On a Regular Charged black Hole with a Nonlinear Electric Source

Abstract

A modified version of the Reissner-Nordstrom metric is proposed on the grounds of the nonlinear electrodynamics model. The source of curvature is an anisotropic fluid with pr = −ρ which resembles the Maxwell stress tensor at r >> q 2 /2m, where q and m are the mass and charge of the particle, respectively. We found the black hole horizon entropy obeys the relation S = |W |/2T = AH/4, with W the Komar energy and AH the horizon area. The electric field around the source depends not only on its charge but also on its mass. The corresponding electrostatic potential Φ(r) is finite everywhere, vanishes at the origin and at r = q 2 /6m and is nonzero asymptotically, with Φ∞ = 3m/2q.

On a regular modified C-metric

“…For that purpose we apply a previous choice [10,11] and introduce the factor exp(−k/r), k > 0 as a cutoff in the KS metric. Therefore, the geometry (2) becomes…”

“…A discussion of the geometry inside the square parantheses from (12) in terms of the values of k has been given in [11] and will not be repeated here. The exponential factor, indeed, makes finite all invariants corresponding to the metric (12) and all the components of the stress tensor.…”

“…(15) where the positive constant k has been replaced with q 2 /2m for a particle of charge q (see [11]). We see from Eqs.…”

“…We found that the const a is the proper acceleration of a static observer and the spacetime is AdS far from the mass m, with a cosmological constant Λ = −3a 2 . To get rid of the curvature singularity at r = 0 we make use of the modified KS geometry [10,11] so that the spacetime becomes AdS both when r → 0 and when r → ∞. Throughout the paper we use geometrical units G = c = 1, unless otherwise specified.…”

Nonlinear electromagnetic quasinormal modes and Hawking radiation of a regular black hole with magnetic charge

“…Fortunately physicists have found a new type of black-hole solutions without singularity in general relativity [1] and more general gravity theories to construct solutions without a singularity, such as string theory and exact conformal field theory [2,3]. Especially with gravitation coupling to a suitable nonlinear electrodynamics (NLED) field, some regular metrics would be obtained [4][5][6][7][8]. Ayona e-mail: cqstarv@hotmail.com b e-mail: lk314159@hotmail.com c e-mail: cqunanyang@hotmail.com Beato, Garcia and Bronnikov successively found some static, spherically symmetric non-singular solutions [5][6][7][8].…”