Dilaton gravity, (quasi-) black holes,and scalar charge

Electrically charged dust is considered in the framework of Einstein–Maxwell–dilaton gravity with a Lagrangian containing the interaction term \(P(\chi )F_{\mu \nu }F^{\mu \nu }\) , where \(P(\chi )\) is an arbitrary function of the dilaton scalar field \(\chi \) , which can be normal or phantom. Without assumption of spatial symmetry, we show that static configurations exist for arbitrary functions \(g_{00} = \exp (2\gamma (x^{i}))\) ( \(i=1,2,3\) ) and \(\chi =\chi (\gamma )\) . If \(\chi = \mathrm{const}\) , the classical Majumdar–Papapetrou (MP) system is restored. We discuss solutions that represent black holes (BHs) and quasi-black holes (QBHs), deduce some general results and confirm them by examples. In particular, we analyze configurations with spherical and cylindrical symmetries. It turns out that cylindrical BHs and QBHs cannot exist without negative energy density somewhere in space. However, in general, BHs and QBHs can be phantom-free, that is, can exist with everywhere nonnegative energy densities of matter, scalar and electromagnetic fields.     

Instability of black holes with scalar charge

Black holes with a conformal scalar field are proved to be unstable under monopole perturbations.     

一般加速带电带磁的动态黑洞中标量场的熵

在一般加速带电带磁的动态黑洞中,化简Klein-Gordon场方程,利用乌龟坐标变换,得到在视界面附近的辐射温度.用薄膜brick-wall模型,选择适当的截断因子和薄膜厚度,得到在视界面附近薄膜上的熵,结果表明黑洞熵与视界面积成正比. 关键词： 黑洞 Hawking温度 薄膜brick-wall模型 熵     

Anomalous production of chiral charge from black holes

The Reissner Nordström solution to Einstein equations coupled to a Yang-Mills field is unstable against the emission of light-charged fermions. We study the flux chirality in this decay process and illustrate the consistency of the result with the prediction of the axial anomaly.     

Magnetic charge,black holes,and cosmic censorship

The possibility of converting a Reissner-Nordström black hole into a naked singularity by means of test particle accretion is considered. The dually charged Reissner-Nordström metric describes a black hole only when M² > Q³ + P². The test particle equations of motion are shown to allow test particles with arbitrarily large magnetic charge/mass ratios to fall radially into electrically charged black holes. To determine the nature of the final state (black hole or naked singularity) an exact solution of Einstein's equations representing a spherical shell of magnetically charged dust falling into an electrically charged black hole is studied. Naked singularities are never formed so long as the weak energy condition is obeyed by the infalling matter. The differences between the spherical shell model and an infalling point test particle are examined and discussed.     

Fermions tunneling from rotating stationary Kerr black hole with electric charge and magnetic charge

In this paper, the method of semi-classical fermion tunneling is extended to explore the fermion tunneling behavior of a Kerr–Newman–Kasuya black hole. Thus, the Hamilton–Jacobi equation in Kerr–Newman–Kasuya space–time is derived by the method presented in Refs. Lin and Yang (2009) [24], [25], [26], the Hawking temperature at the horizon and the tunneling probability of spin- 1/2 fermions are finally obtained following the semi-classical quantum equation. The results indicate the common features of this black hole.     

Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.     

Vacuum polarization and the spontaneous loss of charge by black holes

The spontaneous loss of charge by black holes due to particle emission is discussed. For large black holes (more massive than 10¹⁷ g) the process is shown to be governed by a Schwinger type formula. For smaller black holes the method of calculating the process is described and asymptotic forms for scattering and superradiant coefficients given.     

Black holes with scalar charge

Previously it had been thought that a stationary black hole with an exterior devoid of matter can be parametrized only by mass, angular momentum, and electric charge. We show here that scalar charge is also an admissible parameter. Our starting point is a new solution of Einstein's equations with stress-energy of electromagnetic and conformal scalar fields which we presented earlier. It has a black-hole geometry, and is parametrized by electric and scalar charges. Its conformal scalar field is unbounded at the event horizon, and we originally regarded this feature as incompatible with a black hole interpretation. However, following a suggestion of B. DeWitt, we show here that the infinity in the scalar field need not be physically pathological: it is not associated with an infinite potential barrier for test scalar charges; it does not cause the termination of any trajectories of these test particles at finite proper time; and it is not connected with unbounded tidal accelerations between neighboring trajectories. In view of these facts, we now regard the new solution as a genuine black hole solution.     

Fermions tunneling from the Horowitz-Strominger Dilaton black hole

Based on the work of Kerner and Mann, fermions tunneling from the Horowitz-Strominger Dilaton black hole on the membrane is studied. Owing to the coupling among electromagnetic field, matter field and gravity field, the Dirac equation of charged particles is introduced, and according to that, the expected emission temperature is obtained. After the self-gravitational interaction is considered, it is found that the tunneling rate of fermions also satisfies the underlying Unitary theory as the case of scalar particles. Supported by the Natural Science Foundation of Sichuan Education Office (Grant No. 07ZC039)     

Dilaton gravity approach to three-dimensional Lifshitz black hole

The z=3 Lifshitz black hole is an exact black hole solution to the new massive gravity in three dimensions. In order to understand this black hole clearly, we perform a dimensional reduction to two-dimensional dilaton gravity by utilizing the circular symmetry. Considering the linear dilaton, we find the same Lifshitz black hole in two dimensions. This implies that all thermodynamic quantities of the z=3 Lifshitz black hole could be obtained from its corresponding black hole in two dimensions. As a result, we derive the temperature, mass, heat capacity, Bekenstein–Hawking entropy, and free energy.     

Entropy and supersymmetry of D-dimensional extremal electric black holes versus string states

Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a p-dimensional torus, for D = (10 − p) = 4,…,9. We study in particular a one-parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identified with the entropy of the elementary string state with the corresponding quantum numbers.     

Simple black holes with anisotropic fluid

We study a spherically symmetric spacetime made of an anisotropic fluid whose radial equation-of-state is given by p_1=-ρ. This case allows analytic solutions and is a good example for studying the static configuration of a black hole plus matter. For a given equation-of-state parameter w_2 = p_2/ρ for angular directions, we find the exact solutions of the Einstein equation described by two parameters. We classify the solutions into six types based on the behavior of the metric function. Depending on the parameters, the solutions can have event and cosmological horizons. One of the solution types corresponds to a generalization of the Reissner-Nordstr(o|¨)m black hole, the thermodynamic properties for which are obtained in a simple form. The solutions are stable under radial perturbations.     

Magnetic black holes with string-loop corrections

String-loop corrections to magnetic black holes are studied. 4D effective action is obtained by compactification of the heterotic string theory on the manifold K3×T² or on a suitable orbifold yielding N=1 supersymmetry in 6D. In the resulting 4D theory with N=2 local supersymmetry, the prepotential receives only one-string-loop perturbative correction. The loop-corrected black hole is obtained in two approaches: (i) by solving the system of the Einstein-Maxwell equations of motion derived from the loop-corrected effective action and (ii) by solving the system of spinor Killing equations (conditions for the supersymmetry variations of the fermions to vanish) and Maxwell equations. We consider a particular tree-level solution with the magnetic charges adjusted so that the moduli connected with the metric of the internal two-torus are constant. In this case, the loop correction to the prepotential is independent of coordinates, and it is possible to solve the system of the Einstein-Maxwell and spinor Killing equations in the first order in string coupling analytically. The set of supersymmetric solutions of the loop-corrected spinor Killing equations is contained in a larger set of solutions of the equations of motion derived from the string-loop-corrected effective action. Loop corrections to the metric and dilaton are large at small distances from the center of the black hole.