As the interaction between black holes and highly energetic infalling charged matter receives quantum corrections, basic laws of hole mechanics have to be carefully rederived. Using covariant phase space formalism, we generalize first law mechanics, both ``equilibrium state'' ``physical process'' versions, in presence nonlinear electrodynamics fields, defined by Lagrangians depending on quadratic electromagnetic invariants, ${F}_{ab}{F}^{ab}$ ${F}_{ab}\ensuremath{\star}{F}^{ab}$. Derivation...

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

A bstract We use the framework of Hopf algebra and noncommutative differential geometry to build a (NC) theory gravity in bottom-up approach. Noncommutativity is introduced via deformed diffeomorphisms by means Drinfeld twist. The final result construction general formalism for obtaining NC corrections classical wide class deformations background. This also includes novel proposal Einstein manifold. Moreover, applied case linearized gravitational perturbation describe deformation metric...

Nonlinear extensions of classical Maxwell's electromagnetism are among the prominent candidates for theories admitting regular black hole solutions. A quest such examples has been fruitful, but mostly unsystematic and littered by introduction physically unrealistic Lagrangians. We provide a procedure which admits reconstruction nonlinear electromagnetic Lagrangian, consistent with Euler–Heisenberg Lagrangian in weak-field limit, from given metric representing regular, magnetically charged hole.

Matter fields don't necessarily have to share the symmetries with spacetime they live in. When this happens, we speak of symmetry inheritance fields. In paper classify obstructions by scalar fields, both real and complex, look more closely at special cases stationary axially symmetric spacetimes. Since noninheritance is present in boson stars may enable existence black hole hair, our results narrow possible classes such solutions. Finally, define analyse contributions Komar mass angular...

We prove several inequalities between the curvature invariants, which impose constraints on singularities, as well asymptotic properties of spacetimes. Some hold for a family spacetimes include static, Friedmann--Lema\^itre--Robertson--Walker, and Bianchi type I metrics, independently whether they are solutions some particular field equations. In contrast, others Einstein's gravitational equation energy-momentum tensors, specific form spacetime metric. illustrate different behaviour basic...

A bstract We study gravitational perturbations of the Schwarzschild metric in context noncommutative gravity. r – φ and t noncommutativity are introduced through a Moyal twist Hopf algebra diffeomorphisms. Differential geometric structures such as curvature tensors also twisted. Noncommutative equations motion derived from recently proposed NC vacuum Einstein equation. Here, addition to previously calculated axial potential, we present polar solution which generalizes work done by Zerilli....

We complete the analysis carried out in previous papers by studying Hawking radiation for a Kerr black hole to infinity fermionic currents of any spin. find agreement with thermal spectrum degrees freedom. start showing that near-horizon physics is approximated an effective two-dimensional field theory fields. Then, starting from spin form ${W}_{1+\ensuremath{\infty}}$ algebra, we construct infinite set covariant currents, each which carries corresponding moment radiation. All together they...

We analyze the 3d free massive fermion theory coupled to external sources. The presence of a mass explicitly breaks parity invariance. calculate two- and three-point functions gauge current energy momentum tensor and, for instance, obtain well-known result that in IR limit (but also UV one) we reconstruct relevant CS action. then couple model higher spin currents work out 3 case. In an effective action which was proposed many years ago as possible generalization derive different This...

We present a direct, geometric derivation of the generalized Smarr formula for stationary axially symmetric black holes with nonlinear electromagnetic fields. The additional term is proven to be proportional integral trace energy-momentum tensor and can written as product two conjugate variables. From novel relation we deduce all previously proposed forms formula, which were derived only spherically holes, provide lowest order quantum correction classical from Euler–Heisenberg Lagrangian.

We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or stealth field. The first theorem holds static spacetimes and is independent of the gravitational part action, as long coupling to minimal. second assumes Einstein--Hilbert action relies on positive theorem, but does not assume metric static. In addition, we discuss possible...

A bstract We study the noncommutative corrections to entropy of Reissner-Nordström black hole using a κ -deformed scalar probe within brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from Killing vector fields hole. show that effects naturally lead logarithmic correction Bekenstein-Hawking even at lowest order WKB approximation. In contrast, such commutative setup appear only after quantum are included through higher or loop effects. Our analysis...

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in rising era gravitational wave astronomy. We study dynamics within noncommutative geometry framework, based on a Drinfeld twist and newly proposed Einstein equation, obtain leading correction to Regge-Wheeler potential up first order noncommutativity parameter. By calculating quasinormal mode frequencies we show that Schwarzschild black hole remains stable under axial perturbations.

We show that for general spherically symmetric configurations, contributions of broad class gravitational and mixed gauge-gravitational Chern–Simons (CS) terms to the equations motion vanish identically in D > 3 dimensions. This implies such action do not affect Birkhoff's theorem or any previously known solutions. Furthermore, we investigate thermodynamical properties using procedure described an accompanying paper. find static case, CS contribute entropy either. Moreover, if one requires...

Stealth field configurations by definition have a vanishing energy-momentum tensor, thus do not contribute to the gravitational equations. While only trivial fields can be stealth in Maxwell's electrodynamics, nontrivial appear some nonlinear models of electromagnetism. We find necessary and sufficient conditions for electromagnetic analyse which admit such configurations. Furthermore, we present concrete exact solutions, featuring class black holes dressed with hair, closely related...

Within the framework of noncommutative (NC) deformation gauge field theory by angular twist, we first rederive NC scalar and model from our previous papers then generalize it to second order in Seiberg-Witten (SW) map. It turns out that SW expansion is finite ceases at parameter, ultimately giving rise equation motion for Reissner--Nordstr\"om (RN) metric nonperturbative exact same order. As a further step, show effective put forth constructed work satisfies equations Einstein-Maxwell...

Any recipe to grow black hole hair has circumvent no-hair theorems by violating some of their assumptions. Recently discovered hairy solutions exist due the fact that scalar fields don't inherit symmetries spacetime metric. We present here a general analysis constraints which limit possible forms such hair, for both real and complex fields. These results can be taken as novel piece uniqueness or simply symmetry noninheriting Ans\"atze guide. In addition we introduce new classification...

We extend the classical results on symmetry inheritance of canonical electromagnetic fields, described by Maxwell's Lagrangian, to a much wider class models, which include those Born-Infeld, power Maxwell and Euler-Heisenberg type. Symmetry inheriting fields allow introduction scalar potentials these are proven be constant Killing horizons. Finally, using relations obtained along analysis, we generalize simplify recent proof for 3-dimensional case, as well give first constraint higher...

We prove that the electromagnetic field in a -dimensional spacetime necessarily inherits symmetries of metric large class generalized Einstein–Maxwell theories. The Lagrangians studied theories have general diff-covariant gravitational part and include both gauge Chern–Simons terms.

We consider some general consequences of adding pure gravitational Chern-Simons term to manifestly diff-covariant theories gravity. Extending the result a previous paper we enlarge class metrics for which inclusion gCS in action does not affect solutions and corresponding physical quantities. In case such describe black holes (of horizon topology) show that hole entropy is also unchanged. arrive at these conclusions by proving three theorems studying their consequences. One states...

In this note we present a new proof that Killing horizons are equipotential hypersurfaces for the electric and magnetic scalar potential, makes no use of gravitational field equations or assumption about existence bifurcation surface.