8
votes
Can perfectly stable orbits exist in GR?
As you say, GR implies that all orbits lose energy (very slowly) over time, due to gravitational waves. Also the vacuum of space is not true vacuum and there is some drag from the intergalactic medium ...
- 6,102
8
votes
Can perfectly stable orbits exist in GR?
In the literature, the orbits you are looking for a called “floating orbits”. Floating orbits are not possible in plain GR (See e.g. 1302.1016).
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7
votes
Accepted
Is the size of a black hole singularity smaller than a fundamental particle?
The very short answer to this is: We have no idea.
General relativity predicts that the singularity of a Schwarzschild black hole (which I assume is what you mean by "actual black hole") is ...
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6
votes
Can perfectly stable orbits exist in GR?
In the 1979 paper "Time without end", Freeman Dyson calculates a time in the order of 1020 years until the earth would fall into the sun due to gravitational decay alone, based on the ...
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6
votes
Is the size of a black hole singularity smaller than a fundamental particle?
While @paulina's answer: we don't know is correct, because quantum gravity is not understood, I'll answer for a classical Schwarzschild blackhole as described by Kip Thorne.
The size is zero, however ...
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5
votes
Is the size of a black hole singularity smaller than a fundamental particle?
We know that black hole is infinitely densed.
More exactly: The theory of general relativity predicts
that the center of a black hole is infinitely dense.
This theory predicts very well everything ...
- 40.1k
2
votes
Necessity of Singularity in General Relativity
Well the famous singularity theorems show (very very roughly speaking) that in the theory of classical GR, collapse beyond horizon implies a singularity. Classical GR is not the true theory of physics,...
- 1,447
2
votes
Accepted
Two contradictory derivations of Killing equation
As an overall comment, I stress that conservation of $Q$ is valid for the Killing vector $\xi$ if the considered curve is a geodesic.
Let us come to the issue.
First of all, generally speaking, the ...
- 73.8k
2
votes
Two contradictory derivations of Killing equation
Both approaches are fine.
In the first approach, the analysis is done at the coordinate/component level of the equations. Simply asking the question how does $Q$ very with $\tau$ if we write ...
- 12.5k
1
vote
Distance and luminosity distance
Using the inverse square law we can deduce that the flux F(watts/m^2) received from a source with an intrinsic luminosity L(watts) diminishes as a function of distance squared so $F \propto L/D_e^2$ ...
- 6,102
1
vote
Necessity of Singularity in General Relativity
What is it that preludes the predicted field, even at $r<r_{Schwarzschild}$, from simply terminating at the surface of a collapsar of dense matter, and taking some other form inside it?
This is ...
- 12.7k
1
vote
Boundary conditions on transition maps on general relativity
There's nothing fancy going on with transition maps. What a mathematician means by a "transition map", in the setting of general relativity, is nothing more or less than a coordinate change ...
- 289
1
vote
Hawking Temperature of the BTZ Black Hole
Another option for finding the Hawking temperature of the BTZ black hole is by the formalism of the surface gravity $\kappa$ which connected to the Hawking temperature via:
$$T_H=\frac{\kappa}{2\pi}$$
...
1
vote
Accepted
Cause of Coordinate Acceleration in Free Fall
The acceleration on a particle following a geodesic is defined by the Christoffel symbols which are in turn defined in terms of the metric.
More properly, all inertially-moving objects not affected by ...
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1
vote
Trying to understand a visualization of contravariant and covariant bases
Given the metric tensor for the basis vectors
$$A = \begin{bmatrix}\mathbf e_1 \cdot \mathbf e_1 & \mathbf e_1 \cdot \mathbf e_2 \\
\mathbf e_2 \cdot \mathbf e_1 & \mathbf e_2 \cdot \mathbf ...
- 902
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