Towards a supersymmetric generalization of the Schwarzschild black hole
- Departamento de Fisica, Division de Ciencias e Ingenierias, Campus Leon, Universidad de Guanajuato, P.O. Box E-143, Leon, Guanajuato (Mexico)
The Wheeler-DeWitt (WDW) equation for the Kantowski-Sachs model can also be understood as the WDW equation corresponding to the Schwarzschild black hole due to the well known diffeomorphism between these two metrics. The WDW equation and its solutions are ignorant of the coordinate patch one is using, only by imposing coordinate conditions we can differentiate between cosmological and black hole models. At that point, the foliation parameter t or r will appear in the solution of interest. In this work we supersymmetrize this WDW equation obtaining an extra term in the potential with two possible signs. The WKB method is then applied, giving rise to two classical equations. It is shown that the event horizon can never be reached because very near to it, the extra term in the potential, for each one of the equations, is more relevant than the one that corresponds to Schwarzschild. One can then study the asymptotic cases in which one of the two terms in the Hamiltonian dominates the behavior. One of them corresponds to the usual Schwarzschild black hole. We will study here the other two asymptotic regions; they provide three solutions. All of them have a singularity in r=0 and depending on an integration constant C they can also present a singularity in r=C{sup 2}. Neither of these solutions have a Newtonian limit. The black hole solution we study is analyzed between the singularity r=C{sup 2} and a maximum radius r{sub m}. We find an associated mass, considering the related cosmological solution inside r=C{sup 2}, and based on the holographic principle an entropy can be assigned to this asymptotic solution.
- OSTI ID:
- 21313371
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 10; Other Information: DOI: 10.1103/PhysRevD.80.104020; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
Similar Records
Black holes and phase-space noncommutativity
Phase-space noncommutative quantum cosmology