Scattering of a Klein-Gordon particle by a black hole

By using the curved space-time Klein-Gordon equation, the form of the wave function of a scalar particle near a nonrotating black hole is obtained. It is shown that although the radial wave function oscillates infinitely rapidly near the black hole, the probability density remains finite even on the event horizon. This is consistent with the fact that the Schwarzschild surface is nonsingular. An expression is given for the large angular momentum scattering differential cross section by comparing the asymptotic form of the radial wave equation with the corresponding Coulomb radial wave equation in ordinary quantum mechanics.     

Conformal scalar propagation and Hawking radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by Hawking on the relation between quantum propagation and observation of particles produced by a black hole.     

Schwarzschild黑洞整体正规时空中的测地运动

本文研究了Schwarzschild黑洞整体正规时空中的测地运动,求得了无奇性内部时空中检验粒子测地方程的解析解,并与奇性黑洞情况作了比较。 关键词：     

Conformal scalar propagation inside the Schwarzschild black hole

The analytic expression obtained in the preceding project for the massless conformal scalar propagator in the Hartle–Hawking vacuum state for small values of the Schwarzschild radial coordinate above r = 2M is analytically extended into the interior of the Schwarzschild black hole. The result of the analytical extension coincides with the exact propagator for a small range of values of the Schwarzschild radial coordinate below r = 2M and is an analytic expression which manifestly features its dependence on the background space–time geometry. This feature as well as the absence of any assumptions and prerequisites in the derivation render this Hartle–Hawking scalar propagator in the interior of the Schwarzschild black-hole geometry distinct from previous results. The two propagators obtained in the interior and in the exterior region of the Schwarzschild black hole are matched across the event horizon. The result of that match is a massless conformal scalar propagator in the Hartle–Hawking vacuum state which is shown to describe particle production by the Schwarzschild black hole.

“The future is not what it used to be!” From Alan Parker’s film “Angel Heart”     

Energy levels of a scalar particle in a static gravitational field close to the black hole limit

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.     

Vacuum polarization by a massive scalar field in Schwarzschild spacetime

The vacuum polarization by massive scalar particles in the gravitational field of the Schwarzschild black hole is discussed. The explicit expression for the vacuum energy-momentum tensor is obtained in the case when the Compton length λ_m =?/mc of the massive particle is much less than the gravitational radius of a black hole.     

Approximation in Thin Film Brick-Wall Model

The thin film brick-wall model is an important method on calculating the entropy of the non-static black hole. But we can see in this paper that the approximation used in the thin film brick-wall model is a rate of two infinitesimal parameters in fact. in this paper, we make an exact calculation of the approximation term and give the solution in the Schwarzschild black hole space-time.     

整体正规Schwarzschild黑洞的最大和完备的解析延拓

本文给出了整体正规Schwarzschild黑洞在Kruskal坐标变换中的最大和完备的解析延拓,讨论了零超曲面上的连接条件,比较了奇性和非奇性Schwarzschild黑洞的渐近时空结构。结果表明,可以存在非奇性的稳定的黑洞。 关键词：     

Scalar resonant frequencies and Hawking effect of an f(R) global monopole

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in f(R) gravity.The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions.We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles.     

Black hole as a point radiator and recoil effect on the brane world

A small black hole attached to a brane in a higher-dimensional space emitting quanta into the bulk may leave the brane as a result of a recoil. We construct a field theory model in which such a black hole is described as a massive scalar particle with internal degrees of freedom. In this model, the probability of transition between the different internal levels is identical to the probability of thermal emission calculated for the Schwarzschild black hole. The discussed recoil effect implies that the thermal emission of the black holes, which might be created by interaction of high energy particles in colliders, could be terminated and the energy nonconservation can be observed in the brane experiments.     

Coordinates with Non-Singular Curvature for a Time Dependent Black Hole Horizon

A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found that for a shrinking mass scale due to evaporation, the null radial geodesics that generate the horizon are slightly displaced from the coordinate singularity. In addition, a changing horizon scale significantly alters the form of the coordinate singularity in diagonal (orthogonal) metric coordinates representing the space-time. A Penrose diagram describing the growth and evaporation of an example black hole is constructed to examine the evolution of the coordinate singularity.     

Black holes coupled to scalar fields in higher-dimensional Kaluza-Klein theory

We derive in this paper an exact spherically symmetric solution coupled to scalar fields inn-dimensional Kaluza-Klein theory. A seven-dimensional solution is shown as a special case of the general solution. The solution has two even horizons. The inner horizon corresponds to the Schwarzschild black hole and the outer horizon is due to the scalar fields.     

SCHWARZSCHILD BLACK HOLE,VACUUM C METRIC WHEN m=0 AND RINDLER METRIC

In this paper,vacuum C-metric when m=0 is derived from the metric of a Schwarzschild black hole if its mass and location approach to infinity in an appropriate way.Furthermore,by using coordinate transformation in which there is no acceleration,vacuum C-metric when m=0 is transformed to Rindler metric.The result shows that an infinitesimal neighborhood of the horizon of an infinite Schwarzschild black hole is a Rindler space-time,and the acceleration in the Rindler space-time can arise from the in finite Schwarzschild black hole.     

Scattering and absorption of particles by a black hole involving a global monopole

Under the conditions that the wavelength of a particle is much larger than its radius of central mass, and the Schwarzschild field is weak, the scattering of a particle has been studied by many researchers. They obtained that scalar and vector particles abide by Rutherford’s angle distribution by using the low level perturbation method and the scattered field’s approximation in a weak field. The scattering cross section of a photon coincides with the section in Newton’s field of point mass. We can obtain the photon’s polarization effect by calculating the second-order perturbation in the linear Schwarzschild field. This article discusses the scattering and absorption of a particle by a black hole involving a global monopole by using the aforesaid method.     

Black holes in massive gravity: quasi-normal modes of scalar perturbations

We have studied quasinormal modes of scalar perturbations of a black hole in massive gravity. The parameters of the theory, such as the mass of the black hole, the scalar charge of the black hole and the spherical harmonic index is varied to see how the corresponding quasinormal frequencies change. We have also studied the massive scalar field perturbations. Most of the work is done using WKB approach while sections are devoted to compute quasinormal modes via the unstable null geodesics approach and the Pöschl–Teller approximation. Comparisons are done with the Schwarzschild black hole.     

Junction conditions on null hypersurface

The analytic extension of the globally regular space-time metric for a Schwarzschild black hole is realized by a Kruskal-like coordinate transformation. The junction conditions on null hypersurface are discussed. The reason why a stable black hole bounded with null hypersurface can exist is explained.     

Influence of Dark Energy on Gravitational Time Delay

We investigate the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence. With the analysis and numerical methods, we find that the gravitational time delay of light in the Schwarzschild black hole space-time surrounded by quintessence increases when the normalization factor c increases, and that the gravitational time delay also decreases when the quintessential state parameter ω_q increases.     

Connections between abstract quantum theory and space-time structure. III. Vacuum structure and black holes

Quantum-theoretic considerations for the ground state of a black hole result in a change of its interior solution. It is shown that the interior of a Schwarzschild black hole can be modeled by an ur-theoretically described Robertson-Walker space-time. Thereby the Schwarzschild singularity is changed into a Friedman singularity.     

The Thermal Radiation from Static Spherically Symmetric Black Holes

By use of the radiant emittance near the event horizon of static spherically symmetric black hole, the radiation field around the black hole was studied and found the generalized Stefan Boltzmann coefficient σ of thermal radiation near the event horizon is much greater than the flat space-time blackbody radiation. For Schwarzschild black hole, σ will increased as the black hole mass increases. For Reissner-Nordström black hole, σ has some relation with the quality and the charges of the black hole. Thermal particle model was proposed creatively to study the radiation power and radiant energy flux of static spherically symmetric black hole, found when η take the inherent thickness, for all Schwarzschild black hole the radiation power are the same and the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole, for Reissner-Nordström black hole the radiation power is associated with the quality and the charge of the black hole. When given the mass and charges of the black hole, the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole.     

Absorption Cross Section of Static Einstein-Maxwell Dilation Axion Black Hole for Scalar Particles

The absorption cross section of the static Einstein-Maxwell dilaton axion （EMDA） black hole for scalar particles is investigated. It is shown that the ratio of the absorption cross section of the EMDA black hole to that of the Schwarzschild black hole decreases as the absolute value of the dilaton increases, and it becomes zero as the dilaton tends to its extremal value. It is also shown that the absorption cross section decreases as both the v and the absolute value of the dilaton increase, and it decreases as the mass of the particle decreases.