Cauchy Horizons, Thermodynamics and Closed Time-like Curves in Planar Supersymmetric Space-times

TL;DR

This paper explores special supersymmetric space-times that are free of singularities and contain Cauchy horizons, revealing novel structures with implications for causality and black hole analogs.

Contribution

It introduces new geodesically complete, singularity-free space-times with Cauchy horizons and closed time-like curves, extending understanding of supersymmetric solutions in planar geometries.

Findings

Space-times include infinite Minkowski regions separated by AdS_4 zones.

Cauchy horizons with zero Hawking temperature are identified.

Some solutions contain closed time-like curves connecting finite Minkowski regions.

Abstract

We study geodesically complete, singularity free space-times induced by supersymmetric planar domain walls interpolating between Minkowski and anti-de Sitter ($AdS_4$) vacua. A geodesically complete space-time without closed time-like curves includes an infinite number of semi-infinite Minkowski space-times, separated from each other by a region of $AdS_4$ space-time. These space-times are closely related to the extreme Reissner Nordstr\" om (RN) black hole, exhibiting Cauchy horizons with zero Hawking temperature, but in contrast to the RN black hole there is no entropy. Another geodesically complete extension with closed time-like curves involves space-times connecting a finite number of semi-infinite Minkowski space-times.