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.

learn more… | top users | synonyms (1)

0
votes
0answers
15 views

Angular Optical Resolution [duplicate]

Can a series of optical telescopes from orbit (like the radio Event Horizon Telescope) see an object with higher resolution not possible with one telescope?
2
votes
2answers
126 views

With gravitational lensing could we see our selves from a right angle?

When looking at a black hole the ability to see ourselves is compromised by the small window for the light trajectory to come back to us. The light from the Earth that is bent by (almost) 180° and ...
5
votes
1answer
113 views

Simple metric of stellar collapse

Is there a simple metric (Lorentzian manifold) known which exhibits the formation of a black hole while not having any white hole counterpart and which moreover satisfies the strong and dominant ...
2
votes
1answer
75 views

Proving that Killing form contractions with geodesics are constants of motion

I want to prove the fundamental theorem of Killing forms, namely that $$\frac{d}{d \lambda} \Big( \frac{d P^{\mu}}{d \lambda} \xi_{\mu}(P(\lambda)) \Big) = 0 $$ If $P(\lambda)$ is a Geodesic ...
1
vote
1answer
61 views

Einstein tensor as a conserved current?

As is well-known, the ``traditional" conserved quantities (energy, momentum...) are Noether currents whose conservation depends on the existence of various Killing fields in Minkowski space. In ...
1
vote
2answers
118 views

Why can't gravitational force have repulsive counter part?

The valleys in the space-time curvature signifies the existence of an attractive body which causes the curvature. So why can't we say that the hills in the fabric of space-time is a source of ...
0
votes
0answers
20 views

relativity, light, transformations [duplicate]

is the light itself a reference frame in special relativity? Can we write the special relativity transformations between a photon and other reference frames? If we can't then what other transformation ...
4
votes
4answers
241 views

Can there be acceleration without velocity?

If I was in a spaceship continually accelerating at $9.81m/s^2 =1g$ in a straight line, I would reach near light speed within a year. On Earth, we are in a gravitational field of $1g$, which ...
3
votes
1answer
88 views

The Riemannian Penrose Inequality in higher dimensions

I am reading the proof of the Riemannian Penrose Inequality by Huisken and Ilmamen in The Inverse Mean Curvature Flow and the Riemannian Penrose Inequality and I was wondering why they restrict their ...
5
votes
3answers
404 views

Zero $g$ in a black hole?

At the very centre of the Earth, masses cancel each other out, creating an effective zero-$g$ environment. Would the same happen in a black hole?
1
vote
3answers
178 views

What is the physical meaning of the Levi-Civita connection?

I'm taking a course in General Relativity and I have studied the fundamental theorem of Riemannian geometry: Let $M$ be a manifold with metric $g$. Then exists an unique torsion-free connection ...
3
votes
1answer
122 views

I do not understand this comparison?

It is frequently discussed that to find solutions having some sort of supersymmetry is easier than solving Einstein’s equations of motion. I do not understand this discussion though. Specifically, ...
1
vote
2answers
150 views

Why supergravity is extension of GR?

Why is it that supergravity is an extension to general relativity? In what ways? What I have read until now says the following: GR got itself concerned with gravity after the revolution of special ...
0
votes
1answer
48 views

Rocket or elevator?

I realize the gravitational effect in a rocket can be equivalent to the gravity on the surface of Earth. I always hear there is no way to tell the difference between the two but if there were what are ...
1
vote
0answers
45 views

The spatial Schwarzschild metric

The Schwarzschild spacetime is defined by the following line element \begin{equation*} ds^2 = - \left( 1 - \frac{2m}{r} \right)dt^2 + \frac{1}{1-\frac{2m}{r}}dr^2 + r^2 d\theta^2 + r^2\sin \theta^2 ...
10
votes
3answers
779 views

Using a black hole as a mirror?

http://www.youtube.com/watch?v=ENd8Sz0AFOk The YouTube video is a good example how the gravity of this merging binary black holes bend light around themselves.
1
vote
1answer
99 views

Black hole merger orbital speed

If a ship is close to a black hole and we see it getting slower to the point if could see them not for red shift would almost stop moving. Then how fast is the little black hole moving in this video? ...
0
votes
1answer
53 views

See behind the black hole

Why in this video does the 2nd black hole appears to change size and appear larger the farther away it gets? How can you see behind it? http://www.youtube.com/watch?v=ENd8Sz0AFOk
0
votes
0answers
67 views

Black hole and relativity [duplicate]

This link shows movement around the black whole. It seems impossible for them to move this fast. http://www.youtube.com/watch?v=ENd8Sz0AFOk If we were able to watch a ship of people go into a black ...
0
votes
1answer
114 views

What exactly does the Kretschmann scalar implies and how does it work?

From the General Relativity class lectures I understood that this particular invariant, the Kretschmann scalar namely $$R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho}$$ is really important because, ...
1
vote
1answer
83 views

How can I prove that for a Killing vector $\nabla^a \nabla_a \xi^\mu = -R^b_a \xi^a$? [closed]

I'm taking a course on General Relativity and I'm trying to prove that for a Killing vector field $\xi^\mu$ the following equation holds: $$\nabla^a \nabla_a \xi^\mu = -R^\mu_a \xi^a$$ Where $R_ab$ ...
0
votes
1answer
52 views

Question 17 in section 2.9 in Schutz's A First Course in General Relativity [closed]

The question is as follows: Prove that any timelike vector for which $U^0>0$ and $\vec{U}\cdot \vec{U} = -1$ is the 4-velocity of some world line. I need to show that there exists a 4-vector ...
2
votes
3answers
41 views

What is the gravitational pull if one has as much mass above them as below them? [duplicate]

I understand the previous responses to other answering if you were at the center of a planet, would you be weightless? Yes you would due to the forces of gravity pulling at you from all sides. ...
1
vote
0answers
46 views

Proper time and asymptotic flatness

I'm trying to understand the concept of asymptotic flatness in general relativity, and came up with the following question: If the proper time $\tau$ is infinite for a timelike geodesic, does it mean ...
0
votes
0answers
36 views

Breakdown of correspondence principle: null dust case

In both quantum and general relativity theories we are used to provide results in the "limited" conditions to demonstrate a correspondence between new and old formalism. For instance deflection of ...
-1
votes
1answer
34 views

Comparing durations for two simply described motions in Schwarzschild geometry

I have some basic qualitative questions about the setup with: one satellite $A$ orbiting freely, on a stable circular path, a spherical non-rotating object of mass $M$; and another participant $B$ ...
25
votes
6answers
3k views

Why are Killing fields relevant in physics?

I'm taking a course on General Relativity and the notes that I'm following define a Killing vector field $X$ as those verifying: $$\mathcal{L}_Xg~=~ 0.$$ They seem to be very important in physics ...
0
votes
1answer
53 views

How can I prove that the covariant acceleration is normal to the velocity?

I'm trying to show that the covariant acceleration is normal to the velocity for a massive particle. I think that I understand why this has to happen because I understand the covariant acceleration as ...
3
votes
1answer
121 views

Diffeomorphism group vs. $GL(4,\mathbb{R})$ in General Relativity

I am quite confused with the groups Diff$(M)$ and $GL(4,\mathbb{R})$ in the context of general relativity. I understand that the symmetries of GR are the transformations that leave the equations ...
1
vote
0answers
75 views

How does bending in space-time caused by mass energy translate into acceleration of object? [duplicate]

Let say we have 2 similar apples separated by a distance apart, just their mass energy alone is sufficient to cause bending in the space-time. I think it is this bending in the space-time that cause ...
4
votes
4answers
185 views

What allows us to assume spacetime is flat when no normal matter is present?

Dark matter causes a bend in spacetime. We see this through gravitational lensing. But what allows us to assume spacetime is flat when no normal matter is present? Why can't we say that dark matter ...
1
vote
0answers
42 views

Variation of Bazanski Lagrangian

The Bazanski Lagrangian is defined as $$ L=g_{\alpha \beta }U^{\alpha }\frac{D\psi ^{\beta }}{Ds} $$ and $$ U^{\alpha }=\frac{\mathrm{d} x^{\alpha }}{\mathrm{d} s} $$ $x^{\alpha }$ is the ...
5
votes
3answers
105 views

Why does the curvature of space decrease during inflation but increase after it?

According to the Friedmann equation, curvature of space will increase with time/expansion of space, but I've also read that during Inflation, the expansion caused the Universe to flatten out. What is ...
5
votes
1answer
156 views

Is there a Maupertuis principle for General Relativity?

The motion of a point particle in classical mechanics is given by Newton's equation, $\mathbf{F}=m\mathbf{a}$. Suppose all forces considered are conservative and we have a constant total energy $h$. ...
4
votes
3answers
81 views

Can gravitational effects create a plane of the ecliptic?

Lots of questions about the why of the plane of the ecliptic, and good answers, but I was wondering about gravitational effects. If we picture for example, Saturn as being a few degrees above the ...
18
votes
1answer
530 views

Do light waves precisely follow null geodesic paths in General Relativity?

In special relativity one may show that a plane wave solution of Maxwell's equations (in a vacuum), of the form $A^a=C^a\mathrm{e}^{\mathrm{i}\psi}$ has the following properties: The normal ...
2
votes
1answer
105 views

How did inflation lead to the expansion of space?

Big bang Theory gives a scientific explanation of the evolution of the Universe, where the scientific picture of it starts with Universe(space) uniformly filled with matter and energy, already ...
4
votes
2answers
108 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 ...
8
votes
1answer
362 views

Simple quadrupole field not yet in Lorenz gauge?

I'm having trouble reproducing some of the results regarding gravitational waves in the Wald's General Relativity. In section 4.4 of gravitational radiation, eq.4.4.49 shows the far-field generated ...
6
votes
1answer
123 views

A question about gravity [duplicate]

Some time ago I encouraged by 11 year old son to watch Cosmos: A Spacetime Odyssey with Neil DeGrasse Tyson, and subsequently Cosmos: A personal Voyage with Carl Sagan, as well as other astronomy ...
3
votes
1answer
55 views

How does time look relatively in a gravity well? [duplicate]

Relativistically, when two frames, say A & B are moving apart inertially, then the clock of B will look slow compared to that of A; and the same holds for the clock of A from B. What does the ...
4
votes
0answers
62 views

How does Lorentz Contraction apply to the edge of a spinning disk and is Pi still constant?

This may seem like a dumb question, as I'm not really a physicist, but here it goes. So, π (3.14...) is the number of diameter distances required to equal the circumference of a 2D disk. Relativity ...
0
votes
3answers
99 views

Relativity: A modification on Sea Tower experiment

I first read about it on A Brief History of Time(Stephen Hawking). In 1962, a relativity experiment was executed: identical (classical) watches put on a water tower, one is on very high, other one is ...
0
votes
0answers
30 views

Guesses from a Rindler observer

Suppose an observer travels through Minkowski space $M=\mathbb{R}^4=\left\{x_0,x_1,x_2,x_3\right\}$ on a uniformly accelerated path: \begin{equation} \begin{cases} x_0= R \sinh(\frac{\tau}{R}) \\ x_1= ...
-1
votes
1answer
132 views

Is this picture of relativity correct? [closed]

Can forces be said to exist in a real sense in general relativity?
2
votes
2answers
227 views

Coordinate Singularity in Metric

Suppose I have some metric $$ds^2=g(t)dt^2+\frac{1}{r}dr^2$$ which has a singularity at $r=0$. However, if I make the coordinate transformation $u=\frac{1}{r}$, then I get: $$ds^2=g(t)dt^2+r^3 ...
0
votes
1answer
70 views

Launching of artificial satellites [closed]

Whose theory is used today during launching of artificial satellites, Newton's or Einstein's or any other? Which theory is better in launching of artificial satellites and other orbiting bodies, ...
3
votes
1answer
190 views

Unbounded perturbed geometry due to analyticity

I have an interesting mystery for you, loosely inspired on work related with this question. I have a certain Ansatz for a gravitational wave perturbation of the metric $h_{\mu \nu}$ that is nonzero ...
0
votes
1answer
63 views

Possible inconsistency of mixed index tensor notation

I am posting this here, because in my experience, this sort of thing exists in physics-related works only. Given a local frame $\{e_{(i)}\}$ on some $n$-dimensional manifold $M$, and given a local ...
2
votes
0answers
66 views

Is the equivalence principle Machian?

There is a lot of discussion on the subject of Mach's principle, and whether it has any place in the theory of relativity. But it seems to me that one could argue that Mach's principle is at the heart ...