Classical unattainability of extremality in non-BPS D-brane systems

A bstract For the worldline theory of an extremal black hole, extremality amounts to vanishing ground state energy. In light of recent gravity results one would expect much like the ground-state degeneracy, this fine tuned condition too will not be satisfied. It is unclear, however, whether this should be a quantum artefact or classical effect. In this paper we consider a non-BPS extremal four-charge Reissner Nordström black hole in 𝒩 = 8 String theory. It is shown that the microscopic D-brane description fails to admit any extremal state, even classically. This positive energy is expected to destabilize the near-horizon AdS 2 . The positive minimum energy is a direct consequence of the pattern of supersymmetry breaking by the D-branes. The black hole entropy is found to be the logarithm of the number of isolated minima and hence is related to the configurational entropy of the microscopic potential. We also find multiple continua of local minima corresponding to marginally bound states of the constituent D-branes.