Quantum Kerr(Newman) degenerate stringy vacua in 4D on a non-BPS brane

We investigate some of the quantum gravity effects on a vacuum created pair of $(D{\bar D})_3$-brane by a non-linear $U(1)$ gauge theory on a $D_4$-brane. In particular we obtain a four dimensional quantum Kerr(Newman) black hole in an effective torsion curvature formalism sourced by a two form dynamics in the world-volume of a $D_4$-brane on $S^1$. Interestingly the event horizon is found to be independent of a non-linear electric charge and the $4D$ quantum black hole is shown to describe a degenerate vacua in string theory. We show that the quantum Kerr brane universe possesses its origin in a de Sitter vacuum. In a nearly $S_2$-symmetric limit the Kerr geometries may seen to describe a Schwarzschild and Reissner-Nordstrom quantum black holes. It is argued that a quantum Reissner-Nordstrom tunnels to a large class of degenerate Schwazschild vacua. In a low energy limit the non-linear electric charge becomes significant at the expense of the degeneracies. In the limit the quantum geometries may identify with the semi-classical black holes established in Einstein gravity. Analysis reveals that a quantum geometry on a vacuum created $D_3$-brane universe may be described by a low energy perturbative string vacuum in presence of a non-perturbative quantum correction.

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