Black hole thermodynamics in the presence of nonlinear electromagnetic fields

Abstract

As the interaction between the black holes and highly energetic infalling charged matter receives quantum corrections, the basic laws of black hole mechanics have to be carefully rederived. Using the covariant phase space formalism we generalize the first law of black hole mechanics, both "equilibrium state" and "physical process" version, in the presence of nonlinear electrodynamics fields, defined by Lagrangians depending on both quadratic electromagnetic invariants, F ab F ab and F ab ⋆F ab . Derivation of this law demands a specific treatment of the Lagrangian parameters, similar to embedding of the cosmological constant into thermodynamic context. Furthermore, we discuss the validity of energy conditions, several complementing proofs of the zeroth law of black hole electrodynamics and some aspects of the recently generalized Smarr formula, its (non-)linearity and relation to the first law.

Introductory Notes on Non‐linear Electrodynamics and its Applications

“…For instance, NEDs coupled to gravity have been used to construct new black hole solutions and study their properties and stability (see e.g. [8-10, 12, 35, 77-95] and also [21,52,53,[96][97][98][99][100][101][102][103][104][105] for the latest developments and review), to create cosmological models (which might avoid initial Big-Bang singularities), [106,107] to mimic dark energy and generate an accelerated expansion of the universe, [108][109][110][111][112][113][114][115] as well as the context of AdS/CFT correspondence and gravity/CMT holography (see e.g. [14,[116][117][118][119][120][121][122] and [123] for a recent review and more references).…”

“…Taub-NUT and Reissner-Nordström, accelerated ones and others), and gravitational waves have been explored in a number of papers. [98,102,[129][130][131][132][133][134][135][136][137] Here I will restrict the discussion only to the simplest example of the Reissner-Nordström black hole. The Reissner-Nordström black hole sourced by the ModMax energy momentum tensor has the metric (34) with the scalar function f (r) of the following form…”

No Cauchy Horizon Theorem for Nonlinear Electrodynamics Black Holes with Charged Scalar Hairs

“…[19][20][21][22]. There are various theories with nonlinear electromagnetic interactions in the literature and a recent discussion about the black hole thermodynamics in the presence of nonlinear electromagnetic fields can be found in [23]. Note that one can construct a charged black hole with arbitrary number of horizons by considering NED, see e.g.…”

ModMax meets Susy

“…As we observed in [5], this class of conformal electrodynamics includes (after a constant rescaling of the gauge potential A m ) the conformal and duality-invariant ModMax theory. More recently, investigations similar to those of [6] but specific to ModMax have been carried out and further extended in [7][8][9][10] (see also [11,12]).…”