Some new radiating Kerr-Newman solutions

Three exact non-static solutions of Einstein-Maxwell equations corresponding to a field of flowing null radiation plus an electromagnetic field are presented. These solutions are non-static generalizations of the well known Kerr-Newman solution. The current vector is null in all the three solutions. These solutions are the electromagnetic generalizations of the three generalized radiating Kerr solutions discussed by Vaidya and Patel. The solutions discussed by us describe the exterior gravitational fields of rotating radiating charged bodies. Many known solutions are derived as particular cases.     

Collapsing shear-free radiating fluid spheres

We present a new class of exact solutions of relativistic field equations for a collapsing spherically symmetric shear-free isotopic fluid undergoing radial heat flow. The interior solutions are matched with Vaidya exterior metric over the boundary. Initially the interior solutions represent a static configuration of perfect fluid which then gradually starts evolving into radiating collapse.     

Gravitational field of a radiating rotating body

A nonstationary solution of the Einstein field equations, corresponding to the field of a radiating rotating body, is presented. The solution is algebraically special of Petrov type II with a twisting, shear-free, null congruence identical to that of the Kerr metric. The new metric bears the same relation to the Kerr metric as does Vaidya's metric to the Schwarzschild metric, in the sense that in both cases the radiating solution is generated from the nonradiating one by replacing the mass parameter by an arbitrary function of a retarded time coordinate. The energy-momentum tensor in the present case, however, has two terms, a Vaidya type radiative one and an additional nonradiative residual term. Due to the presence of the nonradiative term in this case, however, the energy-momentum tensor becomes Vaidya-like asymptotically only, thus allowing for a geometrical optics interpretation. Asymptotically, part of the radiation field is purely electromagnetic with a Maxwell tensor which admits only one principal null direction corresponding to the undirectional flow of radiation.     

A Self-Similar Dynamics in Viscous Spheres

We study the evolution of radiating and viscous fluid spheres assuming an additional homothetic symmetry on the spherically symmetric space-time. We match a very simple solution to the symmetry equations with the exterior one (Vaidya). We then obtain a system of two ordinary differential equations which rule the dynamics, and find a self-similar collapse which is shear-free and with a barotropic equation of state. Considering a huge set of initial self-similar dynamics states, we work out a model with an acceptable physical behavior.     

Gravitational Perturbations of a Radiating Spacetime

This paper discusses the problem of gravitational perturbations of radiating spacetimes. We lay out the theoretical framework for describing the interaction of external gravitational fields with a radiating spacetime. This is done by deriving the field perturbation equations for a radiating metric. The equations are then specialized to a Vaidya spacetime. For the Hiscock ansatz of a linear mass model of a radiating blackhole the equations are found separable. Further, the resulting ordinary differential equations are found to admit analytic solutions. We obtain the solutions and discuss their characteristics.     

Radiating fluid sphere immersed in an anisotropic atmosphere

We model a radiating star undergoing dissipative gravitational collapse in the form of radial heat flux. The exterior of the collapsing star is described by the generalised Vaidya solution representing a mixture of null radiation and strings. Our model generalises previously known results of constant string density atmosphere to include inhomogeneities in the exterior spacetime. By utilising a causal heat transport equation of the Maxwell–Cattaneo form we show that relaxational effects are enhanced in the presence of inhomogeneities due to the string density.     

On the relativistic classical motion of a radiating spinning particle in a magnetic field

We propose classical equations of motion for a charged particle with magnetic moment, taking radiation reaction into account. This generalizes the Landau–Lifshitz equations for the spinless case. In the special case of spin-polarized motion in a constant magnetic field (synchrotron motion) we verify that the particle does lose energy. Previous proposals did not predict dissipation of energy and also suffered from runaway solutions analogous to those of the Lorentz–Dirac equations of motion.     

Metric of a rotating radiating charged mass in a de Sitter space

A new exact solution of the Einstein-Maxwell equations is presented for a rotating radiating charge mass in a de Sitter cosmological background. This solution is shown to encompass previous results by various authors.     

Self-similar and charged radiating spheres: an anisotropic approach

Considering charged fluid spheres as anisotropic sources and the diffusion limit as the transport mechanism, we suppose that the inner space–time admits self-similarity. Matching the interior solution with the Reissner–Nordström–Vaidya exterior one, we find an extremely compact and oscillatory final state with a redistribution of the electric charge function and non zero pressure profiles.     

Thermal evolution of the Kramer radiating star

The Kramer radiating star uses the interior Schwarzschild solution as a seed solution to generate a model of dissipative collapse. We investigate the thermal behaviour of the radiating star by employing a causal heat transport equation. The causal temperature is explicitly determined for the first time by integrating the transport equation. We further show that the dissipation of energy to the exterior space-time renders the core more unstable than the cooler surface layers.     

Diffusive and dynamical radiating stars with realistic equations of state

We model the dynamics of a spherically symmetric radiating dynamical star with three spacetime regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. A large family of solutions to the field equations are presented for various realistic equations of state. We demonstrate that it is possible to obtain solutions via a direct integration of the second order equations resulting from the assumption of an equation of state. A comparison of our solutions with earlier well known results is undertaken and we show that all these solutions, including those of Husain, are contained in our family. We then generalise our class of solutions to higher dimensions. Finally we consider the effects of diffusive transport and transparently derive the specific equations of state for which this diffusive behaviour is possible.     

Numerical tests and properties of waves in radiating fluids

We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic equilibrium is periodically driven at the boundary of a one-dimensional domain, and the solution describes the propagation of the waves thus excited. Two modes are excited for a given driving frequency, generally referred to as a radiative acoustic wave and a radiative diffusion wave. While the analytical solution is well known, several features are highlighted here that require care during its numerical implementation. We compare the solution in a wide range of parameter space to a numerical integration with a Lagrangian radiation hydrodynamics code. Our most significant observation is that flux-limited diffusion does not preserve causality for waves on a homogeneous background.     

When can a classical electron accelerate without radiating?

A classical point electron radiates when it accelerates. However, there are classical electron models with extended charge distributions which can accelerate and/or deform without radiating. Can a model be contrived that will undergo radiationless motion while accelerating (on the average) over a distance large compared to its size? The answer is no: we prove that the “center” of the electron is always closer than the electron “diameter” to a fictitious point undergoing constant-velocity motion, if the electron's motion is radiationless.     

On the plane gravitational condensor with the positive gravitational constant

The equations of motion for the plane shell consisting of an ideal fluid and creating the de Sitter solution on one side and the static plane symmetric solution of Einstein equations with positive cosmological constant on the other side are derived. Solution of the equation of motion for the case of “plane gravitational condensor” is found and the necessary agreement with the solution of the problem in the caseA = 0 is demonstrated.     

Radiating stars with generalised Vaidya atmospheres

We model the gravitational behaviour of a radiating star when the exterior geometry is the generalised Vaidya spacetime. The interior matter distribution is shear-free and undergoing radial heat flow. The exterior energy momentum tensor is a superposition of a null fluid and a string fluid. An analysis of the junction conditions at the stellar surface shows that the pressure at the boundary depends on the interior heat flux and the exterior string density. The results for a relativistic radiating star undergoing nonadiabatic collapse are obtained as a special case. For a particular model we demonstrate that the radiating fluid sphere collapses without the appearance of the horizon at the boundary.     

A class of stationary charged dust solutions of Einstein's field equations

We consider a special class of stationary rotating charged dust solutions of Einstein's field equations without cosmological constant. In these space-times, the motion of freely falling particles and of light rays can be visualized by the motion of charged particles in an appropriate model magnetic field. Any curl-free magnetostatic field, given on an open subset of Euclidean 3-space, can serve as a model magnetic field for a charged dust solution in this sense. The simplest example, corresponding to a homogeneous model magnetic field, is given by Som-Raychaudhuri space-time. Some other examples are worked out.     

Expanding and collapsing scalar field thin shell

This paper deals with the dynamics of scalar field thin shell in the Reissner-Nordstr?m geometry. The Israel junction conditions between Reissner-Nordstr?m spacetimes are derived, which lead to the equation of motion of scalar field shell and Klien–Gordon equation. These equations are solved numerically by taking scalar field model with the quadratic scalar potential. It is found that solution represents the expanding and collapsing scalar field shell. For the better understanding of this problem, we investigate the case of massless scalar field (by taking the scalar field potential zero). Also, we evaluate the scalar field potential when p is an explicit function of R. We conclude that both massless as well as massive scalar field shell can expand to infinity at constant rate or collapse to zero size forming a curvature singularity or bounce under suitable conditions.