Classical resolution of black hole singularities in arbitrary dimension

Abstract

A metric-affine approach is employed to study higher-dimensional modified gravity theories involving different powers and contractions of the Ricci tensor. It is shown that the field equations are \emph{always} second-order, as opposed to the standard metric approach, where this is only achieved for Lagrangians of the Lovelock type. We point out that this property might have relevant implications for the AdS/CFT correspondence in black hole scenarios. We illustrate these aspects by considering the case of Born-Infeld gravity in $d$ dimensions, where we work out exact solutions for electrovacuum configurations. Our results put forward that black hole singularities in arbitrary dimensions can be cured in a purely classical geometric scenario governed by second-order field equations.Comment: 14 pages, 2 figures, to appear in PR

Geodesically complete BTZ-type solutions of 2 + 1 Born–Infeld gravity

“…The case s = +1, therefore, admits a geon-like/wormhole interpretation in much the same way as the s = −1 case studied in [41]. It is important to note that the function r(y) near its minimum is smooth for all values of d > 3 (see Fig.3 as an illustration).…”

“…On the other hand, the result regarding wormholes has been observed in four spacetime dimensions both for f (R) gravity [51] and extensions containing Ricci-squared corrections [55], in Born-Infeld gravity (with s = −1 [40]), as well as in higherdimensional generalizations [41]. The results obtained in this paper are in agreement with the two different mechanisms for the resolution of spacetime singularities observed in those works: either the wormhole lies on the future (or past) boundary of the spacetime, since it is reached by null geodesics in an infinite affine time (this is what occurs in the s = −1 case, see Fig.5), or the wormhole can be reached in a finite affine time by null and time-like geodesics but these can be smoothly extended from the throat to arbitrarily large values of the affine parameter (s = +1 case, see Fig.6).…”

Geons as wormholes of modified gravity

“…This representation is valid for f (R) theories 7 , f (R, R μν R μν ) theories 8 , Born-Infeld gravity 9 and in higher-dimensional 13 and braneworld scenarios 15 . The matrix Σ μ ν represents the transformation between the effective metric q μν and the physical metric g μν as q μν = Σ μ α g αν and, though is model-dependent, can be shown to depend only on the matter stress-energy tensor T μ ν , and the same applies to the gravity function f .…”

“…Starting from a slightly different perspective, in a series of papers [7][8][9][10][11][12][13] we have implemented a systematic analysis of classical effective geometries supported by modified theories of gravity. As opposed to the standard procedure in the literature, where a wormhole space-time is given a priori and then the Einstein equations are driven back to find the matter sources generating such a geometry, in our approach we derive them from gravitational actions including additional contractions of the Ricci tensor with the metric, and assuming independent metric and affine structures (Palatini approach).…”

Wormholes as a cure for black hole singularities

“…In what follows, we will summarize the main results found in recent works 15,18,19 for two different gravity models formulatedà la Palatini and coupled to spherically symmetric matter sources. These models yield black hole solutions with up to two event horizons, like the Reissner-Nordstrom solution of GR, but with a wormhole at their center.…”