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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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 ...
5
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1answer
385 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
876 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 ...
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2answers
132 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 ...
4
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2answers
524 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
95 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
284 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?
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2answers
631 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 ...
2
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3answers
270 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. ...
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1answer
77 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
132 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
935 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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1answer
218 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 ...
0
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2answers
158 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
573 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
51 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
5k 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_{\ ...
13
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1answer
783 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 ...
18
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7answers
2k views

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 ...
28
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3answers
1k views

The Pioneer anomaly finally explained?

Pioneer 10 & 11 are robotic space probes launched by the NASA in the early 1970's. After leaving our solar system, an unusual deceleration of both spacecrafts has been measured to be approximately ...
10
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3answers
1k views

Group Theory in General Relativity

In Special Relativity, the Lorentz Group is the set of matrices that preserve the metric, i.e. $\Lambda \eta \Lambda^T=\eta$. Is there any equivalent in General Relativity, like: $\Lambda g ...
20
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5answers
1k views

Does antimatter curve spacetime in the opposite direction as matter?

According to the Dirac equation, antimatter is the negative energy solution to the following relation: $$E^2 = p^2 c^2 + m^2 c^4.$$ And according to general relativity, the Einstein tensor (which ...
18
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3answers
4k 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?
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2answers
718 views

is there a way to split a black hole?

Classically, black holes can merge, becoming a single black hole with an horizon area greater than the sum of both merged components. Is it thermodynamically / statistically possible to split a black ...
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5answers
2k views

Why does no physical energy-momentum tensor exist for the gravitational field?

Starting with the Einstein-Hilbert Lagrangian $$ L_{EH} = -\frac{1}{2}(R + 2\Lambda)$$ one can formally calculate a gravitational energy-momentum tensor $$ T_{EH}^{\mu\nu} = -2 \frac{\delta ...
13
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1answer
497 views

What are the local covariant tensors one can form from the metric?

Normally in differential geometry, we assume that the only way to produce a tensorial quantity by differentiation is to (1) start with a tensor, and then (2) apply a covariant derivative (not a plain ...
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4answers
703 views

Event horizons without singularities

Someone answered this question by saying that black hole entropy conditions and no-hair theorems are asymptotic in nature -- the equations give an ideal solution which is approached quickly but never ...
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3answers
411 views

Is there any relationship between gauge field and spin connection?

For a spinor on curved spacetime, $D_\mu$ is the covariant derivative for fermionic fields is $$D_\mu = \partial_\mu - \frac{i}{4} \omega_{\mu}^{ab} \sigma_{ab}$$ where $\omega_\mu^{ab}$ are the spin ...
30
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4answers
3k views

Why does a flat universe imply an infinite universe?

This article claims that because the universe appears to be flat, it must be infinite. I've heard this idea mentioned in a few other places, but they never explain the reasoning at all.
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3answers
658 views

Is there a thought experiment which brings to light the contradiction between General Relativity and Quantum Mechanics?

I've been told that GR and QM are not compatible, is there an intuitive reason/thought experiment which demonstrates the issue? (Or one of the issues?)
11
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1answer
338 views

General definition of an event horizon?

Horizons are in general observer-dependent. For example, in Minkowski space, an observer who experiences constant proper acceleration has a horizon. Black hole horizons are usually defined as ...
11
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3answers
2k views

What is the exact gravitational force between two masses including relativistic effects?

I was wondering if there is a closed-form formula for the force between two masses $m_1$ and $m_2$ if relativistic effects are included. My understanding is that the classic formula $G \frac{m_1 ...
8
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2answers
1k views

What happens to orbits at small radii in general relativity?

I know that (most) elliptic orbits precess due to the math of general relativity, like this: source: http://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity I also know that something ...
8
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1answer
255 views

Plausible explanations for 3 local space dimensions

Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons). One such of course ...
3
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1answer
632 views

Dirac Equation in General Relativity

Dirac equation for the massless fermions in curved spase time is $γ^ae^μ_aD_μΨ=0$, where $e^μ_a$ are the tetrads. I have to show that Dirac spinors obey the following equation: ...
19
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2answers
971 views

Gravitational slingshot of light using a black hole/massive object

Wikipedia has this page on gravity assists using planets. In some cases this effect was used to accelerate the spacecraft to a higher velocity. This diagram shows this in a very oversimplified manner. ...
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2answers
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How can a singularity in a black hole rotate if it's just a point?

I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely ...
11
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2answers
779 views

Equivalence of definitions of ADM Mass

ADM Mass is a useful measure of a system. It is often defined (Wald 293) $$M_{ADM}=\frac{1}{16\pi} \lim_{r \to \infty} \oint_{s_r} (h_{\mu\nu,\mu}-h_{\mu\mu,\nu})N^{\nu} dA$$ Where $s_r$ is two ...
7
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1answer
805 views

Counting degrees of freedom for gravitational waves as a gauge field

Sean Carroll has a new popularization about the Higgs, The Particle at the End of the Universe. Carroll is a relativist, and I enjoyed seeing how he presented the four forces of nature synoptically, ...
5
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3answers
373 views

Setting up a local-coordinate system in space-time using only a single clock and light beams

I have a question to ask about the operationalist view of space-time. I am a mathematician who happens to be interested in physics, so if anyone thinks that my question is a silly or vague one, please ...
4
votes
2answers
438 views

Diff(M) and requirements on GR observables

This question is kind of inspired in this one: Diff(M) as a gauge group and local observables in theories with gravity The conundrum i'm trying to understand is how is derived the (quite) ...
1
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2answers
222 views

Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
10
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3answers
653 views

Equation of motion of a photon in a given metric

I have this metric: $$ds^2=-dt^2+e^tdx^2$$ and I want to find the equation of motion (of x). for that i thought I have two options: using E.L. with the Lagrangian: $L=-\dot t ^2+e^t\dot x ^2 $. ...
10
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4answers
2k views

Can spacetime exist in the absence of matter and energy?

I'm pretty sure Ernst Mach would have said that spacetime cannot exist without matter in it. But I'm also pretty sure that a black hole can be described as a self-sustaining gravitational field, ...
10
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3answers
1k views

What is the capture cross-section of a black hole region for ultra-relativistic particles?

What is the capture cross-section of a black hole region for ultra-relativistic particles? I have read that it is $$\sigma ~=~ \frac{27}{4}\pi R^{2}_{s}$$ for a Schwarzschild BH in the geometric ...
10
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1answer
938 views

Open problems in General Relativity [closed]

I would like to know if there are some open mathematical problems in General Relativity, that are important from the point of view of Physics. I mean is there something that still needs to be ...
8
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6answers
483 views

Objects in Physics as a mathematician would see them

I'm a mathematician with hardly any knowledge of physics. Before I start reading volumes of physics books, I have a few questions that have been bugging me and that will help me start reading physics. ...
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2answers
601 views

Parallel Transport of a 4-vector

Why does the parallel transported $4$-vector change from $X^a(x)$ to $X^a(x) + \bar{\delta}X^a(x)$ ? This is also discussed in D'Inverno's relativity book [page - 72]; but the reason is not clear.
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1answer
125 views

Explanation for “if all accelerated systems are equivalent, then Euclidean geometry cannot hold in all of them”

I'm doing an EPQ (mini college research paper) on gravity, and I found a site that explained things in simple terms. I am having trouble understanding how Einstein came to his revelation space-time ...