Kerr-Newman BH Mass: Relationship to Angular Momentum & Charge

[Hiranya Pasan]

I've been trying to find out the relationship between Kerr-Newman BH mass, Angular momentum and Charge. But I cannot find it. If some know please let me know.

Thank you

 

[Orodruin]

Why do you think there is such a relationship? These are independent properties.

 

[Hiranya Pasan]

Why do you think there is such a relationship? These are independent properties.

Really?, I thought Kerr black holes having the relationship angular momentum and mass (J=aM), Kerr-Newman black holes also have that kind of a relationship

 

[Orodruin]

(J=aM)

That is just exchanging the angular momentum for a length scale parameter. Since that parameter is a priori independent of the mass, the angular momentum does not have a one to one relationship with the mass. As an example, the Schwarzschild black hole is a Kerr black hole with J = 0 (or, equivalently, a=0).

 

[pervect]

I've been trying to find out the relationship between Kerr-Newman BH mass, Angular momentum and Charge. But I cannot find it. If some know please let me know.

Thank you

Perhpas you are looking for the relationship

$$M^2 >= Q^2 + (S/M)^2$$

where M is the mass of the black hole, Q is the charge, and S is the angular momentum, all in geometric units. S/M is called a in my text, which is MTW's "Gravitation". A body which violates this condition would not be a black hole, but a 'naked singularity'.