A large family of new black hole solutions in 2 þ 1-dimensional Einstein-power-Maxwell gravity with prescribed physical properties is derived. We show with particular examples that according to the power parameter k of the Maxwell field, the obtained solutions may be asymptotically flat for 1=2 < k < 1 or nonflat for k > 1 in the vanishing cosmological constant limit. We study the thermodynamic properties of the solution with two different models, and it is shown that thermodynamic quantities satisfy the first law. The behavior of the heat capacity indicates that by employing the 1 þ 1-dimensional dilaton analogy the local thermodynamic stability is satisfied.
We obtain a class of magnetically charged solutions in 2 þ 1 dimensional Einstein-Power-Maxwell theory. In the linear Maxwell limit, such horizonless solutions are known to exist. We show that in 3D geometry, black hole solutions with magnetic charge do not exist even if it is sourced by the powerMaxwell field. Physical properties of the solution with particular power k of the Maxwell field is investigated. The true timelike naked curvature singularity develops when k > 1 which constitutes one of the striking effects of the power-Maxwell field. For specific power parameter k, the occurrence of a timelike naked singularity is analyzed in the quantum mechanical point of view. Quantum test fields obeying the Klein-Gordon and the Dirac equations are used to probe the singularity. It is shown that the class of static pure magnetic spacetime in the power-Maxwell theory is quantum-mechanically singular when it is probed with fields obeying Klein-Gordon and Dirac equations in the generic case.
We give a general class of static, spherically symmetric, non-asymptotically flat and asymptotically non-(anti) de Sitter black hole solutions in Einstein-Maxwell-Dilaton (EMD) theory of gravity in 4-dimensions. In this general study we couple a magnetic Maxwell field with a general dilaton potential, while double Liouville-type potentials are coupled with the gravity. We show that the dilatonic parameters play the key role in switching between the Bertotti-Robinson and Reissner-Nordström spacetimes. We study the stability of such black holes under a linear radial perturbation, and in this sense we find exceptional cases that the EMD black holes are unstable.In continuation we give a detailed study of the spin-weighted harmonics in dilatonic Hawking radiation spectrum and compare our results with the previously known ones. Finally, we investigate the status of resulting naked singularities of our general solution when probed with quantum test particles.We revisit the 4−dimensional Einstein-Maxwell-Dilaton (EMD) theory and show that there are still plenty of rooms available to contribute the subject. Double Liouville potential and general dilaton coupling is considered to obtain more general solutions with extra parameters and diagonal metric in the theory. From the outset we remind that, depending on the relative parameters, the double Liouville potential has the advantage of admitting local extrema and critical points. The Higgs potential also shares such features, whereas single Liouville potential lacks these properties. Double Liouville-type potentials arise also when higher-dimensional theories are compactified to 4−dimensional spacetimes and expectedly bring in further richness. All known solutions to date can be obtained [1-3] as particular limits of our general solution, and it contains new solutions as well. In the most general form our solution covers Reissner-Nordstrom (RN) type black holes and Bertotti-Robinson (BR) spacetimes interpolated within the same metric. Interpolation of two different solutions in general relativity is not a new idea [4]. Particular limits of the dilatonic parameter yield the RN and BR spacetimes. In between the two, the linear dilaton black hole (LDBH) lies for the specific choice of the parameters. It is well-known that the near horizon geometry of the extremal RN black hole yields the BR electromagnetic universe. The latter [5] is important for various reasons: It is a singularity free non-black hole solution which admits maximal symmetry and finds application in conformal field theory correspondence (i.e. AdS/ CFT). Particles in the BR universe move with uniform acceleration in a conformally flat background. These features are mostly valid not only in N = 4 but in higher dimensions (N > 4) as well. The topological structure of the BR spacetime is still AdS 2 × S N −2 in N−dimensions with the radius of S N −2 depending on the dimension of the space. Recently we have extended the Maxwell part of the BR spacetime to cover the Yang-Mills (YM) field and obtained common feature...
We present a theorem in d-dimensional static, spherically symmetric spacetime in generic Lovelock gravity coupled with a non-linear electrodynamic source to generate solutions. The theorem states that irrespective of the order of the Lovelock gravity and non-linear Maxwell (NLM) Lagrangian, for the pure electric field case the NLM equations are satisfied by virtue of the Einstein-Lovelock equations. Applications of the theorem, specifically to the study of black hole solutions in Chern-Simons (CS) theory is given. Radiating version of the theorem has been considered, which generalizes the Bonnor-Vaidya (BV) metric to the Lovelock gravity with a NLM field as a radiating source. We consider also the radiating power -Maxwell source ( i.e. (F µν F µν ) q , q = finely -tuned constant ) within the context of Lovelock gravity.
Generalization of a known theorem to generate static, spherically symmetric black-hole solutions in higher dimensional Lovelock gravity is presented. Particular limits, such as Gauss-Bonnet (GB) and/or Einstein-Hilbert (EH) in any dimension N yield all the solutions known to date with an energy-momentum. In our generalization, with special emphasis on the third order Lovelock gravity, we have found two different class of solutions characterized by the matter field parameter.Several particular cases are studied and properties related to asymptotic behaviours are discussed.Our general solution which covers topological black holes as well, splits naturally into distinct classes such as Chern-Simon (CS) and Born-Infeld (BI) in higher dimensions. The occurence of naked singularities are studied and it is found that, the spacetime behaves nonsingular in quantum mechanical sense when it is probed with quantum test particles. The theorem is extended to cover Bertotti-Robinson (BR) type solutions in the presence of the GB parameter alone. Finally we prove also that extension of the theorem for a scalar-tensor source of higher dimensions (N > 4) fails to work.
Quantum singularities considered in the 3D BTZ spacetime by Pitelli and Letelier (Phys. Rev. D77: 124030, 2008) is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and non-linear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analysed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields; the conical geometry near r = 0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence, the classical central singularity at r = 0 turns out to be quantum mechanically singular for quantum particles obeying Klein-Gordon equation but nonsingular for fermions obeying Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes do not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.
We introduce a class of solutions in 2 + 1-dimensional Einstein-Power-Maxwell theory for a circularly symmetric electric field. The electromagnetic field is considered with an angular component given byFirst, we show that the metric for zero cosmological constant and the Power-MaxwellLagrangian of the form of F μν F μν coincides with the solution given in 2 + 1-dimensional gravity coupled with a massless, self-interacting real scalar field. With the same Lagrangian and a non-zero cosmological constant we obtain a non-asymptotically flat wormhole solution in 2 + 1 dimensions. The confining motions of massive charged and chargeless particles are investigated too. Secondly, another interesting solution is given for zero cosmological constant together with the conformal invariant condition. The formation of a timelike naked singularity for this particular case is investigated within the framework of the quantum mechanics. Quantum fields obeying the Klein-Gordon and Dirac equations are used to probe the singularity and test the quantum mechanical status of the singularity.
In this paper, we extend the gravitational bending of light studies in Kottler metrics to comprise nonlinear electrodynamics within the framework of Einstein -power -Maxwell theory. We show that the closest approach distance and the gravitational bending of light are affected from the presence of charge for particular values of the power parameter k, which is defined by means of energy conditions. It is shown that the bending angle of light is stronger in the case of a strong electric field, which is the case for k = 1.2.
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