A new type of solution of the Schwarzschild problem for a point-source

A new type of a solution of the Schwarzschild problem for a point particle has been obtained. In contrast to the standard forms of solutions, the Schwarzschild singularity in the given solution coincides with the central singularity.     

The evolution and efficiency of energy release of magnetized black-hole accretion disks

On the basis of the equivalent circuit model, we investigate two different mechanisms of extracting energy of rotation and angular momentum from a black hole by magnetic field, namely, the Blandford-Znajek (BZ) process and the magnetic coupling (MC) process. The contributions to the efficiency of energy release via pure accretion process, BZ process and MC process are compared in detail by studying the evolutionary characteristics of the spin parameter of the black hole at the center of the magnetized accretion disk. It is shown that the MC process is an important new mechanism of extracting energy from the rotating black hole and its efficiency of energy release is almost as high as that of the BZ process. The efficiency of energy release via pure accretion process is higher than those of BZ process and magnetic coupling process. However, when the rotation of a black hole approaches that of an extreme Kerr black hole,the efficiency of energy release is mainly due to the contributions of BZ process and MC process.     

Charged analogues of Schwarzschild interior solution in terms of pressure

Recently, Bijalwan (Astrophys. Space Sci., doi:, 2011a) discussed charged fluid spheres with pressure while Bijalwan and Gupta (Astrophys. Space Sci. 317, 251–260, 2008) suggested using a monotonically decreasing function f to generate all possible physically viable charged analogues of Schwarzschild interior solutions analytically. They discussed some previously known and new solutions for Schwarzschild parameter u( = \fracGMc²a ) ￡ 0.142u( =\frac{GM}{c^{2}a} ) \le 0.142, a being radius of star. In this paper we investigate wide range of u by generating a class of solutions that are well behaved and suitable for modeling Neutron star charge matter. We have exploited the range u≤0.142 by considering pressure p=p(ω) and f = ( f₀(1 - \fracR²(1 - w)a²) +f_a\fracR²(1 - w)a² )f = ( f_{0}(1 - \frac{R^{2}(1 - \omega )}{a^{2}}) +f_{a}\frac{R^{2}(1 - \omega )}{a^{2}} ), where w = 1 -\fracr²R²\omega = 1 -\frac{r^{2}}{R^{2}} to explore new class of solutions. Hence, class of charged analogues of Schwarzschild interior is found for barotropic equation of state relating the radial pressure to the energy density. The analytical models thus found are well behaved with surface red shift z _s ≤0.181, central red shift z _c ≤0.282, mass to radius ratio M/a≤0.149, total charge to total mass ratio e/M≤0.807 and satisfy Andreasson’s (Commun. Math. Phys. 288, 715–730, 2009) stability condition. Red-shift, velocity of sound and p/c ² ρ are monotonically decreasing towards the surface while adiabatic index is monotonically increasing. The maximum mass found to be 1.512 M _Θ with linear dimension 14.964 km. Class of charged analogues of Schwarzschild interior discussed in this paper doesn’t have neutral counter part. These solutions completely describe interior of a stable Neutron star charge matter since at centre the charge distribution is zero, e/M≤0.807 and a typical neutral Neutron star has mass between 1.35 and about 2.1 solar mass, with a corresponding radius of about 12 km (Kiziltan et al., [astro-ph.GA], 2010).     

Thermodynamical analysis of acoustic Schwarzschild black hole

In this paper, we analyze the thermodynamic properties of acoustic Schwarzschild black holes with its parameter. The study is conducted in the extended phase space displaying the phase transition. This phase transition is examined through Gibbs free energy, specific heat, and heat capacity. Later, we discuss the thermal stability of acoustic black holes through Hawking temperature by identifying their stable and unstable regions. We calculate the corrected entropy to examine the thermal fluctuations. Through the corrected entropy we observe that there is no fluctuation in the case of small black holes. We also discuss the energy emission process from acoustic black holes. Moreover, we employ the generalized uncertainty principle to obtain a modified Lagrangian equation. We analyze the tunneling and Hawking temperature of the acoustic Schwarzschild black hole after solving the field equations.     

Exact solution of anisotropic compact stars via mass function

Studying relativistic compact objects is important in modern astrophysics to understand several astrophysical issues. It is therefore natural to ask for an internal structure and physical properties of specific classes of compact stars from astrophysical observations. We obtain a class of new relativistic solutions with anisotropic distribution of matter for compact stars. More specifically, stellar models, described by an anisotropic fluid, establishing a relation between metric potentials and generating a specific form of mass function, are explicitly constructed within the framework of General Relativity. New solutions can be used to model compact objects, which adequately describe compact strange star candidates like SMC X-1, Her X-1 and 4U 1538-52, with observational data taken from Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431:3216, 2013). As a possible astrophysical application the obtained solutions could explain the physics of selfgravitating objects, and might be useful for strong-field regimes where data are currently inadequate.     

Exact solution of a triaxial gyrostat with one rotor

The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of integrals of motion it can be reduced to only one degree-of-freedom problem. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This representation shows that the problem is equivalent to a quadratic Hamiltonian depending on two parameters. We find the exact solution of the orbits in terms of elliptic functions. By making use of properties of elliptic functions we find the solution at each region of the parametric partition from the solution of one region. We also prove that heteroclinic orbits are planar curves.     

Exact solution of a line-transfer problem in kernel approximation

In recent years approximate solutions for line-transfer problems using a kernel representation have been discussed by several authors (cf. Avrett and Loeser, 1966; Hummer and Rybicki, 1967). In this paper, extending an invariant imbedding method to the line-transfer problem with a kernel approximation as a sum of exponentials, we show how to get an exact solution of Milne's integral equation for the frequency-independent line source function with the aid of the resolvent kernel. A Cauchy system for an auxiliary function and the resolvent is suitable for numerical computation by means of high-speed digital computers.     

Exact solution of transport equation in finite multiplying media

One speed neutron transport equation in a finite multiplying medium is exactly and uniquely solved following the first author's new technique (Das Gupta, 1978b) based on Laplace transformation and Wiener-Hopf technique, to obtain the angular neutron density at any depth. Criticality condition is derived.     

Exact solution of a radiative transfer problem by the Laplace Transform and Wiener-Hopf Technique

In this paper the authors have extended Bayin's (1978) work to the case of charged fluid spheres. These solutions are matched at the boundary with the Reissner-Nordström solution.     

Gravitational singularities via acceleration: The case of the Schwarzschild solution and Bach's gamma metric

The so called gamma metric corresponds to a two‐parameter family of axially symmetric, static solutions of Einstein's equations found by Bach. It contains the Schwarzschild solution for a particular value of one of the parameters, that rules a deviation from spherical symmetry. It is shown that there is invariantly definable singular behaviour beyond the one displayed by the Kretschmann scalar when a unique, hypersurface orthogonal, timelike Killing vector exists. In this case, a particle can be defined to be at rest when its world‐line is a corresponding Killing orbit. The norm of the acceleration on such an orbit proves to be singular not only for metrics that deviate from Schwarzschild's metric, but also on approaching the horizon of Schwarzschild metric itself, in contrast to the discontinuous behaviour of the curvature scalar.     

Exact solution of the transport equation for imperfect rayleigh scattering in a semi-infinite atmosphere

By performing the one-sided Laplace transform on the matrix integro-differential equation for a semi-infinite plane parallel imperfect Rayleigh scattering atmosphere we derive an integral equation for the emergent intensity matrix. Application of the Wiener-Hopf technique to this integral equation will give the emergent intensity matrix in terms of singularH-matrix and an unknown matrix. The unknown matrix has been determined considering the boundary condition at infinity to be identical with the asymptotic solution for the intensity matrix.     

Exact solution of the equation of transfer with planetary phase function

We have considered the transport equation for radiative transfer to a problem in semi-infinite atmosphere with no incident radiation and scattering according to planetary phase function w(1 + xcos ). Using Laplace transform and the Wiener-Hopf technique, we have determined the emergent intensity and the intensity at any optical depth. The emergent intensity is in agreement with that of Chandrasekhar (1960).     

Exact solution of the problem of diffuse reflection for a combination of Rayleigh and isotropic scattering

We consider the basic vector equation of transfer for radiation in a semi-infinite atmosphere for diffuse reflection which scatters radiation in accordance with the phase matrix obtained from a combination of Rayleight and isotropic scattering. This equation will give an integral equation for emergent intensity while subjected to the Laplace transform. The integral equation will give rise to the emergent intensity matrix on application of the Wiener-Hopf technique. This is an exact method.     

Numerical solution of the time-dependent heat energy equations for the magnetosphere

A new solution of the magnetospheric heat equations capable of covering the whole region from 300 km along a field line to the equatorial plane has been achieved by adapting the searching procedure of Murphy (1974). It has been found that the protonospheric heat reservoir is sufficient to maintain T_e >T_n down to the height of the F2-peak electron density all through the night at mid-latitudes. Full solution of the equations has also shown that T_i >T_e in the protonosphere at night and the ions constitute a significant source of heat for the electrons.     

Exact solution of a basic equation in finite atmosphere by the method of Laplace transform and linear singular operators

A finite atmosphere having distribution of intensity at both surfaces with definite form of scattering function and source function is considered here. The basic integro-differential equation for the intensity distribution at any optical depth is subjected to the finite Laplace transform to have linear integral equations for the surface quantities under interest. These linear integral equations are transformed into linear singular integral equations by use of the Plemelj's formulae. The solution of these linear singular integral equations are obtained in terms of theX-Y equations of Chandrasekhar by use of the theory of linear singular operators which is applied in Das (1978a).     

Gravitational energy, momentum and angular momentum of Schwarzschild Anti-de Sitter space-times in the teleparallel equivalent of general relativity

We give a class of spherically symmetric-Anti de Sitter (Ads), exact solution in the teleparallel equivalent of general relativity (TEGR). The solution depends on an arbitrary function F(R)\mathcal{F}(R) and reproduce the metric of Schwarzschild Ads space-time. In the context of the Hamiltonian formulation of the TEGR we compute the gravitational energy of this class. The calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. We show that the form of the energy depends on the arbitrary function. We make a constrain on this arbitrary function to give the correct form of energy.     

Exact solution of the problem of diffuse reflection and transmission by the method of Laplace transform and linear singular operators

The basic integro-differential equation is subjected to a one-sided finite Laplace transform to obtain linear integral equations of angular distribution of bounding faces. These linear integral equations have been transformed into linear singular integral equations which have been solved exactly to get the emergent distributions from the bounding faces by the theory of linear singular operators. Some solutions of linear singular integral equations have also been derived for future use in radiative transfer problems.     

Exact solution of a simple time-dependent integro-differential equation by the method of Laplace transform and the theory of linear singular operators

The simplest form of the equation of transfer for a time dependent radiation field in finite atmosphere is considered. This equation of transfer is an integro-differential equation, the solution of this equation is based on the theory of separation of variables, the Laplace transform and the theory of linear singular operators. The emergent intensities from the bounding faces of the finite atmosphere are determined in terms ofX-Y equations of Chandrasekhar.