Basic Generic Properties of Regular Rotating Black Holes and Solitons

Irina Dymnikova,Evgeny Galaktionov

doi:10.1155/2017/1035381

Irina Dymnikova, Evgeny Galaktionov

Open Access

https://doi.org/10.1155/2017/1035381

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Abstract

We present a systematic description of the basic generic properties of regular rotating black holes and solitons (compact nonsingular nondissipative objects without horizons related by self-interaction and replacing naked singularities). Rotating objects are described by axially symmetric solutions typically obtained by the Gürses-Gürsey algorithm, which is based on the Trautman-Newman techniques and includes the Newman-Janis complex transformation, from spherically symmetric solutions of the Kerr-Schild class specified by Ttt=Trr(pr=-ρ). Regular spherical solutions of this class satisfying the weak energy condition have obligatory de Sitter center. Rotation transforms de Sitter center into the equatorial de Sitter vacuum disk. Regular solutions have the Kerr or Kerr-Newman asymptotics for a distant observer, at most two horizons and two ergospheres, and two different kinds of interiors. For regular rotating solutions originated from spherical solutions satisfying the dominant energy condition, there can exist the interior S-surface of de Sitter vacuum which contains the de Sitter disk as a bridge. In the case when a related spherical solution violates the dominant energy condition, vacuum interior of a rotating object reduces to the de Sitter disk only.

Highlights

Presented in the current literature, regular rotating solutions [1,2,3,4,5,6,7,8,9,10] are obtained from regular spherical solutions with using the Newman-Janis complex translation [11]
In [12], it was shown that the Newman-Janis translation works for algebraically special metrics which belong to the Kerr-Schild class [13] and can be presented as gμ] = ημ] + 2f(r)kμk], where ημ] is the Minkowski metric and kμ are principal null congruences
In the black hole case, ergospheres and ergoregions exist for any density profile (the curve (3a) for the case of two horizons and the curve (3b) for the double-horizon case)

Summary

Introduction

Presented in the current literature, regular rotating solutions [1,2,3,4,5,6,7,8,9,10] are obtained from regular spherical solutions with using the Newman-Janis complex translation [11]. Regular axially symmetric solutions satisfy condition (3) in the corotating reference frame [24, 25] and describe regular rotating objects, asymptotically Kerr or Kerr-Newman for a distant observer with the mass parameter M = M(r → ∞). Solutions of this class describe regular rotating black holes and spinning solitons with de Sitter vacuum interiors [25,26,27,28]. A spherical metric function g(r) in (2) in the asymptotically flat case can have at most two zero points and one minimum between them [18]. Solitons can have two ergospheres and ergoregion between them (the curve (4a)), one ergosphere and ergoregion involving the whole interior (the curve (4b)), or no ergospheres [27, 28]

Internal Structure of Regular Rotating Objects

Electrically Charged Regular Black Holes and Solitons

Summary and Discussion