Dark Matter Candidates with Dark Energy Interiors Determined by Energy Conditions

Irina Dymnikova

doi:10.3390/sym12040662

Abstract

We outline the basic properties of regular black holes, their remnants and self-gravitating solitons G-lumps with the de Sitter and phantom interiors, which can be considered as heavy dark matter (DM) candidates generically related to a dark energy (DE). They are specified by the condition T t t = T r r and described by regular solutions of the Kerr-Shild class. Solutions for spinning objects can be obtained from spherical solutions by the Newman-Janis algorithm. Basic feature of all spinning objects is the existence of the equatorial de Sitter vacuum disk in their deep interiors. Energy conditions distinguish two types of their interiors, preserving or violating the weak energy condition dependently on violation or satisfaction of the energy dominance condition for original spherical solutions. For the 2-nd type the weak energy condition is violated and the interior contains the phantom energy confined by an additional de Sitter vacuum surface. For spinning solitons G-lumps a phantom energy is not screened by horizons and influences their observational signatures, providing a source of information about the scale and properties of a phantom energy. Regular BH remnants and G-lumps can form graviatoms binding electrically charged particles. Their observational signature is the electromagnetic radiation with the frequencies depending on the energy scale of the interior de Sitter vacuum within the range available for observations. A nontrivial observational signature of all DM candidates with de Sitter interiors predicted by analysis of dynamical equations is the induced proton decay in an underground detector like IceCUBE, due to non-conservation of baryon and lepton numbers in their GUT scale false vacuum interiors.

Highlights

Regular spherical black holes with the de Sitter interiors and self-gravitating solitons replacing naked singularities are described by the Einstein equations with source terms specified by [1,2]Ttt = Trr (1)and satisfying the weak energy condition (WEC) which requires non-negativity of density for any observer on a time-like curve.The early hypotheses concerning replacement of a singularity with a de Sitter core related appearance of the de Sitter vacuum with the self-regulation of geometry due to vacuum polarization effects [3], with the existence of the limiting curvature [4], and with the symmetry restoration at the GUT scale in the final stage of the gravitational collapse [1,5]
Primordial regular black holes (RBHs), their remnants and G-lumps can be considered as heavy dark matter candidates generically related to a vacuum dark energy via their de Sitter interiors [18,32]
In their GUT scale false vacuum interiors baryon and lepton numbers are not conserved, as a result they can induce proton decay in an underground detector like IceCUBE, which would present their observational signature in heavy dark matter searches [32]

Summary

Introduction

Regular spherical black holes with the de Sitter interiors and self-gravitating solitons replacing naked singularities are described by the Einstein equations with source terms specified by [1,2]. Solutions to the Einstein equations present, dependently on coordinate mapping, regular cosmological models with variable λ(ρvac ) including initial, final and intermediate (if necessary) de Sitter stages [14,15,16] (for a review, see Reference [17]), and regular black holes (RBHs) and self-gravitating solitons G-lumps (particlelike structures without horizons replacing naked singularities) with the de Sitter interiors [13,18] (for a review, see Reference [19]). Primordial RBHs, their remnants and G-lumps can be considered as heavy dark matter candidates generically related to a vacuum dark energy via their de Sitter interiors [18,32] In their GUT scale false vacuum interiors baryon and lepton numbers are not conserved, as a result they can induce proton decay in an underground detector like IceCUBE, which would present their observational signature in heavy dark matter searches [32].

Spherical Objects with de Sitter Vacuum Interiors

Regular Spinning Compact Objects with DE Interiors

Summary and Discussion