# Tag Info

### Why don't we put satellites into an orbit where there is (almost) no time dilation/contraction compared to Earth's surface?

The higher the satellite's orbit, the more of the Earth it can see (and hence the fewer satellites you need to ensure complete coverage of the Earth). The particular orbits chosen for navigation ...

### Why don't we put satellites into an orbit where there is (almost) no time dilation/contraction compared to Earth's surface?

You have to differentiate between corrections that are sources of error and corrections that are well understood and can be accounted for. Time dilation is a well understood effect, and if you wanted ...
Accepted

### What exactly makes a black hole STAY a black hole?

After writing this answer, I noticed there are a couple alternative explanations that might be interesting to mention, so I'll add them as well. Explanation 1 What makes something into a black hole ...
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### If gravity is not a force, then how come gravitational assists work?

Well, gravity is a force and it isn't. What is a force anyway? It's what makes you accelerate, which is already a statement about a second-order derivative of one variable with respect to another, and ...

### Where does the curvature of space happen?

I think maybe it is the terminology that causes the difficulty. You don't have to use the word "curvature". You can start from the following observations. Observation 1. Define a straight ...

### Why don't two accelerated clocks behave like two clocks in a gravitational field?

Acceleration in special relativity works a bit differently from the Newtonian version. It takes a while to build up a new set of intuitions. A uniformly accelerating particle moves along a hyperbola ...

### What is the relevance of the Lorentz factor in general relativity?

$γ$ is a geometrical factor that would appear in Euclidean geometry also if it were taught in a slightly different way. A transformation between two Cartesian coordinate systems with a common origin ...
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### How do we know the assumptions of the Schwarzschild solution are valid?

This is a very long-winded answer, so let me state the punchline up front: the boundary condition you pointed out really is physically suspect, and probably not realized in Nature -- however using it ...
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### Is energy "equal" to the curvature of spacetime?

It is common see Einstein's equations described as "curvature equals energy", but that is not a complete description. The full description is complicated, which is exactly why we express it ...

### What is the cause of the constancy of the speed of light in vacuum?

The constancy of $c$ is an experimental result, verified to great precision. When we make mathematical models that assume the constancy of $c$, we get predictions that match other experimental results ...

### Torus shaped event horizon

There is a result in four-dimensional General Relativity that forbids such situations. Namely, the Hawking's Theorem on the Topology of Black Holes. It is given, e.g., on the classic book by Hawking ...

### How can a grain of sand be "spaghettified" when nearing a black hole?

The difference in gravity between the "front" and the "rear" of a grain of sand sent towards a black hole should/must be negligible, considering how weak gravity as a force is, ...

### Is spacetime isomorphic to a metric space?

Yes it is, but the found structure has no physical meaning in general. As a matter of fact, as a general result on differentiable (paracompact) manifolds, every smooth manifold $M$ (without a ...

### Why does acceleration in special relativity give rise to general relativity (and thus gravity)?

If we include accelerated motion in special relativity, the result is general relativity. This is simply not true. Special relativity can easily handle accelerated motion on its own. The result of ...
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### Why the ant on rubber rope paradox does not work in our universe or de Sitter universe?

In the ant-on-rope problem as stated in the Wikipedia article, the rope's expansion is linear. That means the ant's speed as a fraction of the rope length per unit time goes like $t^{-1}$, so the ...

### Schwarzschild metric with negative mass

Yes, the Schwarzschild solution with $M<0$ is still a vacuum solution to the Einstein equations. Bondi explored some ideas about negative mass in GR in this paper, in which he says As long as ...
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### Test for inertial frame of reference

The falling elevator's frame is inertial! Congratulations, you've found Einstein's equivalence principle. In relativity, we have to consider the proper acceleration, which is a 4-vector. Gravitational ...