Hawking radiation from a general spherically symmetric evaporating black hole

By means of generalized tortoise coordinates both the Klein-Gordon equation and the Dirac equation are reduced near the event horizon of a general spherically symmetric evaporating black hole. The location and the temperature of the event horizon are given automatically without calculating the energy-momentum tensor. The Hawking thermal spectra of the Klein-Gordon particles and the Dirac particles are obtained, respectively.     

Viscous fluid in static spherically symmetric space-time

The paper presents a static spherically symmetric viscous fluid solution of Einstein field equation, assuming an equation of statep=(γ?1)ρ. Though static, the solution has expansion, shear, and acceleration and can explain cosmological red shift. Also it has a particle horizon. The singularity at the origin and larger viscosity make it unfit to represent a real universe.     

String cosmology in higher dimensional spherically symmetric space-time

Some cosmological solutions for string model are derived in higher dimensional spherically symmetric space-time, following the techniques used by Letelier. The equations of state for strings have been used for different solutions. Also polynomial relation between the metric coefficients has been assumed in some cases.     

Remark concerning spherically symmetric nonstatic solutions to the Einstein equations in the comoving frame

All nonstatic spherically symmetric fluid solutions to the Einstein equations in the comoving frame $$ds^2 = e^{\lambda (r,t)} dr^2 + e^{\mu (r,t)} d\Omega ^2 - e^{v(r,t)} dt^2$$ are found subject to the conditions: (i) \(\dot \lambda = {\rm A}\dot \mu\) ,A = const, (ii) λ,μ, andν are separable functions ofr andt, (iii) the heat flux vanishes, and (iv) the coefficient of shear viscosity vanishes. There are but two classes of solutions: (i)A= 1, in which case the metric reduces to the Robertson-Walker form, and (ii)A=0, in which case there are four solutions, all with nonvanishing acceleration, expansion, and shear. WithA=0, the solutions are either singular at the origin or degenerate into spaces of constant curvature.     

Topological defect solutions in the spherically symmetric space-time admitting conformal motion

In this paper, we have examined strings with monopole and electric field and domain walls with matter and electric field in the spherically symmetric space-time admitting a one-parameter group of conformal motions. For this purpose, we have solved Einstein's field equations for a spherically symmetric space-time via conformal motions. Also, we have discussed the features of the obtained solutions.     

Further remark concerning spherically symmetric nonstatic separable solutions to the Einstein equations in the comoving frame

We consider nonstatic spherically symmetric fluid solutions to the Einstein equations which, in the comoving frame, have metric coefficients that are separable functions of their arguments and that have an origin. Subject to the vanishing of the heat flux, we show that all such solutions with shear and non-vanishing shear viscosity have a scalar polynomial singularity at the origin if the fluid satisfies both the weak and strong energy conditions. When combined with previous results [1] we conclude that for the metric forms under consideration, the only fluid solutions to the Einstein equations with vanishing heat flux which satisfy the energy conditions and are free of singularities at the origin are the Robertson-Walker solutions.     

A spherically symmetric gravitational collapse-field with radiation

An interior spherically symmetric solution of Einstein’s field equations corresponding to perfect fluid plus a flowing radiation-field is presented. The physical 3-spacet=constant of our solution is spheroidal. Vaidya’s pure radiation field is taken as the exterior solution. The inward motion of the collapsing boundary surface follows from the equations of fit. An approximation procedure is used to get a generalization of the standard Oppenheimer-Snyder model of collapse with outflow of radiation. One such explicit solution has been given correct to second power of eccentricity of the spheroidal 3-space.     

Generalized scalar tensor theory in four and higher dimensional spherically symmetric space-time

In this paper, we have studied generalized scalar tensor theory for spherically symmetric models, both in four and higher dimensions with a bulk viscous fluid. We have considered both exponential and power law solutions with some assumptions among the physical parameters and solutions have been discussed.     

Force multipole moments for a spherically symmetric particle in solution

We present a general theorem for the force multipole moments of arbitrary order induced in a spherically symmetric particle immersed in a fluid whose motion satisfies the linear Navier-Stokes equation for steady incompressible viscous flow. The multipole moments are expressed in terms of the unperturbed fluid velocity field. It is shown that for a particle with a finite extension only a few terms give rise to fluid perturbations which are not confined to the interior of the particle. We give explicit results for a polymer satisfying the Debye-Bueche-Brinkman equations and for a hard sphere with mixed slip-stick boundary conditions.     

Hawking effect in Vaidya-Bonner space-time

A new method determining the location and the temperature of event horizons of evaporating black holes is suggested. Both the Klein-Gordon equation and the Dirac equation are studied with the method in a Vaidya-Bonner space-time. These equations are reduced near the event horizon when the generalized tortoise coordinates are adopted. The location and the temperature of the event horizon are shown automatically. The first approximation of our result is the same as that obtained by using the calculation of the vacuum expectation value of the renormalized energy-momentum tensor when the evaporation of the black hole is very slow.     

Hawking effect in Vaidya-de Sitter space-time

The solutions of both the Klein-Gordon equation and the Dirac equation near the event horizons are given in the Vaidya-de Sitter space-time. With a new method the locations of the black hole event horizon and universe horizon, as well as their Hawking temperatures, are shown automatically and easily.     

Hawking radiation and page curves of the black holes in thermal environment

As realistic objects in the Universe, the black holes are surrounded by complex environment. By taking the effect of thermal environment into account, we investigate the evaporation process and the time evolutions (page curves) of the entanglement entropies of Hawking radiation of various types of black holes. It is found that the black holes with the thermal environments evaporate slower than those without the environments due to the environmental contribution of the energy flux in addition to Hawking radiation. For Schwarzschild black hole and Reissner-Nordström black hole in flat spaces, when the initial temperature of the black hole is higher than the environment temperature, the black holes evaporate completely and the Hawking radiation is eventually purified. For Schwarzschild-AdS black hole, it will evaporate completely and the Hawking radiation is purified when the environment temperature is lower than the critical temperature. Otherwise, it will reach an equilibrium state with the environment and the radiation is maximally entangled with the black hole. Our results indicate that the final state of the black hole is determined by the environmental temperature and the temporal evolution and the speed of the information purification process characterized by the page curve of the Hawking radiation is also influenced by the thermal environment significantly.     

球对称动态黑洞视界附近的瞬时辐射能通量及瞬时辐射功率

采用黑洞的薄膜模型和局域热平衡的假定,研究球对称动态黑洞视界附近的瞬时辐射能通量和瞬时辐射功率,得到了当截断距离η取定后,Vaidya黑洞视界附近标量场的瞬时辐射能通量与黑洞的质量和视界变化率有关,其瞬时辐射功率仅与黑洞的视界变化率有关.Vaidya-Bonner黑洞的瞬时辐射能通量和瞬时辐射功率与黑洞的质量、电荷和视界变化率有关.表明黑洞周围的引力场、电磁场以及视界的变化均对黑洞的热辐射产生影响.     

Majumdar-Papapetrou class of nonstatic cylindrically symmetric Brans-Dicke-Maxwell fields

We have obtained relations between certain components of the metric and the electromagnetic potentials for source-free Brans-Dicke-Maxwell fields described by a nonstatic cylindrically symmetric Einstein-Rosen metric. These are important, in the sense that they generate a class of solutions that in a way can be said to belong to the class generated by similar relations obtained by Majumdar [1] and Papapetrou [2] for generalized static Einstein-Maxwell fields. The relations have further been used to reduce the B-D Maxwell equations to B-D vacuum equations and vice versa.     

静态球对称黑洞的热质点模型及辐射功率

利用静态球对称黑洞的热质点模型,研究了黑洞的热辐射规律,得到了当η取固有厚度时,对所有Schwarzschild黑洞,其辐射功率都相同,其视界处的辐射能通量与黑洞的质量的平方成反比,而距黑洞遥远的观察者所接收到的辐射能通量与观测者到黑洞的距离的平方成反比; Reissner-Nordstrm黑洞视界处的辐射能通量和辐射功率不仅与黑洞的质量有关,还与黑洞的电荷有关,而距黑洞遥远的观察者所接收到的辐射能通量,当截断的固有厚度η、黑洞的质量m和电荷Q取定后与观测者到黑洞之间的距离的 关键词： 静态球对称黑洞 热质点模型 辐射功率 辐射能通量     

Measurement of the space-time correlation function of thermal acoustic radiation

The space-time correlation function of thermal acoustic radiation pressure is measured for a stationary heated source (a narrow plasticine plate). The correlation dependence is obtained by the multiplication of two signals shifted in time with respect to each other and measured by two receivers. The dependence exhibits an oscillating behavior and changes sign when the source is displaced by half the spatial period of the correlation function.     

On the spherically symmetric gauge fields

The spherically symmetric gauge fields with a compact gauge group over 4-dimensional Minkowski space are determined completely. Expressions for the gauge potentials of these fields are obtained.