes
0answers
62 views

How can a black hole slow time down without increasing its own speed?

I read that speed of light is the only "speed" or rate of change allowed in universe when you consider 4-dimensional space-time where space and time are orthogonal to each other, which explains why ...
2
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3answers
299 views

Books on cosmology

I am a 14 year old who is independently studying physics. I finished the book: Spacetime and Geometry: An Introduction to General Relativity by Sean Carroll. I am specifically interested in cosmology, ...
8
votes
1answer
224 views

Is John Nash's “Interesting Equation” really interesting?

As recently mentioned in the news, before his passing, John Nash worked on general relativity. According to the linked article John Nash's work is available online from his webpage. His work is ...
2
votes
1answer
342 views

What happens to the total volume of a chunk of space that is being sucked into a black hole?

Does it increased, decrease, or stay the same? Maybe it explodes to infinity... Here is a similar question: Do black holes have infinite areas and volumes? But it's different because it asks how to ...
8
votes
2answers
538 views

How (or why) equivalence principle led to Einstein field equations?

If equivalence principle was origin of general relativity what was the process that this principle led Einstein to developed his theory of general relativity?
2
votes
2answers
282 views

How can we feel the effects of a Black Hole if all the mass is gone?

This question may help me learn more about the subtleties involved between the notions of gravity, in the Newtonian sense and those of curved spacetime, in the General Relativity sense. I will take ...
2
votes
0answers
26 views

How does one show that asymptotically $AdS_3$ spacetimes are locally $AdS_3$?

Time and again I keep reading that any asymptotic $AdS_3$ spacetime is locally isomorphic to $AdS_3$. I tried to find proof of this by analyzing the Riemann tensor $R_{\rho\sigma\mu\nu} $ in Ricci ...
1
vote
1answer
41 views

Interpretation for negative energy of curves

Let $(M,g)$ be a Lorentz manifold and $\gamma :[a,b] \to M$ a differentiable curve. I understand we define the energy of $\gamma $ as: $$E[\gamma] = \frac{1}{2} \int_a^b ...
4
votes
3answers
106 views

Closed timelike curves in the region beyond the ring singularity in the maximal Kerr spacetime

The region beyond the ring singularity in the maximal Kerr spacetime is described as having closed timeline curves. Why and/or how is the question. Now if you look a Kruskal-Szkeres Diagram (or a ...
1
vote
1answer
76 views

Are all elementary interactions arising from a gauge theory?

The standard model of particle physics is based on the gauge group $U(1) \times SU(2) \times SU(3)$ and describes all well-known physical interactions but with exception that gravity isn't involved. ...
1
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1answer
43 views

Will the rotation of a neutron star prevent it becoming a Black Hole?

This question, to me anyways, is basically a balancing act between 2 possibly opposing effects. Take a neutron star with just too small a mass to overcome it's degeneracy pressure, failing to ...
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0answers
35 views

Does the total particle energy increase in FRW Universe?

If a particle travels on a geodesic with 4-momentum $P^\mu$ in a spacetime with a Killing vector $K_\mu$ then we have a constant of motion, $K$, given by: $$K=K_\mu P^\mu$$ Using the relationships: ...
2
votes
1answer
73 views

Do Einstein's equations allow multiple solutions that agree in a neighborhood of a spacelike hypersurface?

This question is an extension of my a question that I have recently asked: Why doesn't a global frame of reference exist for GR?, where it was recommended that I post another question (so I am ...
2
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5answers
178 views

A ball in the gravity potential field of a black hole — seems a paradox

As illustrated in the following diagram (A, B, C, D are 4 specified space points, and C is close to a black hole), a small ball at distance of a black hole is stationary (suppose now it's mass is m0) ...