A theory that describes how matter produces and responds to 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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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 ...
9
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5answers
2k views

What methods can astronomers use to find a black hole?

How can astronomers say, we know there are black holes at the centre of each galaxy? What methods of indirect detection are there to know where and how big a black hole is?
6
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1answer
208 views

What makes us think we can actually detect gravitational waves?

This refers to the discussion about gravitational waves for the YouTube video LIGO Gravitational Wave Observatory. I have two questions: When the gravitational wave passes through the space where ...
5
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1answer
343 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
759 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
128 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
349 views

Another faster-than-light question

Imagine we have something very heavy (i.e supermassive black hole) and some object that we can throw with 0.999999 speed of light (i.e proton). We are throwing our particle in the direction of hole. ...
4
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2answers
468 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
2k views

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. ...
3
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1answer
156 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 ...
2
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1answer
124 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 ...
2
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2answers
552 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
257 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
266 views

How much extra distance to an event horizon?

How much extra distance would I have to travel through space to get from Earth to a stellar mass event horizon? (compared to the same point in space without a black hole)
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3answers
231 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
879 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
133 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
402 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 ...
12
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1answer
731 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 ...
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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 ...
20
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3answers
1k views

Is topology of universe observable?

There is an idea that the geometry of physical space is not observable(i.e. it can't be fixed by mere observation). It was introduced by H. Poincare. In brief it says that we can formulate our ...
18
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5answers
2k views

How does “warp drive” not violate Special Relativity causality constraints?

I'm talking about this nonsense: http://www.washingtonpost.com/news/post-nation/wp/2014/06/11/this-is-the-amazing-design-for-nasas-star-trek-style-space-ship-the-ixs-enterprise/ Now, I'm aware that ...
19
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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
3k 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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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 ...
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3answers
5k views

Why you need a graviton when you have the higgs boson?

Since I studied General Relativity I had this question running on my mind. As I see it (just taking lectures of Quantum Field Theory right now) "Why you need a gauge boson for gravity when the higgs ...
17
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3answers
323 views

Comparing predictions and reality for the gravitational attraction due to light beams

While doing some on-the-side reading, I stumbled across this question: Do two beams of light attract each other in general theory of relativity?. Great question and a great, easily understandable ...
17
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2answers
656 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
465 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 ...
11
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1answer
304 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 ...
10
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1answer
267 views

Spacetime Torsion, the Spin tensor, and intrinsic spin in Einstein-Cartan theory

In Einstein-Cartan gravity, the action is the usual Einstein-Hilbert action but now the Torsion tensor is allowed to vary as well (in usual GR, it is just set to zero). Variation with respect to the ...
5
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3answers
343 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 ...
19
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2answers
848 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. ...
18
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4answers
2k views

What does this depiction of a black hole in the movie Interstellar mean?

I was expecting a whirlpool in 3D and the matter glowing from friction as it nears the center, as I expected a event horizon to be negligible visually. How does this depiction work? How big is the ...
17
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4answers
1k views

Is there experimental evidence that massless particles such as photons attract massive objects?

For instance evidence that a highly energetic laser beam attracts objects nearby? In the framework of Einstein's general relativity all energy curves spacetime and hence exerts an attraction, but my ...
15
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3answers
1k views

No hair theorem for black holes and the baryon number

The no hair theorem says that a black hole can be characterized by a small number of parameters that are visible from distance - mass, angular momentum and electric charge. For me it is puzzling why ...
15
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4answers
729 views

Redshifting of Light and the expansion of the universe

So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light ...
11
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2answers
2k views

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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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 ...
11
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2answers
643 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 ...
8
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2answers
799 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 ...
7
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1answer
248 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 ...
6
votes
6answers
746 views

Physical meaning of non-trivial solutions of vacuum Einstein's field equations

According to Einstein, the space-time is curved and the origin of the curvature is the presence of matter i.e. the presence of the energy-momentum tensor $T_{ab}$ in Einstein's field equations. If our ...
4
votes
2answers
415 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) ...
2
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1answer
546 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: ...
16
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1answer
428 views

Building a wormhole

We regularly get questions about wormholes on this site. See for example Negative Energy and Wormholes and How would you connect a destination to a wormhole from your starting point to travel through ...
10
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4answers
1k 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
913 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 ...