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Register a new userBlack Holes-Hedgehogs and Strings as Defects of the Universal Vacua
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In the present paper, assuming the Multiple Point Principle (MPP) as a new law of Nature, we considered the existence of the two degenerate vacua of the Universe: a) the first Electroweak (EW) vacuum at $v_1approx 246$ GeV -- true vacuum, and b) the second Planck scale false vacuum at $v_2 sim 10^{18}$ GeV. In these vacua we investigated different topological defects. The main aim of this paper is an investigation of the black-hole-hedgehogs configurations as defects of the false vacuum. In the framework of the $f(R)$ gravity, described by the Gravi-Weak unification model, we considered a black-hole solution, which corresponds to a hedgehog -- global monopole, that has been swallowed by the black-hole with mass core $M_{BH}sim 10^{18}$ GeV and radius $deltasim 10^{-21}$ GeV$^{-1}$. Considering the results of the hedgehog lattice theory in the framework of the $SU(2)$ Yang-Mills gauge-invariant theory with hedgehogs in the Wilson loops, we have used the critical value of temperature for the hedgehogs confinement phase ($T_csim 10^{18}$ GeV). This result gave us the possibility to conclude that the SM shows a new physics (with contributions of the $SU(2)$-triplet Higgs bosons) at the scale $sim 10$ TeV. Theory predicts the stability of the EW-vacuum and the accuracy of the MPP.
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We prove that a generalized Schwarzschild-like ansatz can be consistently employed to construct $d$-dimensional static vacuum black hole solutions in any metric theory of gravity for which the Lagrangian is a scalar invariant constructed from the Riemann tensor and its covariant derivatives of arbitrary order. Namely, we show that, apart from containing two arbitrary functions $a(r)$ and $f(r)$ (essentially, the $g_{tt}$ and $g_{rr}$ components), in any such theory the line-element may admit as a base space {em any} isotropy-irreducible homogeneous space. Technically, this ensures that the field equations generically reduce to two ODEs for $a(r)$ and $f(r)$, and dramatically enlarges the space of black hole solutions and permitted horizon geometries for the considered theories. We then exemplify our results in concrete contexts by constructing solutions in particular theories such as Gauss-Bonnet, quadratic, $F(R)$ and $F$(Lovelock) gravity, and certain conformal gravities.
Recent results of arXiv:1907.08788 on universal black holes in $d$ dimensions are summarized. These are static metrics with an isotropy-irreducible homogeneous base space which can be consistently employed to construct solutions to virtually any metric theory of gravity in vacuum.
We review the properties of static, higher dimensional black hole solutions in theories where non-abelian gauge fields are minimally coupled to gravity. It is shown that black holes with hyperspherically symmetric horizon topology do not exist in $d > 4$, but that hyperspherically symmetric black holes can be constructed numerically in generalized Einstein-Yang-Mills models. 5-dimensional black strings with horizon topology S^2 x S^1 are also discussed. These are so-called undeformed and deformed non-abelian black strings, which are translationally invariant and correspond to 4-dimensional non-abelian black holes trivially extended into one extra dimensions. The fact that black strings can be deformed, i.e. axially symmetric for constant values of the extra coordinate is a new feature as compared to black string solutions of Einstein (-Maxwell) theory. It is argued that these non-abelian black strings are thermodynamically unstable.
The Schwarzschild, Schwarzschild-AdS, and Schwarzschild-de Sitter solutions all admit freely acting discrete involutions which commute with the continuous symmetries of the spacetimes. Intuitively, these involutions correspond to the antipodal map of the corresponding spacetimes. In analogy with the ordinary de Sitter example, this allows us to construct new vacua by performing a Mottola-Allen transform on the modes associated with the Hartle-Hawking, or Euclidean, vacuum. These vacua are the `alpha-vacua for these black holes. The causal structure of a typical black hole may ameliorate certain difficulties which are encountered in the case of de Sitter alpha-vacua. For Schwarzschild-AdS black holes, a Bogoliubov transformation which mixes operators of the two boundary CFTs provides a construction of the dual CFT alpha-states. Finally, we analyze the thermal properties of these vacua.
A light-front renormalization group analysis is applied to study matter which falls into massive black holes, and the related problem of matter with transplankian energies. One finds that the rate of matter spreading over the black holes horizon unexpectedly saturates the causality bound. This is related to the transverse growth behavior of transplankian particles as their longitudinal momentum increases. This growth behavior suggests a natural mechanism to impliment tHoofts scenario that the universe is an image of data stored on a 2 + 1 dimensional hologram-like projection.
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