Orbits around a Schwarzschild/Kerr black hole

In summary, the conversation discusses the precession of a test particle around a black hole and whether there is an exact expression for the rate of precession for both a Schwarzschild and Kerr black hole. It is mentioned that such expressions exist for a Schwarzschild black hole and that a freely accessible program may be available to compute such orbits. The paper "Geometric transport along circular orbits in stationary axisymmetric spacetimes" is recommended as well as the paper "Precession of Mercury in General Relativity, the Cosmological Constant and Jacobi's Inversion problem."
  • #1
FunWarrior
4
1
Hi everybody,

Around a black hole, a test particle can experience two types precession: of its pericenter and of its angular momentum vector. I would like to know if there exist an EXACT expression for the rate at which these two precession occurs both for a Schwarzschild and a Kerr black hole for a given orbit (with known energy and angular momentum vector).

If I am not mistaken, such expressions exist for a Schwarzschild black hole. In this case, there is no precession of the angular momentum vector (the orbit is planar) and the apsidal precession rate is obtained through an elliptical integral. However, I am not sure about the case of a Kerr black hole.

Could you help me with my problem? Also, I was wondering if there exist a freely accessible program to compute such orbits.

Thank you in advance.
 
Physics news on Phys.org
  • #2
You might find the following paper useful-

Geometric transport along circular orbits in stationary axisymmetric spacetimes
Donato Bini, Christian Cherubini, Gianluca Cruciani, Robert T. Jantzen
http://arxiv.org/abs/gr-qc/0407004
 
  • #3
Here is the exact solution of Schwarzschild elliptical orbits

G. V. Kraniotis, S. B. Whitehouse,
Precession of Mercury in General Relativity, the Cosmological Constant and Jacobi's Inversion
problem.
Preprint http://128.84.158.119/abs/astro-ph/0305181v3
 

1. How does the presence of a black hole affect the orbits of surrounding objects?

The presence of a black hole creates a strong gravitational pull that can significantly alter the orbits of surrounding objects. This is due to the intense curvature of spacetime around the black hole, which can cause objects to follow highly elliptical or even spiral orbits.

2. Can objects orbit around a black hole at different distances?

Yes, objects can orbit around a black hole at different distances depending on their initial velocity and the strength of the black hole's gravitational pull. Objects closer to the black hole will experience a stronger pull and orbit at a faster speed, while objects further away will have a slower speed and larger orbit.

3. How does the spin of a black hole affect the orbits of objects?

The spin of a black hole, known as its angular momentum, can greatly influence the orbits of objects around it. In a Kerr black hole, the spin creates a region called the ergosphere, where objects can be dragged along with the rotation of the black hole. This can result in highly curved or even unstable orbits.

4. Can objects ever escape the gravitational pull of a black hole once they enter its orbit?

It is extremely difficult for objects to escape the gravitational pull of a black hole once they enter its orbit. This is because the escape velocity, or the speed needed to overcome the black hole's gravitational pull, is greater than the speed of light. As a result, objects within the event horizon of a black hole are essentially trapped and cannot escape.

5. How do the orbits around a Schwarzschild black hole differ from those around a Kerr black hole?

The orbits around a Schwarzschild black hole, which has no spin, tend to be more stable and circular compared to those around a Kerr black hole. This is because the Kerr black hole's spin creates a more complex gravitational field that can cause objects to follow more unpredictable and curved orbits.

Similar threads

I Spin (or not) of a Kerr Black Hole
    • Special and General Relativity
Replies
9
Views
1K
B Black hole electromagnetic spectrum
    • Special and General Relativity
Replies
4
Views
398
I Does Kerr's argument against singularities apply to all black holes?
    • Special and General Relativity
Replies
12
Views
373
I Kerr disputes singularities in Kerr Black Holes
    • Special and General Relativity
Replies
7
Views
1K
A Do Black Holes have Singularities?
    • Special and General Relativity
Replies
20
Views
833
A Kerr Black Hole Angular Momentum Limit
    • Special and General Relativity
Replies
1
Views
918
I What are the effects on a stationary observer for Kerr metric?
    • Special and General Relativity
2
Replies
43
Views
2K
B Can we see 2 black holes orbiting each other?
    • Special and General Relativity
2
Replies
57
Views
1K
I Effect of Black Hole Spin on Gravity
    • Special and General Relativity
Replies
18
Views
1K
I Appearance of a Kerr black hole from above
    • Special and General Relativity
Replies
20
Views
2K

Hot Threads

Recent Insights

Back
Top