A note on singular and non-singular black holes

A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or black hole continuum spectrum.

Section: Introductionmentioning

confidence: 99%

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

Gao

et al. 2018

“…However, the PSM is not the Reissner-Nordström metric. To deal with this problem, our method is to use the nonlinear electrodynamics [64][65][66][67][68]. The action for general relativity with nonlinear electrodynamics can be written as 15) where 16) where ∂ I L = ∂L/∂I.…”

Section: Existence Of the Psm In General Relativity With Nonlinearmentioning

confidence: 99%

Testing the Schwarzschild metric in a strong field region with the Event Horizon Telescope

Tian

Zhu

2019

Testing gravity theory in the strong field region becomes a reality due to the observations of gravitational waves and black hole shadows. In this paper, we discuss how to constrain the possible deviations of the classical general relativity with the image of M87* observed by the Event Horizon Telescope. More precisely, we want to know where is the event horizon for a non-rotating black hole. General relativity predicts the horizon is located at the Schwarzschild radius rs, while other gravity theories may give different predictions. We propose a parameterized Schwarzschild metric (PSM) in which the horizon is located at r = nrs, where n is a real free parameter, and prove general relativity with nonlinear electrodynamics allows n = 1. In the weak field region, the PSM is equivalent to the Schwarzschild metric regardless of the value of n. In the strong field region, the difference between the PSM and Schwarzschild metric would leave an imprint on the shadow image. We present detailed calculations and discussions on the black hole shadows with large background light source and accretion disk in the PSM framework. More importantly, we point out that n ≈ 2 can be used to explain why the black hole mass measured by the shadow is a factor of about two larger than the previous gas dynamics measurements. If this explanation is confirmed to be right, then this phenomenon, together with the late-time cosmological acceleration, will be very important to test gravity theories.

“…In this section, we will develop the formalism to study the solutions of regular black holes with multihorizons in the context of general relativity, so that we can generalize these results later to the alternative theories of gravity. This procedure was developed in [92] and used to study multihorizon solutions in [91]. The action that describes the nonlinear electromagnetic theory coupled with general relativity is…”

Section: The Formalism With General Relativitymentioning

confidence: 99%

Regular multihorizon black holes in f(G) gravity with nonlinear electrodynamics

Rodrigues

Silva

2019

In this work, we study the existence of regular black holes solutions with multihorizons in general relativity and in some alternative theories of gravity. We consider the coupling between the gravitational theory and nonlinear electrodynamics. The coupling generates modifications in the electromagnetic sector. This paper has as main objective generalize solutions already known from general relativity to the f (G) theory. To do that, we first correct some misprints of the Odintsov and Nojiri's work in order to introduce the formalism that will be used in the f (G) gravity. In order to satisfy all field equations, the method to find solutions in alternative theories generates different f (R) and f (G) functions for each solution, where only the nonlinear term of f (G) contributes to the field equations. We also analyze the energy conditions, since it is expected that some must be violated to find regular black holes, and using an auxiliary field, we analyze the nonlinearity of the electromagnetic theory. PACS numbers: 04.50.Kd, 04.70.Bw I. INTRODUCTIONBlack holes are one of the most interesting predictions of general relativity [1]. These objects have a region of non-scape where the boundary is a surface which permits the passage only in one direction, the event horizon [2]. The most simple black hole solution is described by the Schwarzschild metric, which is characterized only by its mass [3]. The structure of the Schwarzschild black hole is composed by an event horizon and a singularity in the black hole center [4]. There are several metrics that are more general than the Schwarzschild solution, such as the Reissner-Nordström (electrically charged), Kerr (with rotation) or de Sitter-like solutions (cosmological constant) [5]. The presence of these other parameters can lead to changes in the structure of black holes such as the Cauchy and cosmological horizon [3,5].Although some solutions have a singularity, this characteristic is not necessary for black holes. Actually, it is possible to find solutions that have an event horizon without singularity; this kind of solution is known as regular black hole [6]. James Bardeen proposed a metric which was later interpreted as a solution to the Einstein equations for nonlinear electrodynamics [7], without the presence of singularities [8]. As in the Reissner-Nordström case, due to the charge, Bardeen solution presents a Cauchy horizon [9]. Many solutions of regular black holes have arisen since then , and several studies of their properties have been conduct, such as absorption [32][33][34], scattering [35,36], quasinormal modes [37-50], thermodynamics [51-61] and even tidal forces [62].Beyond general relativity, we have the alternatives theories of gravity [63]. The Einstein equations could be obtained from the variational principle if we consider the Einstein-Hilbert action [64]. Modify this action is a way to find the field equations of these alternative theories [65]. One of the most studied modifications the f (R) theory [63], with R being the curvature scalar, whi...