Naked Singularities, Topological Defects and Brane Couplings

Abstract

A conical defect in (2+1) anti-de Sitter space is a BTZ solution with a negative mass parameter. This is a naked singularity, but a rather harmless one: it is a point particle. Naturally, the energy density and the spacetime curvature have a delta-like singularity at the apex of the conical defect, but that doesn't give rise to any unphysical situations. Since the conical solution implies the presence of a source, applying reverse enginnering, one can identify the coupling term that is required in the action to account for that source. In that way, a relation is established between the identification operation that gives rise to the topological defect and the interaction term in the action that produces it. This idea has a natural extension to higher dimensions, where instead of a point particle (zero-brane) one finds membranes of even spatial dimensions (p-branes, with p=2n). The generalization to other abelian and nonabelian gauge theories --including (super-) gravities-- is fairly straightforward: the 2n-brane couple to a (2n+1) Chern-Simons form. The construction suggests a generic role for Chern-Simons forms as the natural way to couple a gauge connection to a brane and avoids the inconsistency that results from the minimal coupling between a brane and a fundamental p-form field.

11 pages, no figures. To appear in "Quantum Gravity and the Foundations of Physics", conference held in honor of Prof. Mario Castagnino's 75th birthday, Rosario, Argentina, March 2010

References in corpus (6)

• Instability of charged and rotating naked singularities
• Dynamics and BPS states of AdS5 supergravity with a Gauss-Bonnet term
• General Relativity from a gauged WZW term
• The Universe as a topological defect
• Couplings between Chern-Simons gravities and 2p-branes
• Instabilities of naked singularities and black hole interiors in General Relativity