The discussion centers on the properties of black holes, specifically whether there exist metrics in which black holes do not have a Schwarzschild radius. Participants explore the nature of event horizons in various black hole solutions, including stationary and non-stationary cases.
Participants express differing views on the properties of black holes and the applicability of the Schwarzschild radius. There is no consensus on whether all black holes must have an event horizon proportional to mass, with multiple competing perspectives presented.
Some participants highlight the limitations of existing definitions and the need for careful consideration of the assumptions involved in different black hole metrics. The discussion includes references to specific mathematical formulations and conditions that affect the properties of black holes.
This discussion may be of interest to those studying general relativity, black hole physics, and the mathematical properties of different black hole solutions.
The event horizon for a rotating black hole does not only depend on the mass but also on the angular momentum.Andru10 said:Are there any known metrics in which black holes do not have the Schwarzschild radius? Specifically, I'm interested in whether it's possible for a black hole to have an event horizon which is not of the form: constant * mass.
No. The most general black hole is represented by the Kerr-Newman solution, and it has this property.Specifically, I'm interested in whether it's possible for a black hole to have an event horizon which is not of the form: constant * mass.
Finbar said:Kerr-Newman don't have the property that the radius is proportional to the mass times a constant. It depends on both the angular momentum(as passionflower said) and the charge.
WannabeNewton said:The OP asked if there are black holes which do not have a schwarzchild radius i.e. r = 2GM. The kerr - newman solution is the most general stationary solution that DOES have this property.
Finbar said:No, for a kerr black hole
r = M + \sqrt{M^2-a^2} in units G=1 where a = J/M and J is angular momentum.
Go read a book!
The point is that a is restricted to the range 0 < a < M, so M < r < 2M. The inner horizon is no longer spherical, but its size is proportional to M. In fact this must be the case, since M is the only parameter in the solution that sets the scale.No, for a kerr black hole r = M + √(M2 - a2)
WannabeNewton said:That is a definition of r to find the location of the horizon in the kerr geometry i.e. at g_{rr} = \infty. This has nothing to with the fact that r = 2M IS the schwarzchild radius for a kerr black hole.
Bill_K said:The point is that a is restricted to the range 0 < a < M, so M < r < 2M. The inner horizon is no longer spherical, but its size is proportional to M. In fact this must be the case, since M is the only parameter in the solution that sets the scale.
Finbar said:r=2M has nothing to do with the event horizon of a Kerr black hole.
The OP asked whether the event horizon of a black hole is proportional to the mass times a constant. This is only the case for schwarzschild black hole.
Andru10 said:Are there any known metrics in which black holes do not have the Schwarzschild radius? Specifically, I'm interested in whether it's possible for a black hole to have an event horizon which is not of the form: constant * mass.
Finbar said:Kerr-Newman don't have the property that the radius is proportional to the mass times a constant. It depends on both the angular momentum(as passionflower said) and the charge.
Also Kerr-Newman is not the most general black hole. It is only the most general stationary solution to the Einstein-Maxwell equations in four dimensions. There are obviously many more general solutions like for example time dependent ones with matter falling to the horizon.
The Schwarzschild solution is a very very special case.
Finbar said:Also Kerr-Newman is not the most general black hole. It is only the most general stationary solution to the Einstein-Maxwell equations in four dimensions. There are obviously many more general solutions like for example time dependent ones with matter falling to the horizon.
edguy99 said:I would appreciate if you had any good links to the subject "Kerr-Newman is not the most general black hole"
I am interested in black holes where a lot of material is falling in from close to the top and bottem of the spinning black hole. Mostly in 3D aspects as I find many references and drawings on the internet really only seem to be 2D in nature (the axis of rotation is not precessing).