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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What experimental proof has been found of Einstein's theory?

As a casual science reader, I've always found the implications of relativity (inconsistent clocks after near-light-speed travel and various space-time paradoxes) to be confusing and magical-sounding. ...
9
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2answers
1k views

Is there an energy density limit in GR?

I am speaking about GR with classical fields and energy. One question, spread over three increasingly strict situations: Is there an energy density limit in GR? (literally, can the energy density ...
8
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3answers
831 views

Covariant and contravariant vectors

Reading Weinberg's Gravitation and Cosmology, I came across the sentence (p.115, above equation (4.11.8)) The partial derivative operator $\partial/\partial x^\mu$ is a covariant vector, or in ...
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574 views

What is the geometrical interpretation of Ricci tensor?

In differential geometry and general relativity space is said to be flat if the Riemann tensor $R=0$. If the Ricci tensor on manifold $M$ is zero, it doesn't mean that the manifold itself is flat. So ...
6
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2answers
519 views

How general relativity gets to an inverse-square law

I understand that a general interpretation of the $1/r^2$ interactions is that virtual particles are exchanged, and to conserve their flux through spheres of different radii, one must assume the ...
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2answers
3k views

Does String Theory disagree with General Relativity?

I would like to expand on what I mean by the title of this question to focus the answers. Normally whenever a theory (e.g. General Relativity) replaces another (e.g. Newtonian Gravity) there is a ...
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1answer
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How could we travel to the nearest supermassive Black hole?

I have just watched a trailer for the upcoming movie Interstellar and started to wonder about some physics involved. In the end of the trailer, they are obviously plunging into a Black hole hoping to ...
5
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1answer
316 views

What is the entropy of the universe today?

What's the entropy of the universe today? How does one go about calculating this? I've heard the statement that black holes account for the bulk of the entropy in the universe today, but don't know ...
5
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3answers
550 views

References for ADM formalism and cosmological perturbation theory [closed]

What would you consider the best online resources for learning the 3+1 ADM formalism and gauge invariant perturbation theory in cosmology? (Assuming intermediate level GR and QFT familiarity)
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What is the evidence for Inflation of the early universe?

The theory of Inflation explains the apparent consistency of the universe by proposing that the early universe grew exponentially for a 1E-36 seconds. Isn't a simpler explanation that the universe is ...
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1answer
101 views

Bending of light - photon's inertia instead of mass

Using classical mechanics, the formula for gravitational attraction is $$F = G\frac{m_1m_2}{r^2}.$$ This formula does not work for photons, and we need to use Einstein's theory of gravity to ...
4
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2answers
1k views

Equation of everything

Is this equation in the image true? Can you give some topics that I can cover the equation? Similar equation from http://www.preposterousuniverse.com:
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740 views

The uncertainty principle and black holes

What are the consequences of applying the uncertainty principle to black holes? Does the uncertainty principle need to be modified in the context of a black hole and if so what are the implications ...
4
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1answer
732 views

How does Newton's 2nd law correspond to GR in the weak field limit?

I can only perform the demonstration from the much simpler $E = mc^2$. Take as given the Einstein field equation: $G_{\mu\nu} = 8 \pi \, T_{\mu\nu}$ ... can it be proved that Newton's formulation ...
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1answer
582 views

How does an object falling into a plain Schwarschild black hole appear from near the black hole?

I know that when viewed from infinity (or from a very large distance from the black hole event horizon), an object that falls into the black hole will appear to slow down and will become more and more ...
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2answers
482 views

Introduction to relativity books for an engineer [duplicate]

Possible Duplicate: Getting started general relativity I am an engineer who loves to read science fiction books especially when there's more science than fiction but usually I see that I ...
4
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1answer
651 views
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234 views

Time slowing down vs. universe expanding

Einstein said that it is impossible to distinguish between the effect of gravity and acceleration (so if you stand in an accelerating elevator in space it would not feel any different than if you were ...
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3answers
288 views

Can a single particle create a black hole?

Let us suppose a particle with so much energy $ E= h \frac{c}{\lambda} $ so $ \lambda $ is smaller than Planck's length ? Would it be possible? I mean if the particle has so much energy then its mass ...
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2answers
504 views

How does time dilate in a gravitational field having a relative velocity of v with the field?

Consider a Mass on earth. The time dilation on the surface of Earth is $$T' = T \sqrt{1 - \frac{2GM}{rc^2}}$$ Now if the mass is moving around the earth at velocity of v w.r.t Earth, what will be ...
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687 views

Anti-matter repelled by gravity - is it a serious hypothesis? [duplicate]

Possible Duplicate: Why would Antimatter behave differently via Gravity? Regarding the following statement in this article: Most important of these is whether ordinary gravity attracts ...
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3answers
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Is the speed of sound almost as high as the speed of light in neutron stars?

Have you ever wondered about the elastic properties of neutron stars? Such stars, being immensely dense, in which neutrons are bound together by the strong nuclear force on top of the strong gravity ...
7
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1answer
618 views

Can a deformable object “swim” in curved space-time? [duplicate]

Possible Duplicate: Swimming in Spacetime - apparent conserved quantity violation It is well known that a deformable object can perform a finite rotation in space by performing deformations ...
6
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2answers
204 views

Speed of gravity in cosmological codes and ephemeris generation

There are few questions in Phys.SE concerning the speed of gravity, and the answers are traditionally that the speed of gravity equals to the speed of light. But in that case I have three more ...
5
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1answer
414 views

If a magnetic monopole falls into a schwarzchild black hole, what happens to the magnetic field?

By the no-hair theorem, black holes can only have mass, charge and angular momentum. Does "charge" include "magnetic charge" (such as from a magnetic monopole)? Can black holes have magnetic charge ...
5
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1answer
933 views

Is 4-volume element a scalar or a pseudoscalar in special relativity?

In general relativity 4-volume element $\mathrm{d}^4 x = \mathrm{d} x^0\mathrm{d} x^1 \mathrm{d} x^2\mathrm{d} x^3$ is clearly a pseudoscalar (or scalar density) of weight 1 since it transforms as ...
4
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2answers
194 views

Why doesn't the light get out?

You're standing on a gedanken planet holding a laser pointer straight up. The light doesn't curve round, or slow down as it ascends, or fall down. It goes straight up. Now I wave my magic gedanken ...
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137 views

What is the notion of a spatial angle in general relativity?

Is there a notion of spatial angles in general relativity? Example: The world line of a photon is given by $x^{\mu}(\lambda)$. Suppose it flies into my lab where I have a mirror. I align the mirror ...
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565 views

Is it possible to have faster-than-light movement in General Relativity?

The speed of light as the maximal possible speed is build into Special Relativity as a premise of the theory. However I know of no such premise in General Relativity. When looking at two stars laying ...
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2answers
105 views

Are time and gravity affected when at rest compared to free fall?

A falling object moves along a geodesic path ('straight path') in spacetime. When it comes to rest it now follows a 'curved path' through spacetime. Is the passage of time and force of gravity ...
2
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1answer
329 views

A clock in freefall

Time dilation calculated using Schwarzschild metric for a non rotating spherical body is: $$t_0=t_f\sqrt{1-\frac{2GM}{rc^2}}$$ For such a non rotating spherical body, what would the time dilation of ...
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3answers
2k views

How energy curves spacetime?

We know through General Relativity (GR) that matter curves spacetime (ST) like a "ball curves a trampoline" but then how energy curves spacetime? Is it just like matter curvature of ST?
2
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1answer
148 views

From Euler-Lagrange equation to non affine geodesic equation

I have some problems to demonstrate the non affine geodesic equation from Euler-Lagrange's equations. I start defining the Lagrangian $L=\sqrt f$, but then I'm not able to find the Christoffel ...
2
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2answers
448 views

Local inertial coordinates/Fermi normal coordinates

It is said that we can introduce local inertial coordinates/Fermi normal coordinates for any timelike geodesic. But why only for timelike geodesics? What about null geodesics? Perhaps it has to do ...
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2answers
698 views

Expression for distance of closest approach in Schwarzschild Geodesics

The Wikipedia article Two-body problem in General Relativity uses two length-scale variables, $a$ and $b$, to simplify the math. For some information about these, consider these statements from the ...
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3answers
285 views

Why can't we think of free fall as upside down rocket?

/\ / \ | | | m | | | ------ <--- floor (Rocket A) This rocket is accelerated (g) upwards then mass(m) falls on the floor. ...
2
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1answer
658 views

$N$-body simulation in General Relativity

How would one perform an $N$-body simulation in General Relativity (GR) for something like galaxy formation or galactic dynamics? Suppose one wants to simulate the rotation curve $v(r)$ for galaxies ...
2
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7answers
459 views

Can astronomers directly detect black holes?

Are there any methods of direct detection for black holes? I'm not referring to gravitational lensing, or measuring the orbits of a star in a binary pair. Is there any way of directly 'seeing' them? ...
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1answer
81 views

Tidal affect on an object and the length contraction in Relativity Theory

According to the equivalence principle in general relativity theory; If an object are in free falling in a gravitational field,the object will not detect gravitational force on it. From this ...
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1answer
303 views

How to calculate spatial distance in space-time?

Pinning two test particles at two different points in space, how can I calculate their spatial distance, when the geometry is given by the Schwarzschild metric? Let's say particle 1 is pinned at ...
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1answer
137 views

Can the vanishing of the Riemann tensor be determined from causal relations?

Given a Lorentzian manifold and metric tensor, "$( M, g )$", the corresponding causal relations between its elements (events) may be derived; i.e. for every pair (in general) of distinct events in set ...
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2answers
987 views

Neutrino unaffected by gravity

Are neutrinos affected by gravity? If not, could that be a plausible reason for a neutrino taking a shorter path than light, since light is affected by gravity?
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2answers
189 views

Can relativistic momentum (photons) be used as propulsion for 'free' after the initial generation?

In discussing this question about propelling a spacecraft with photons and their relativistic momentum, the author asked that I restate my comment as another question. If photons can really be used ...
0
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2answers
660 views

Time Dilation in Orbits in the Schwarzschild Metric

I am wondering if there exist closed form-expressions for the time dilation experienced by an observer in different orbits around a Schwarzschild black hole, outside the event horizon, relative to ...
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1answer
54 views

What is the relationship between $a$ and $m$

$a$ is defined in HERE What is the relationship between the length-scale $a$ and the mass $m$?
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4answers
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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_{\ ...
15
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1answer
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Euclidean derivation of the black hole temperature; conical singularities

I am studying the derivation of the black hole temperature by means of the Euclidean approach, i.e. by Wick rotating, compactifying the Euclidean time and identifying the period with the inverse ...
17
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2answers
488 views

Global Properties of Spacetime Manifolds

When solving the Einstein field equations, $$R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R = 8\pi GT_{\mu\nu}$$ for a particular stress-energy tensor, we obtain the metric of the spacetime manifold, ...
13
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1answer
833 views

Why is there no dynamics in 3D general relativity?

I heard a couple of times that there is no dynamics in 3D (2+1) GR, that it's something like a topological theory. I got the argument in the 2D case (the metric is conformally flat, Einstein equations ...
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7answers
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How precisely does a star collapse into a black hole?

I think we all heard general statements like "once big enough star burns out there is nothing to prevent the gravitational collapse ending in a black hole". But I can't remember even seeing the ...