静态球对称黑洞热力学与爱因斯坦场方程

建立在广义相对论基础上的黑洞理论与热力学定律之间有着深刻的内在联系.具体考虑球对称黑洞,研究表明通过史瓦西黑洞和Reissner-Nordstrom黑洞在其视界附近的爱因斯坦场方程可以直接得到对应的黑洞热力学第一定律.这揭示了爱因斯坦引力场方程与黑洞热力学的关系,表明了在广义相对论理论框架下黑洞热力学规律的必然性.     

Odd-Soliton Solutions to the Einstein Equations

Using the Inverse Scattering Method (ISM) of Belinskii and Zakharov a new odd-soliton solutions to the Einstein's field equations for an axially symmetric space-time in general relativity are obtained in the determinant form and shown to include Weyl's half-integral delta static solutions in a special case.     

Primordial black hole as a source of the boost factor

Primordial black holes (PBHs) accumulate weakly interacting massive particles (WIMPs) around them and form ultracompact minihalos (UCMHs), if the WIMP is a dominant component of the dark matter (DM). In this Letter, we discuss that the UCMHs seeded by the PBHs with sub-earth mass enhance the WIMP annihilation in the present Universe and can successfully explain the positron and/or electron excess in cosmic ray observed by PAMELA/Fermi experiments. The signal is very similar to that from a decaying dark matter, which can explain the PAMELA and/or Fermi anomaly without conflict with any constraints as long as the decay mode is proper. In this scenario, the boost factor can be as large as 10⁵. In addition, we discuss testability of our scenario by gamma-ray point source and gravitational-wave experiments.     

Black hole critical phenomena without black holes

Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.     

Black hole physics in globally hyperbolic space-times

The usual definition of a black hole is modified to make it applicable in a globally hyperbolic space-time. It is shown that in a closed globally hyperbolic universe the surface area of a black hole must eventually decrease. The implications of this breakdown of the black hole area theorem are discussed in the context of thermodynamics and cosmology. A modified definition of surface gravity is also given for non-stationary universes. The limitations of these concepts are illustrated by the explicit example of the Kerr-Vaidya metric.     

Thermodynamical quantities around a RNAdS black hole

The entropy density, energy density, pressure and equationof state around the RNAdS black hole are calculated in the WKBapproximation on the Teukolsky-type master equation. Theappearance of spin-dependent terms is demonstrated. The existenceof these terms shows that the black hole radiation is not exactlythermal radiation and the black hole entropy is not strictly proportional tothe area of the event horizon.     

Photon Stars

We discuss numerical solutions of Einstein's field equation describing static, spherically symmetric conglomerations of a photon gas. These equations imply a back reaction of the metric on the energy density of the photon gas according to Tolman's equation. The 3–fold of solutions corresponds to a class of physically different solutions which is parameterized by only two quantities, i.e. mass and surface temperature. The energy density is typically concentrated on a shell because the center contains a repelling singularity, which can, however, not be reached by timelike geodesics and only by radial null geodesics. The physical relevance of these solutions is completely open, although their existence may raise some doubts w.r.t. the stability of black holes.     

Formation of black hole and emission of gravitational waves

Numerical simulations were performed for the formation process of rotating black holes. It is suggested that Kerr black holes are formed for wide ranges of initial parameters. The nature of gravitational waves from a test particle falling into a Kerr black hole as well as the development of 3D numerical relativity for the coalescing binary neutron stars are discussed.     

Pre-low-mass X-ray binaries containing a black hole: investigating a detection mechanism

This work investigates the feasibility of detecting close, detached, black hole-red dwarf binaries, which are expected to be evolutionary precursors of low-mass X-ray binaries (LMXBs). Although this pre-low-mass X-ray binary (pre-LMXB) phase of evolution is predicted theoretically, as yet no such systems have been identified observationally. The calculations presented here suggest that the X-ray luminosity of black hole wind accretion in a pre-LMXB system could exceed the intrinsic X-ray luminosity of the red dwarf secondary star, thereby providing a detection mechanism. However, there is significant uncertainty regarding the efficiency of the conversion of gravitational potential energy to X-ray luminosity resulting from accretion onto a black hole, for example energy may be lost via advection across the event horizon. Still, sources with X-ray luminosities greater than that expected for a red dwarf star, but whose positions coincide with that of a red dwarf would represent candidate pre-LMXB systems. These candidates should be surveyed for the radial velocity shifts that would occur as a result of the orbital motion of a red dwarf star within a close binary system containing a black hole.      

On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invafiance group properties of the governing system of partial differential equations （PDEs） and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.     

Schwarzschild Metrics and Quasi-Universes

The exterior and interior Schwarzschild solutions are rewritten replacing the usual radial variable with an angular one. This allows us to obtain some results that otherwise are less apparent or even hidden in other coordinate systems.     

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an U(1) gauge field for which the density is given by a power of the Maxwell Lagrangian. In d-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as d/4. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking–Page phase transition in spite of conformally invariant Maxwell field.     

Charged particle trajectories in a magnetic field on a curved space-time

In this paper we have studied the motion of charged particles in a dipole magnetic field on the Schwarzscbild background geometry. A detailed analysis has been made in the equatorial plane through the study of the effective potential curves. In the case of positive canonical angular momentum the effective potential has two maxima and two minima giving rise to a well-defined potential well rear the event horizon. This feature of the effective potential categorises the particle orbits into four classes, depending on their energies. (i) Particles, coming from infinity with energy less than the absolute maximum ofV _eff, would scatter away after being turned away by the magnetic field. (ii) Whereas those with energies higher than this would go into the central star seeing no barrier. (iii) Particles initially located within the potential well are naturally trapped, and they execute Larmor motion in bound gyrating orbits. (iv) and those with initial positions corresponding to the extrema ofV _eff follow circular orbits which are stable for non-relativistic particles and unstable for relativistic ones. We have also considered the case of negative canonical angular momentum and found that no trapping in bound orbits occur for this case. In the case when particles are not confined to the equatorial plane we have found that the particles execute oscillatory motion between two mirror points if the magnetic field is sufficiently high, but would continuously fall towards the event horizon otherwise. An erratum to this article is available at .     

Factor structure of the Tomimatsu‐Sato solutions and their recurrence relations

We consider stationary axisymmetric vacuum solutions of Einstein's equations for which the Ernst potential is rational in prolate spheroidal coordinates. Extending an earlier study we show that there are several new expressions which are factorizable. In particular, we concentrate on the Tomimatsu‐Sato solutions and their recurrence relations. Various continuum limits of the recurrence relations will be discussed.     

Thermodynamics of regular black hole

We investigate thermodynamics for a magnetically charged regular black hole (MCRBH), which comes from the action of general relativity and nonlinear electromagnetics, comparing with the Reissner–Norström (RN) black hole in both four and two dimensions after dimensional reduction. We find that there is no thermodynamic difference between the regular and RN black holes for a fixed charge Q in both dimensions. This means that the condition for either singularity or regularity at the origin of coordinate does not affect the thermodynamics of black hole. Furthermore, we describe the near-horizon AdS₂ thermodynamics of the MCRBH with the connection of the Jackiw–Teitelboim theory. We also identify the near-horizon entropy as the statistical entropy by using the AdS₂/CFT₁ correspondence.     

Magnetically charged regular black hole in a model of nonlinear electrodynamics

We obtain a magnetically charged regular black hole in general relativity. The source to the Einstein field equations is nonlinear electrodynamic field in a physically reasonable model of nonlinear electrodynamics (NED). “Physically” here means the NED model is constructed on the basis of three conditions: the Maxwell asymptotic in the weak electromagnetic field limit; the presence of vacuum birefringence phenomenon; and satisfying the weak energy condition (WEC). In addition, we analyze the thermodynamic properties of the regular black hole in two ways. According to the usual black hole thermodynamics, we calculate the heat capacity at constant charge, from which we know the smaller black hole is more stable. We also employ the horizon thermodynamics to discuss the thermodynamic quantities, especially the heat capacity at constant pressure.