Gravitating defects of codimension-two

TL;DR

This paper proposes a new way to resolve inconsistencies in modeling thin gravitating defects of codimension two in higher-dimensional gravity, leading to modified cosmological and black hole solutions.

Contribution

It introduces generalized matching conditions for codimension-two defects that are consistent with bulk gravity, extending the standard Israel conditions.

Findings

Consistent matching conditions derived for axially symmetric defects.

Modified cosmological evolution with different density dependence for dust.

A new black hole solution with short-distance corrections.

Abstract

Thin gravitating defects with conical singularities in higher codimensions and with generalized Israel matching conditions are known to be inconsistent for generic energy-momentum. A way to remove this inconsistency is proposed and is realized for an axially symmetric gravitating codimension-two defect in six dimensional Einstein gravity. By varying with respect to the brane embedding fields, alternative matching conditions are derived, which are generalizations of the Nambu-Goto equations of motion of the defect, consistent with bulk gravity. For a maximally symmetric defect the standard picture is recovered. The four-dimensional perfect fluid cosmology coincides with conventional FRW in the case of radiation, but for dust it has rho^{4/3} instead of rho. A four-dimensional black hole solution is presented having the Schwarzschild form with a short-distance correction r^{-2}.