Arbitrary black-string deformations in the black string-black hole transitions

TL;DR

This paper investigates the transition between black strings and black holes by analyzing apparent horizons, demonstrating the possibility of arbitrarily deforming black strings at time symmetry, with limitations on hyperspherical black hole deformations.

Contribution

It introduces a method to generate arbitrarily deformed black strings and compares deformation limits with hyperspherical black holes.

Findings

Arbitrarily deformed black strings can be generated at time symmetry.

Hyperspherical black holes have an upper limit on deformation along the extra dimension.

Apparent horizon analysis reveals structural differences in black string and black hole deformations.

Abstract

We study the possible black string-black hole transition by analyzing the structure of the apparent horizon for a large family of time-symmetric initial data. We observe that, as judged by the apparent horizon, it is possible to generate arbitrarily deformed black strings at a moment of time symmetry. A similar study for hyperspherical black holes reveals that although arbitrarily deformed hyperspherical black holes can be constructed, the proper distance between the north and south poles along the extra direction has an upper limit.