All Questions
17
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Does Mass Actually Displace Space-Time, or does Mass only Distort it?
1. Question
If a planet displaces space-time within it, and if a planet distorts the surrounding space-time surrounding it, then what does the phenomena of space-time look like from within that planet?...
- 99
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59
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Time dilatation of a free falling observer [duplicate]
I have two questions about time dilation near a black hole.
(I question) The relation $d\tau^2 = (1-\frac{r_s}{r}) dt^2$ between the proper time $d\tau$ of an observer near a B.H. and the time dt ...
- 21
2
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0
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419
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Clock synchronization and definition of simultaneity along a curve or contour in general relativity
What I understand so far
Fix a point $A$ with coordinates $x^\alpha$ with respect to a frame $K$ with metric tensor $g_{\alpha\beta}$. Then take an arbitrary point $B$ infinitesimally close to it with ...
- 21
1
vote
1
answer
436
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How do you get time dilation from $g_{00}$ in general and from the Schwarzchild metric in particular?
1.Why is the observer at the bottom measuring the proper time rather than the coordinate time?
2.How do we go from time dilation to $g_{00}$ or from $g_{00}$ to time dilation?
I'm trying to understand ...
user288901
2
votes
2
answers
262
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How do I deal with the radius-coordinate of the schwarzschild-metric in this numerical problem?
It is well known that if a black hole fulfills certain conditions, it's tidal forces will rip incoming objects apart even before they cross the event horizon. So at some point, the curvature of space ...
- 101
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1
answer
79
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Does Coordinate time make sense in a universe with wormholes?
Let us say that you have a spacetime with wormholes, and a coordinate system. The two ends are created at almost the same point in spacetime. Then the one end is taken far away and time dilated; (note:...
- 2,172
2
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52
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How is force transmitted through a gravitational well via matter in GR?
Lets say we have a hollow spherical shell of mass with a small hole in it. Inside the shell, the gravitation time dilation makes time pass $t_d$ times as fast as time passes infinitely far away. There ...
- 780
1
vote
1
answer
42
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Is our metrics and/or constants geocentric?
Considering that all our metrics is now based on physical constants as measured here on earth,
With earth having both gravity and velocity, as well as the whole solar system having too, and special ...
- 133
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2
answers
223
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What is the physical interpretation of the equation for the invariant interval in general relativity?
In my GR lecture I was given the following equation for the spacetime interval (signature $(+,-,-,-)$):
$$ ds^2=(1+\frac{2\phi}{c^2})c^2 \, dt^2-(1-\frac{2\phi}{c^2})\delta_{ij}\, dx^{i}dx^{j} \tag{1}...
- 1,037
2
votes
1
answer
200
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Spacetime geometry measurements inside an extremely dense spherical shell
From http://jila.colorado.edu/~ajsh/bh/schwp.html
The amount by which radial distance is "squished" is:
$ \dfrac{1}{\sqrt{ 1 - r_s/r}}$
where the Schwarzschild radial distance (or "...
- 347
0
votes
2
answers
463
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Gravitational Time Dilation Inside a Massive, Non-Uniform, Non-Rotating Sphere
I know the time dilation (relative to an observer at infinity) outside a non-rotating sphere can be found from the Schwarzschild metric to be $$t_{0}=t_{f}\sqrt{1-\frac{r_{s}}{r}}$$ where $r_{s}$ is ...
- 68
7
votes
1
answer
366
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How does time behave inside a massive spherical shell?
According to General relativity the clocks in our satellites in the atmosphere tick faster than those on Earth, as they are farther from the gravitational well of Earth and are free falling.
...
- 5,568
104
votes
2
answers
8k
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Is there such thing as imaginary time dilation?
When I was doing research on General Relativity, I found Einstein's equation for Gravitational Time Dilation. I discovered that when you plugged in a large enough value for $M$ (around $10^{19}$ ...
- 3,967
2
votes
1
answer
121
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Gravitational waves induce changes in the $h_{00}$ (time) component of the metric?
I'm rather stumped by a subtle point regarding metric perturbations of GW. I'm well aware the GW are able to produce changes in the flat space metric, They are transverse and have planes of ...
- 21
16
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2
answers
1k
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Time Dilation inside a hollow shell
Assuming I have a hollow shell with total mass $M$ and radius $r$.
On the surface, the gravitational time dilation would be
$$\tau=t \cdot \sqrt{1-\frac{v_{esc}^2}{c^2}}$$
where
$$v_{esc} = \sqrt{\...
- 12.4k