Stable causality of the Pomeransky–Senkov black holes

Abstract

AbstractWeshowstablecausalityofthePomeransky-Senkovblackrings. 1 Introduction Five-dimensional black rings, and their generalisations, have attracted a lotof attention in recent literature (see, e.g., [2]). In [1] it has been shown thatthe Pomeransky-Senkov [4] metrics, with appropriate values of parameters,do not contain naked singularities in their domains of outer communications(d.o.c.). In that reference the question of causality violations within thed.o.c. has been left open, except for reporting some numerical evidence. Theobject of this note is to point out that the Pomeransky-Senkov (PS) blackholes are stably causal.Ideally one would like to show that the d.o.c.’s of the PS metrics areglobally hyperbolic, but such a result lies outside of the scope of this work. ∗ PTCwassupportedinpartbytheECprojectKRAGEOMP-MTKD-CT-2006-042360,andbythePolishMinistryofScienceandHigherEducationgrantNrNN201372736. † SSz was supported in part by the Polish Ministry of Science and Higher EducationgrantNrNN202079235,andbytheFoundationforPolishScience.