Abstract
A new modified Hayward metric of magnetically charged non-singular black hole spacetime in the framework of nonlinear electrodynamics is constructed. When the fundamental length introduced, characterising quantum gravity effects, vanishes, one comes to the general relativity coupled with the Bronnikov model of nonlinear electrodynamics. The metric can have one (an extreme) horizon, two horizons of black holes, or no horizons corresponding to the particle-like solution. Corrections to the Reissner–Nordström solution are found as the radius approaches infinity. As r → 0 the metric has a de Sitter core showing the absence of singularities, the asymptotic of the Ricci and Kretschmann scalars are obtained and they are finite everywhere. The thermodynamics of black holes, by calculating the Hawking temperature and the heat capacity, is studied. It is demonstrated that phase transitions take place when the Hawking temperature possesses the maximum. Black holes are thermodynamically stable at some range of parameters.
Highlights
It is well-known that General Relativity (GR) is ultraviolet (UV) incomplete
The thermodynamics for a magnetically charged regular black holes (BHs), which comes from the action of GR and nonlinear electrodynamics (NED), was investigated in Reference [34]
To describe the magnetically charged BH solution we consider the Lagrangian density of NED [15]: L=−
Summary
It is well-known that General Relativity (GR) is ultraviolet (UV) incomplete. In addition, there is a problem of singularities in the classical Einstein theory of gravity. In References [13,14] the regular electrically charged BH solution in GR was presented, where the source is a nonlinear electrodynamics (NED) field satisfying the weak energy condition. We consider the spherically symmetric non-singular model of the magnetically charged BH based on NED. With the help of the modified Hayward metric, we study regular magnetically charged BH solutions within NED considered in Reference [15]. The thermodynamics for a magnetically charged regular BH, which comes from the action of GR and NED, was investigated in Reference [34]. In the present study we use the NED of Reference [15], explore a phenomenological extension of GR by introducing a fundamental length l using the modified Hayward metric, and investigate the magnetically charged BH.
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