Nonlinear Charged Black Hole Solution in Rastall Gravity

Abstract

We show that the spherically symmetric black hole (BH) solution of a charged (linear case) field equation of Rastall gravitational theory is not affected by the Rastall parameter and this is consistent with the results presented in the literature. However, when we apply the field equation of Rastall’s theory to a special form of nonlinear electrodynamics (NED) source, we derive a novel spherically symmetric BH solution that involves the Rastall parameter. The main source of the appearance of this parameter is the trace part of the NED source, which has a non-vanishing value, unlike the linear charged field equation. We show that the new BH solution is Anti−de-Sitter Reissner−Nordström spacetime in which the Rastall parameter is absorbed into the cosmological constant. This solution coincides with Reissner−Nordström solution in the GR limit, i.e., when Rastall’s parameter is vanishing. To gain more insight into this BH, we study the stability using the deviation of geodesic equations to derive the stability condition. Moreover, we explain the thermodynamic properties of this BH and show that it is stable, unlike the linear charged case that has a second-order phase transition. Finally, we prove the validity of the first law of thermodynamics.

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“…The Rastall theory provides a straightforward and tractable form for the EFE that yields interesting features from astrophysical and cosmological perspectives. In the recent past, Rastall theory has been found to be successful in the formalism of black hole solutions [51], charged and rotating NUT black holes [52], rotating blak holes [53], Kerr-Newman-AdS black holes [54], black holes inspired by non-commutative geometry [55], nonlinear charged black holes [56] etc. The Rastall theory has also been important in compact star modeling.…”

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“…In particular, quark-nugget dark matter [65][66][67] and axion-like particles [68][69][70] are investigated. After that, the subjects of dark energy [71,72] and modified gravity theories [73] are explored. In the end, acting as a summary of sorts, a recent review on modern cosmology in terms of dark energy, dark matter, as well as inflation [74] is included in this Special Issue.…”

“…In Ref. [73], a solution of charged, nonlinear black holes with is explored as part of the Rastall gravity theory. The model parameter in the theory does not influence the solution of the linear gravitational field equation for a charged black hole with spherical symmetry.…”