Negative spectrum of the2+1black hole

Abstract

In ($2+1$)-dimensional gravity with negative cosmological constant, the states in the negative energy range, between anti-de Sitter (AdS) ($M=\ensuremath{-}1$) and the so-called Ba\~nados-Teitelboim-Zanelli black hole ($M\ensuremath{\ge}0$), correspond to topological defects with angular deficit $0<\ensuremath{\alpha}<2\ensuremath{\pi}$. These defects are produced by (static or spinning) 0-branes which, in the extreme case $M\ensuremath{\ell}=\ensuremath{-}|J|$, admit globally-defined covariantly constant spinors. Thus, these branes correspond to Bogomol'nyi-Prasad-Sommerfield solitons and are stable ground state candidates for the corresponding supersymmetric extension of $2+1$ AdS gravity. These branes constitute external currents that couple in a gauge-invariant way to three-dimensional AdS gravity.