All Questions
66
questions
2
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3
answers
246
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Orbit description in Schwarzschild metric
Suppose to have a restricted 2-body system (BH + star with $M_{BH}\gg M_{\mathrm{star}}$) and you want to describe the orbit of the star relative to the BH, i.e. in the Schwarzschild metric.
Usually, ...
- 169
0
votes
1
answer
63
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Don't Geodesics change due to other geodesics?
So the geodesics that point towards the Earth brings space-time towards the Earth and then back out again, but then the moon has its own geodesics so wouldn't it be kind of like geodesics affecting ...
- 1,534
0
votes
1
answer
76
views
What is the expression for strong field Schwarzschild circular orbit perihelion precession?
How can you calculate how large the perihelion shift should be under Schwarzschild conditions in general relativity for minimally disturbed circular orbits in the strong field limit?
I think there is ...
- 729
1
vote
0
answers
81
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Photon speed for an observer at the photon sphere [closed]
I am asked to compute the orbital period of a photon, in the Scwarzschild spacetime, at the photon sphere for an observer at the same radius, $r^\star=3M$. I have computed the result, $\Delta T=6\pi M$...
1
vote
2
answers
230
views
Can the Schwarzschild orbit equation be solved exactly?
The Schwarzschild orbit is
$U'' + U = 1 + \varepsilon \cdot U^2$.
I've only seen turning-point analysis that demonstrates shift of perihelion.
Is there an exact solution?
- 77
1
vote
2
answers
173
views
How does the speed (and kinetic energy) necessary to orbit a black hole vary with the radius of orbit?
I understand that closer orbits around Schwarzschild black holes require faster speeds, culminating in a required speed of $c$ at the photon sphere ($r = 3M$ in Schwarzschild coordinates). I'd love to ...
- 235
0
votes
4
answers
244
views
Can Schwarzschild acceleration be written in exact form as a function of position and velocity vector?
For the special case of only one massive point-shaped or spherically symmetric non-rotating body and a small "test mass" body under general relativity the movement of that small body is ...
- 729
0
votes
1
answer
47
views
Inclination angle of a ray in a static spacetime
In accordance with Synge (equation 8) of the ray with respect to the radial direction in a static Schwarzschild spacetime is
$$ \cot \psi = \left(1 - \rho^{-1} \right)^{-1/2} \rho^{-1} \frac{d \rho}{d ...
- 115
3
votes
1
answer
94
views
In a binary black hole system, can one of the black holes get ejected before merging in some contexts?
As it is said here (https://physicsworld.com/a/couple-emerges-from-trio-of-supermassive-black-holes/) a system of two orbiting black holes could disrupt the gas and stars at the center of the galaxy ...
- 2,462
0
votes
1
answer
51
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Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? [duplicate]
Could a Star orbit a rotating black hole inside the ergosphere? If so, how big should the black hole be? I imagine it should be absolutely massive so that tidal forces are minimal.
And if all this is ...
1
vote
1
answer
115
views
Innermost stable circular orbit for rotating black holes + length contraction
I viewed many relevant threads but didn't quite find the answer. I don't really know what I'm talking about so I'm mostly looking for a lead on how I should be thinking about this
From my ...
3
votes
4
answers
773
views
Orbital Velocity Formula in Schwarzschild metric
What is the orbital velocity formula in Schwarzschild metric assuming that the orbit is circular? this formula should also work for relativistic velocities.
- 31
1
vote
1
answer
331
views
What is innermost unstable circular orbit (IUCO)?
In the paper Tachyon motion in a black hole gravitational field by V. M. Lipunov he writes:
(…) Circular orbits for tachyons begin at the distance of $ 3/2~r_g $, i.e., at the distance of the ...
- 1,948
1
vote
1
answer
46
views
Closest possible orbital radius for equal masses
If you have two objects of equal mass, then what’s the closest distance that they can orbit at in terms of their schwarzschild radii? How fast would they be orbiting?
What About stable orbits?
- 2,908
3
votes
0
answers
98
views
Can light orbit an object that is NOT a black hole?
I know that light can enter into an unstable circular orbit around a black hole, at a distance of its innermost bound circular orbit (IBCO) $\frac{3r_s}{2}$ where $r_s$ is the Schwarzschild radius of ...
- 31