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” versions, in the presence of nonlinear electrodynamics fields, defined by Lagrangians depending on both quadratic electromagnetic invariants, $F_{ab}{F}^{ab}$ and $F_{ab}\star F^{ab}$. 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.

In this paper, we derive Lorentz force and Maxwell’s equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to noncommutative space-time. We also show the equivalence of minimal coupling prescription and Feynman’s approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this noncommutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.

One of the long-standing problems is a quest for regular black hole solutions, in which a resolution of the spacetime singularity has been achieved by some physically reasonable, classical field, before one resorts to the quantum gravity. The prospect of using nonlinear electromagnetic fields for this goal has been limited by the Bronnikov’s no-go theorems, focused on Lagrangians depending on the electromagnetic invariant $F_{ab}{F}^{ab}$ only. We extend Bronnikov’s results by taking into account Lagrangians that depend on both electromagnetic invariants, $F_{ab}{F}^{ab}$ and $F_{ab}\star F^{ab}$, and prove that the tension between the Lagrangian’s Maxwellian weak field limit and boundedness of the curvature invariants persists in more general class of theories.

In this paper, we derive corrections to the geodesic equation due to the $\kappa$-deformation of curved spacetime, up to the first order in the deformation parameter $a$. This is done by generalizing the method from our previous paper [ Phys. Rev. D 84, 085020 (2011)] to include curvature effects. We show that the effect of $\kappa$-noncommutativity can be interpreted as an extra drag that acts on the particle while moving in this $\kappa$-deformed curved spacetime. We have derived the Newtonian limit of the geodesic equation and using this, we discuss possible bounds on the deformation parameter. We also derive the generalized uncertainty relations valid in the nonrelativistic limit of the $\kappa$-spacetime.

We obtain an exact analytic expression for the quasinormal modes of a non-commutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that the noncommutativity leads to a non-equispaced (discrete) area and entropy spectra.

The BTZ black hole geometry is probed with a noncommutative scalar field which obeys theκ-Minkowski algebra. The entropy of the BTZ black hole is calculated using the brick wall method. The contribution of the noncommutativity to the black hole entropy is explicitly evaluated up to the first order in the deformation parameter. We also argue that such a correction to the black hole entropy can be interpreted as arising from the renormalization of the Newton’s constant due to the effects of the noncommutativity.