Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

The Higgs Mechanism and Spacetime Symmetry

In this review, we summarize the results of the analysis of the inherent relation between the Higgs mechanism and spacetime symmetry provided by generic incorporation of the de Sitter vacuum as a false vacuum with the equation of state p=−ρ. This relation has been verified by the application for the interpretation of the experimental results on the negative mass squares for neutrinos, and of the appearance of the minimal length in the annihilation reaction e+e−→γγ(γ). An additional verification is expected for the dark matter candidates with the interior de Sitter vacuum of the GUT scale, whose predicted observational signatures include the induced proton decay in the matter of an underground detector, such as IceCUBE.

The Fundamental Roles of the de Sitter Vacuum

We overview the fundamental roles of the de Sitter vacuum in cosmology where it is responsible for powering the early inflationary stage(s) and the present accelerated expansion, in black hole physics where it provides the existence of a wide class of regular black holes and self-gravitating solitons replacing naked singularities, and in particle physics where it ensures the intrinsic relation of the Higgs mechanism with gravity and spacetime symmetry breaking.

Dark Matter Candidates with Dark Energy Interiors Determined by Energy Conditions

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.

Universes Inside a Black Hole with the de Sitter Interior

We outline the basic ideas and analyze the possibilities of the quantum birth of universes inside regular black holes with the de Sitter interior replacing a singularity. We compare different cases and show that the most plausible case is the birth of a flat universe from an initial quantum fluctuation with a small admixture of radiation and strings with the negative deficit angle, which provides the existence of a potential barrier needed for quantum tunneling.

Spacetime Symmetry and LemaîTre Class Dark Energy Models

We present the regular cosmological models of the Lemaître class with time-dependent and spatially inhomogeneous vacuum dark energy, which describe relaxation of the cosmological constant from its value powering inflation to the final non-zero value responsible for the present acceleration in the frame of one self-consistent theoretical scheme based on the algebraic classification of stress-energy tensors and spacetime symmetry directly related to their structure. Cosmological evolution starts with the nonsingular non-simultaneous de Sitter bang, followed by the Kasner-type anisotropic expansion, and goes towards the present de Sitter state. Spacetime symmetry provides a mechanism of reducing cosmological constant to a certain non-zero value involving the holographic principle which singles out the special class of the Lemaître dark energy models with the global structure of the de Sitter spacetime. For this class cosmological evolution is guided by quantum evaporation of the cosmological horizon whose dynamics entirely determines the final value of the cosmological constant. For the choice of the density profile modeling vacuum polarization in a spherical gravitational field and the GUT scale for the inflationary value of cosmological constant, its final value agrees with that given by observations. Anisotropy grows quickly at the postinflationary stage, then remains constant and decreases to A < 10 − 6 when the vacuum density starts to dominate.