Classification of Circular Equatorial Orbits around Regular Rotating Black Holes and Solitons with the de Sitter/ Phantom Interiors

Irina Dymnikova,Bożena Sołtysek,Anna Dobosz

doi:10.3390/universe8020065

Irina Dymnikova, Bożena Sołtysek + Show 1 more

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https://doi.org/10.3390/universe8020065

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Abstract

We study the basic properties of the circular equatorial orbits for the regular axially symmetric solutions, obtained with using the Gürses–Gürsey formalism which includes the Newman–Janis algorithm, from regular spherically symmetric metrics of the Kerr–Schild class specified by Ttt=Trr. Solutions of this class describe regular rotating black holes and spinning solitons replacing naked singularities. All these objects have the interior de Sitter equatorial disk, and can have two kinds of interiors determined by the energy conditions. One of them contains an additional interior de Sitter vacuum S-surface with the de Sitter disk as a bridge, whose internal cavities are filled with a phantom fluid. We study in detail the innermost equatorial circular orbits and show that in the field of spinning solitons, the innermost orbits exist within ergoregions related to phantom regions. We show also that around spinning solitons there can exist four corotating light rings and around a regular black hole, one corotating light ring, which is stable for a certain class of black holes. For all objects there exists one counterrotating light ring.

Highlights

Presented in the current literature, regular solutions for rotating black holes [1,2,3,4,5,6,7,8,9,10](for a review [11]) are typically obtained from regular spherical solutions with using the Newman–Janis complex translation [12]
The potentials decrease from V (r ) → ∞ to their minima, and as a result the situation is essentially different
The innnermost stable direct photon orbits in the field of a soliton, for a > adh where adh corresponds to the double horizon r±, with rγ < r±, meets the branching point at the unstable orbit rγ = r±

Summary

Introduction

Presented in the current literature, regular solutions for rotating black holes [1,2,3,4,5,6,7,8,9,10]. In this paper we study the basic properties and classification of circular equatorial orbits in the field of the regular de Sitter–Kerr black holes and spinning solitons. These orbits play the essential role in the geodesic structure of a spacetime and provide a diagnostic tool for an investigation of generic features and typical behavior of considered objects. The present paper is devoted to the general analysis and classification of equatorial circular orbits in the field of regular de Sitter–Kerr black holes and spinning solitons, with special attention to the innermost orbits and their location with respect to ergospheres.

Structure of the de Sitter–Kerr Compact Objects

Basic Equations

Photon Orbits

Particle Orbits

Summary and Discussion