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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Is causality a total order?

I've read that it is physically not possible to violate causality defined as a total order on the spacetime graph. So I was wondering if at least causality can be broked down to a partial order and if ...
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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?
4
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4answers
239 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 ...
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2answers
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Incompatibility Between Relativity and Quantum Mechanics

Why does Gravity distort space and time while the electromagnetic, strong, and weak forces do not? Does this have to do with why Quantum Mechanics and Relativity are incompatible?
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4answers
4k views

How is inertial mass different from gravitational mass? [duplicate]

I recently read that the mass we deal with in Equation $F=M_{i}a$ is called inertial mass and the mass we deal with in $F=M_{g}g$ is gravitational mass. Suppose I take a ball in a free fall and in ...
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3answers
853 views

General relativity (gravitation) in time and one spatial dimension

I don't have any idea of general relativity but intend to learn. Is it a good idea to study general relativity in two dimensions (time and single spatial dimension) in the begining to get good idea on ...
2
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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 ...
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6answers
9k views

Why is gravitation force always attractive?

Why is the gravitational force always attractive? Is there another way to explain this without the curvature of space time? PS: If the simple answer to this question is that mass makes space-time ...
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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 ...
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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 ...
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2answers
4k views

maximum rotational speed

I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
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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 ...
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2answers
87 views

How to calculate the event horizon and the cosmological radius in a metric?

From reading about general relativity, the event horizon and the cosmological radius are the radius when $f(r)=0$, in the metric $$ ds^{2}=-f(r)dt^{2}+\frac{dr^{2}}{f(r)}+r^{2}d\Omega^{2} $$ However, ...
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1answer
89 views

Physical motivation for mathematically extending solutions to Einstein's equations

Sorry if this question gets a little long; I want to explain why I'm asking it. The usual Schwarzchild metric $$ds^2 = -\left(1-\frac{2M}{r}\right) dt^2 + \left(1-\frac{2M}{r}\right)^{-1} dr^2 + ...
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3answers
403 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?
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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 ...
3
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1answer
87 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 ...
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3answers
176 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 ...
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3answers
247 views

Why doesn't a global frame of reference exist for GR?

I only have at best a layperson's familiarity with GR, so forgive me if I am asking a basic question, but I have heard that in GR, we cannot have a global frame of reference, that is a frame of ...
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1answer
102 views

Free fall and gravitational time dilation

An observer A at rest in a gravitational field has some amount of time dilation relative to an observer B far away from the gravitational field. Would the clock of an observer C in free fall at the ...
2
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1answer
235 views

Do free falling observers see gravitational blueshift?

Observers at rest in gravitational fields will see infalling light signals as blueshifted. Do inertial observers in free fall in a gravitational field see the same shift? If someone is standing on a ...
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4answers
7k views

What is the physical meaning of the connection and the curvature tensor?

Regarding general relativity: What is the physical meaning of the Christoffel symbol ($\Gamma^i_{\ jk}$)? What are the (preferably physical) differences between the Riemann curvature tensor ($R^i_{\ ...
3
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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, ...
3
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3answers
9k views

Can a light be bent by a magnetic field?

I'm struck with two competing ideas on the question in the title. Listing #1: http://van.physics.illinois.edu/qa/listing.php?id=2009 How far can a magnetic field bend light? A: Unfortunately, the ...
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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 ...
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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 ...
6
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4answers
400 views

What is the general relativity explanation for why objects at the center of the Earth are weightless?

The idea that as you move through the earth you get a symmetric cancelling of gravitational acceleration which approaches zero acceleration due to gravity at the center of the earth makes a lot of ...
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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 ...
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1answer
113 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, ...
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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
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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 ...
2
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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
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1answer
82 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
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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 ...
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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 ...
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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 ...
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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 ...
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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 $B$ ...
12
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4answers
809 views

Why didn't Newton have a cosmological constant

Einstein initially added the Cosmological Constant because (if I get this right) it seemed to him that the universe should be static. I agree that back then this would have been an obvious assumption. ...
0
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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 ...
4
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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 ...
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 ...
20
votes
4answers
7k views

Does gravity slow the speed that light travels?

Does gravity slow the speed that light travels? Can we actual measure the time it takes light from the sun to reach us? Is that light delayed as it climbs out of the sun's gravity well?
8
votes
1answer
361 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 ...
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 ...
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 $h$. ...
13
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3answers
4k views

Is gravitational time dilation different from other forms of time dilation?

Is gravitational time dilation caused by gravity, or is it an effect of the inertial force caused by gravity? Is gravitational time dilation fundamentally different from time dilation due to ...
5
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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 ...
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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 ...
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1answer
132 views

Is this picture of relativity correct? [closed]

Can forces be said to exist in a real sense in general relativity?