The Third Law of Thermodynamics for Kerr BlackHoles
Abstract
At first the thermodynamic and evolutionary properties of Kerr black holes are clarified using the MJ plane, where M is the hole's mass and J is its angular momentum. In this plane Schwarzschild black holes with h = 0 are distributed along the Maxis and extreme Kerr holes with h = 1 lie on the line J = M^{2}, where h ≡ J/4S is a nondimensional parameter and S is the entropy. Taking into account possible accretion processes, we then derive the condition under which the third law of blackhole thermodynamics for Kerr holes is not violated. The condition is given in the form of as α ≥ 1, where the rate of change of a hole's state, dh/dM, is proportional to (1h)^α in the neighbourhood of h ≃ 1. If the rate is proportional to the vanishing surface gravity, g_{H}, with which the hole has to accrete matter and angular momentum, α is given by α= 1+2/C, where dh/dM=Cg_H=C(1h^2)/4M, and C is a proportionality constant. In this case M, J and S diverge to infinity as a power law for h \to 1, and therefore no Kerr holes can reach the extreme Kerr state with the absolute zero temperature by accreting finite amounts of mass and angular momentum.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 May 1991
 DOI:
 10.1093/mnras/250.2.300
 Bibcode:
 1991MNRAS.250..300O
 Keywords:

 Black Holes (Astronomy);
 Computational Astrophysics;
 Stellar Evolution;
 Stellar Mass Accretion;
 Thermodynamics;
 Angular Momentum;
 Stellar Models;
 Astrophysics