Supergravity $p$-branes with scalar charge

TL;DR

This paper explores supergravity p-branes with independent scalar charges, including singular solutions, and investigates their properties, geodesics, and potential quantum resolution of singularities, extending beyond traditional no-hair constraints.

Contribution

It introduces new singular brane solutions with independent scalar charges and analyzes their physical and quantum properties, challenging the no-hair theorem limitations.

Findings

Singular branes with independent scalar charges can have naked singularities.

Certain solutions exhibit geodesic completeness despite singularities.

Quantum effects may potentially resolve classical singularities.

Abstract

Standard dilatonic supergravity $p$-branes have scalar charges that are not independent parameters, but are determined by the brane tension and Page charges. This feature can be traced to the no-hair theorem in the four-dimensional Einstein-scalar gravity, implying that more general solutions with independent scalar charges can have naked singularities. Since singular branes are also of interest as tentative classical counterparts of unstable tachyonic branes and/or brane-antibrane systems, it is worth investigating branes with independent scalar charges in more detail. Here we study singular branes associated with the Fisher-Janis-Newman-Winicour solution of four-dimensional gravity. In the case of codimension three, we also construct singular branes endowed with a Zipoy-Voorhees-type oblateness parameter. It is expected that such branes will not be supersymmetric in the string theory. We demonstrate this in the special case of NS5-branes of type II theory. We analyze geodesics and test scalar perturbations of new solutions focusing on possible quantum healing of classical singularities.