Regular black holes and horizonless ultra-compact objects in Lorentz-violating gravity

Abstract

There is growing evidence that Hořava gravity may be a viable quantum theory of gravity. It is thus legitimate to expect that gravitational collapse in the full, non-projectable version of the theory should result in geometries that are free of space-time singularities. Previous analyses have shown that such geometries must belong to one of the following classes: simply connected regular black holes with inner horizons; non-connected black holes “hiding” a wormhole mouth (black bounces); simply connected or non-connected horizonless compact objects. Here, we consider a singular black hole in the low-energy limit of non-projectable Hořava gravity, i.e. khronometric theory, and describe examples of its possible “regularisations”, covering all of the viable classes. To our knowledge, these examples constitute the first instances of black holes with inner universal horizons, of black bounces and of stars with a de Sitter core in the context of Lorentz-violating theories of gravity.

Newman-Janis algorithm’s application to regular black hole models

“…which comes from (27) after inverting (26), u ¼ b cot ϕ ph ffiffi 2 p . As for the rotating case, we intend to complexify the scalar field (26), the potential (27), or the Lagrangian density itself, i.e., replace it, as in the previous section, with new ones ϕ ph ðu; ūÞ, Vðu; ūÞ, and Lðu; ūÞ and apply the complex transformation coordinates x μ → x 0μ , see (14). Then, for the scalar field (26), dropping coordinate prime indices, we have…”

“…Despite the long history of efforts at spacelike singularity resolution in general relativity (GR) classical solutions, the investigation of the nonsingular (or so-called regular) black holes and their regular rotating counterparts is extremely popular nowadays [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]; see also recent reviews [17][18][19] and references therein. To construct a static regular solution, one relies on one of the following approaches: (i) to solve Einstein's field equations associated with a special kind of spacetime symmetry and matter sources [20][21][22][23][24][25][26][27][28][29], (ii) to derive a solution as quantum corrections to the classical one [30][31][32][33][34][35], or (iii) to write the metric ad hoc, motivating it by phenomenological "tractability" [5][6][7][8][9][10][36][37][38], and try to analyze the effective matter content.…”

Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time

“…Since its formulation, countless works have explored the consequences of Hořava's proposal [4]. A far from exhaustive list includes: understanding the infra-red (IR) dynamics of the theory [5,6]; the structure of constraints [7,8]; its perturbative UV dynamics [9][10][11][12][13][14][15]; the search for black-hole [16][17][18][19], regular [20,21], and cosmological solutions [22]; the interaction with matter fields [23,24], and low-energy signatures in observations [25][26][27][28][29][30][31][32][33][34], among others. However, despite incredible advances, the problem of classically solving and dynamically evolving equations of motion exhibiting the scaling (1.2) is still mostly unexplored, except in the simplest situations -such as for static and spherically symmetric space-times, or in the perturbative limit [35], where the coefficients accompanying the higher derivative terms are small enough.…”