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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.

2
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What the mechanics arises if to take limit of general relativity with massless particles interacting with strong fields? Suppose there a system of attracting particles that have zero rest mass. Wha …
answered Dec 7 '12 by Stan Liou
4
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Not necessarily the original source of the term, but the earliest use I can find, occurs in Brandeis University Summer Institute in Theoretical Physics, 1964 Vol. 1: Lectures on General Relativity, wh …
answered Jun 3 '14 by Stan Liou
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Thinking from conservation of energy, It seems like for an object moving toward them, they should be able to "swing" into and out of a black Hole's event horizon no matter how strong the gravitatio …
answered Oct 28 '15 by Stan Liou
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There is no mention of Euclidean space here, because the $2$-spheres are not Euclidean. They're not going to be embedded in Euclidean space either. The Schwarzschild $r$ coordinate is defined so as to …
answered Dec 20 '13 by Stan Liou
4
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It's worthwhile to extend the thrust of Ted Bunn's approach to more general cases. Suppose you have a general static spacetime $$ds^2 = -e^{2\nu} dt^2 + h_{ij}dx^idx^j,$$ where the Latin indices sum o …
answered Aug 16 '11 by Stan Liou
46
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The general answer is "it depends." Light has energy, momentum, and puts a pressure in the direction of motion, and these are all equal in magnitude (in units of c = 1). All of these things contribute …
answered Mar 2 '11 by Stan Liou
4
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The signature of the metric, i.e., the number of positive and negative eigenvalues, is coordinate-independent, so if you already require your metric to have a certain signature, that's not going to ch …
answered Dec 22 '13 by Stan Liou
5
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In standard formulations of general relativity, it is simply an assumption of the theory designed so that the affine geodesics given by the connection match the metrical geodesics given by extremizing …
answered Mar 15 '14 by Stan Liou
5
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In special relativity, unaccelerated observers cannot do any experiment to determine their state of motion in any absolute sense--all meaningful motion is relative to something else. We want to gen …
answered Aug 12 '11 by Stan Liou
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In the weak-field case, $$\mathrm{d}s^2 = -\left(1+2\frac{\Phi}{c^2}\right)c^2\mathrm{d}t^2 - \frac{4}{c}A_i\mathrm{d}t\mathrm{d}x^i + \left(1-2\frac{\Phi}{c^2}\right)\mathrm{d}S^2\text{,}$$ where $\P …
answered Apr 21 '13 by Stan Liou
2
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The weak-field static metric is appropriate for the Earth: $$ds^2 = -(1+2\Phi)dt^2 + (1-2\Phi)\underbrace{(dx^2+dy^2+dz^2)}_{dS^2}\text{,}$$ where $\Phi$ is the gravitational potential, so the time di …
answered Feb 20 '14 by Stan Liou
14
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The event horizon is a lightlike surface, and so its area is coordinate-invariant. For a Schwarzschild black hole, $$ds^2 = -\left(1-\frac{2m}{r}\right)dt^2 + \left(1-\frac{2m}{r}\right)^{-1}dr^2 + r^ …
answered Dec 5 '12 by Stan Liou
8
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This is cool because $E=mc^2$ can act as some sort of uncertainty relation; if you have a population of photons with energy $E$, they are engendered with a mass $\frac{E}{c^2}$, no matter what my i …
answered Nov 29 '12 by Stan Liou
2
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Some of the conditions for Newtonian gravitation to work are: All particles must be slow, as compared to the speed of light in vacuum. The Newtonian potential $\Phi$ must must likewise not change to …
answered Apr 27 '13 by Stan Liou
2
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A black hole is a region of spacetime enclosed by an event horizon. Thus, the singularity, while a fact about black holes as far as we understand them, is not an defining feature of what black hole is …
answered Apr 19 '15 by Stan Liou

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