Comments on deformed phase-space cosmology, SUSY and black holes

Abstract

This paper presents the construction of the supersymmetric (SUSY) deformed version of the time dependent metric that describes the interior of the Schwarzschild BH. First, the noncommutative bosonic model is constructed by inducing the deformation in the minisuperspace coordinates and the associated canonical momentum. Following the methods of SUSY quantum mechanics, the supercharges of the deformed models are constructed and the deformed SUSY Wheeler-DeWitt equation is obtained. The classical dynamics are also obtained using the WKB approximation, we find the classical solutions and the conditions to satisfy the Hamiltonian constraint for both the SUSY and bosonic cases. Finally, the effects of the deformation in the context of deformed phase space cosmology and black holes are discussed.