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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.

6 votes
Accepted

Empty universe in the past, non-empty in the future

I believe that no such spacetime exists, if the matter is assumed to satisfy an inequality known as the dominant energy condition. The dominant energy condition says that, if $\xi$ is a future-directe …
Ted Bunn's user avatar
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5 votes

Should a neutron fall faster than a proton?

Yes, it should. There are a lot of subtleties involved in some questions like this (see some articles by Stephen Parrott available on arxiv.org if you want to start digging into this), but fortunatel …
Ted Bunn's user avatar
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2 votes

Should a neutron fall faster than a proton?

In addition to my original answer, I've scattered bits of an argument through various comments in this thread, but I don't think I've tied them all together very clearly. More importantly, I think I m …
Ted Bunn's user avatar
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10 votes
Accepted

Does gravitation of a sphere equal gravitation of a point?

Actually, the same result is true in general relativity: any spherically symmetric mass distribution gravitates in exactly the same way as a point mass. Here's the more precise statement: any spheri …
Ted Bunn's user avatar
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12 votes
Accepted

Brachistochrone problem in general relativity

Update: I made a number of mistakes in the original version of this post, although I think all the big ideas are right. I tried to fix everything, but I wouldn't be at all surprised if I've made addit …
Ted Bunn's user avatar
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4 votes
Accepted

Einstein's Field equations and impulse-energy tensor

The stress-energy tensor $T_{\mu\nu}$ on the right side of the Einstein equation characterizes all of the various forms of "stuff" in the spacetime. If there are electromagnetic fields in the spacetim …
Ted Bunn's user avatar
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5 votes

General Relativity Paradox: Holding a string across a gravitational gradient

It certainly is possible for two observers to remain at rest near a black hole, as long as they are both outside the horizon. They can stretch a string from one to the other, and they can bounce light …
Ted Bunn's user avatar
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14 votes

In GR, how do particles know how to fall in instead of out of a gravitational well?

If you take any solution to the geodesic equation, the time-reversal of that will also be a solution. If one describes a rock falling down in the Earth's gravitational field, the other will describe a …
Ted Bunn's user avatar
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20 votes
Accepted

Gravitational time dilation at the earth's center

The rule I mentioned in another question, that the time dilation factor is $1+\Delta\Phi/c^2$, applies here. The derivation (found in various textbooks) depends only on the assumptions that fields are …
Ted Bunn's user avatar
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26 votes
Accepted

Can a non-Euclidean space be descripted through an Euclidean space of higher dimension? So w...

You have to add more than one dimension, in general. Mathematicians have studied in great detail the question of how many extra dimensions you need in order to embed a curved manifold in a flat one. O …
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9 votes

Voyager local time dilation (caused by gravity)

There is in principle a "gravitational blueshift" for signals traveling from Voyager to us. The data rate we receive will be higher than the data rate transmitted by a factor $(1+\Delta\Phi/c^2)$, whe …
Ted Bunn's user avatar
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7 votes
Accepted

asymptotic curvature of the universe and correlation with local curvature

You have to be careful to distinguish between curvature of space and curvature of spacetime. When we say that the Universe is flat on large scales, we're talking about space -- that is, about a slice …
Ted Bunn's user avatar
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11 votes

How does the curvature of spacetime induce gravitational attraction?

I'm a bit worried about getting a reputation for citing myself too much, but I'll go for it anyway. (In my defense, I always admit it when I'm doing it!) John Baez's and my pedagogical paper The Mea …
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14 votes

Effect of gravitation on light

Michael Luciuk's answer is right, but there's an even stronger reason for rejecting this hypothesis: refraction in the corona would be wavelength-dependent, but the gravitational bending due to the Su …
Ted Bunn's user avatar
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14 votes

How will the Twin Paradox become, for Time Dilation, if no acceleration was ever involved?

You say that both twins are "exactly 20 years old." I assume you mean that they are both 20 years old at the same time. But part of the point of special relativity is that a phrase like "at the same t …
Ted Bunn's user avatar
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