On the Kalb–Ramond modified Lorentz violating hairy black holes and Thorne’s hoop conjecture

K. K. Nandi; R. N. Izmailov; R. Kh. Karimov; A. A. Potapov

doi:10.1140/epjc/s10052-023-12172-9

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 984
https://doi.org/10.1140/epjc/s10052-023-12172-9

Regular Article - Theoretical Physics

On the Kalb–Ramond modified Lorentz violating hairy black holes and Thorne’s hoop conjecture

K. K. Nandi¹^,2, R. N. Izmailov¹^b, R. Kh. Karimov¹ and A. A. Potapov³

¹ Zel’dovich International Center for Astrophysics, M. Akmullah Bashkir State Pedagogical University, 3A, October Revolution Street, 450008, Ufa, RB, Russia
² High Energy Cosmic Ray Research Center, University of North Bengal, 734013, Siliguri, WB, India
³ Ufa University of Science and Technology, Sterlitamak Campus, Lenin Avenue, 49, 453103, Sterlitamak, RB, Russia

^b izmailov.ramil@gmail.com

Received: 17 August 2023
Accepted: 19 October 2023
Published online: 31 October 2023

Abstract

Recently, a class of static spherically symmetric power law corrected Lorentz violating (LV) Schwarzschild black holes in the Kalb–Ramond model have been derived and studied in the specific range of LV parameters ( $0 < λ \leq 2, Υ \geq 0$ $0<\lambda \le 2,\Upsilon \ge 0$ ) that correspond to energy condition preserving ( $ρ > 0$ $\rho >0$ ) source. On the other hand, there exist well known black holes that do not preserve the energy conditions. In this paper, we shall therefore relax energy conditions and numerically explore the horizon patterns of the enlarged class of LSMA black holes. Four generic types of LV corrected black holes emerge, which interestingly include the analogue of the braneworld black hole ( $ρ < 0$ $\rho <0$ ) lending to $Υ$ $\Upsilon$ a new interpretation of “tidal charge” known as an imprint from the 5d bulk in the Randall–Sundrum scenario. We shall then show that Thorne’s hoop conjecture, $H \leq 1$ $\mathcal {H} \le 1$ , where $H$ $\mathcal {H}$ is the Hod function, consistently holds for three types and their generalizations. However, intriguingly, it turns out that, for the remaining type (viz., Schwarzschild–de Sitter and its generalizations), the hoop conjecture does not hold. It is also shown that braneworld tidal charge black holes increases the LV correction to planetary perihelion advance in contrast to the decrease due to ordinary black holes thereby providing a qualitative distinction between them.

K. K. Nandi, R. N. Izmailov, R. Kh. Karimov and A. A. Potapov contributed equally to this work.

© The Author(s) 2023

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