Classical Unattainability of Extremality in non-BPS D-brane Systems

TL;DR

This paper demonstrates that non-BPS four-charge extremal black holes in N=8 string theory cannot attain true extremality, with positive energy states destabilizing the near horizon geometry, highlighting classical barriers to extremality.

Contribution

It shows that classical and quantum effects prevent extremality in non-BPS D-brane systems, revealing a fundamental obstacle to achieving extremal black holes in this context.

Findings

Microscopic D-brane description lacks extremal states.

Positive energy destabilizes near horizon AdS2.

Black hole entropy relates to configurational minima.

Abstract

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 met. It is unclear though whether this should be a quantum artefact or classical. In this paper we consider a non-BPS extremal four-charge Reissner Nordstrom 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 AdS2. 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.