Correction to: Nonlinear electrodynamics and regular black holes

Abstract

In this work, an exact regular black hole solution in general relativity is presented. The source is a nonlinear electromagnetic field with the algebraic structure T 0 0 = T 1 1 for the energy-momentum tensor, partially satisfying the weak energy condition but not the strong energy condition. In the weak field limit, the EM field behaves like the Maxwell field. The solution corresponds to a charged black hole with q ≤ 0.79 m. The metric, the curvature invariants, and the electric field are regular everywhere. The BH is stable against small perturbations of space time and using the Weinhold metric, geometrothermodynamical stability has been investigated. Finally we investigate the idea that the observable universe lives inside a regular black hole. We argue that this picture might provide a viable description of universe. Because of the great number of mistakes in it, the entire corrected article is republished here as correction article.

Thermodynamic Stability of a New Three Dimensional Regular Black Hole

“…, (10) which indicates that this is an anisotropic fluid. Considering other previous regular black hole solutions (for example, see the energy-momentum tensor of [35] for a particular mass density and [88] for special nonlinear electrodynamics), one finds that although the functional form of energy density (𝜌(r)) is not the same for different models, the equation of state undergoes the same anisotropic fluid in specific d−dimensions as P r (r) = −𝜌(r),…”

“…\end{equation}$$Moreover, we can obtain the equation of sate regarding the tangential pressure as follows $$$$\begin{equation} P_\phi =-\rho \, {\left[1+ 2\,k{\left({\left[{\frac{2\pi \,L}{k-1}}\right]}^{\frac{ 1}{k}}{\rho }^{\frac{1}{k}}-1\right)}\right]}, \end{equation}$$$$which indicates that this is an anisotropic fluid. Considering other previous regular black hole solutions (for example, see the energy‐momentum tensor of [ 35 ] for a particular mass density and [ 88 ] for special nonlinear electrodynamics), one finds that although the functional form of energy density ($$\rho (r)$$) is not the same for different models, the equation of state undergoes the same anisotropic fluid in specific $$d-$$dimensions as $$$$\begin{eqnarray*} &&P_{r}(r)=-\rho (r), \nonumber \\ &&P_\phi (r)=- {\left[\frac{r}{d-2} \rho ^\prime (r)+ \rho (r) \right]}, \nonumber \end{eqnarray*}$$$$which is completely in agreement in our three dimensional results, ().…”

Stability of the Hayward black hole under electromagnetic perturbations

“…Two things can happen when a black hole is perturbed: either the perturbations grow indefinitely (and the black hole is unstable) or the perturbations remain bounded (and the black hole is stable). Papers that deal with the study of the stability of regular black holes are for example [19][20][21][22][23][24][25], in particular, [19] deals with the stability of electrically charged black holes coupled with non linear electrodynamics with the aim to find under which conditions they are stable. See also [26] for the study of the stability of regular black holes in higher dimensions.…”