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Quantum Kerr tunneling vacua on a $(D{\bar D})_4$-brane: An emergent Kerr black hole in five dimensions

We revisit a non-perturbative space-time curvature theory, underlying a two form U(1) gauge dynamics, on a D4-brane. In particular, two different gauge choices for a two form are explored underlying the dynamics of a geometric torsion in a second order formalism. We obtain two non-extremal quantum Kerr geometries in five dimensions on a pair of $(D{\bar D})_4$-brane in a type IIA superstring theory. The quantum vacua are described by a vanishing torsion in a gauge choice, underlying a geometric realization, on a non-BPS brane. It is argued that the quantum Kerr vacua undergo tunneling and lead to a five dimensional Kerr black hole in Einstein vacuum. A low energy limit in the quantum Kerr vacua further re-assures an emergent Kerr black hole.