The effective gravitational mass as well as the energy and momentum distributions of a radiating charged particle in Einstein's universe are evaluated. The Moller's energy–momentum complex is employed for this computation. The spacetime under study is a generalization of Bonnor and Vaidya spacetime in the sense that the metric is described in the cosmological background of Einstein's universe in lieu of the flat background. Several spacetimes are limiting cases of the one considered here. In particular for the Reissner–Nordstrom black hole background, our results are exactly the same as those derived by Cohen and Gautreau using Whittaker's theorem and by Cohen and de Felice using Komar's mass. Furthermore, the power output for the spacetime under consideration is obtained.

Effective mass of a radiating charged particle in einstein's universe

This paper deals with a particular case of Lyra's modification of Riemannian geometry in which the consequences of the thermodynamic equilibrium of a gravitating fluid sphere have been considered. These considerations lead to a zero red shift in this static model.

Thermodynamic equilibrium of a gravitating sphere in Lyra's geometry

We show that the linear dynamics of cosmological perturbations can be described by coupled wave equations, allowing their efficient numerical and, in certain limits, analytical integration directly in position space. The linear evolution of any perturbation can then be analyzed with the Green's function method. Prior to hydrogen recombination, assuming tight coupling between photons and baryons, neglecting neutrino perturbations, and taking isentropic (adiabatic) initial conditions, the obtained Green's functions for all metric, density, and velocity perturbations vanish beyond the acoustic horizon. A localized primordial cosmological perturbation expands as an acoustic wave of photon-baryon density perturbation with narrow spikes at its acoustic wave fronts. These spikes provide one of the main contributions to the cosmic microwave background radiation anisotropy on all experimentally accessible scales. The gravitational interaction between cold dark matter and baryons causes a dip in the observed temperature of the radiation at the center of the initial perturbation. We first model the radiation by a perfect fluid and then extend our analysis to account for finite photon mean free path. The resulting diffusive corrections smear the sharp features in the photon and baryon density Green's functions over the scale of Silk damping.

Dynamics of cosmological perturbations in position space

The equations describing the adiabatic, small radial oscillations of general relativistic stars are generalized to include the effects of a cosmological constant. The generalized eigenvalue equation for the normal modes is used to study the changes in the stability of the homogeneous sphere induced by the presence of the cosmological constant. The variation of the critical adiabatic index as a function of the central pressure is studied numerically for different trial functions. The presence of a large cosmological constant significantly increases the value of the critical adiabatic index. The dynamical stability condition of the homogeneous star in the Schwarzschild –de Sitter geometry is obtained and several bounds on the maximum allowable value for a cosmological constant are derived from stability considerations.

Dynamical instability of fluid spheres in the presence of a cosmological constant

The main subject of the book is an up-to-date and in-depth survey of the theory of normal frames and coordinates in differential geometry. The book can be used as a reference manual, review of the existing results and introduction to some new ideas and developments. In the book can be found practically all existing essential results and methods concerning normal frames and coordinates. Most of the results are represented in full detail with full, in some cases new, proofs. All classical results are expanded and generalized in various directions. Theorems of existence, uniqueness and, possibly, holonomicity of the normal frames and coordinates are proved: mostly, the proofs are constructive and some their parts can be used independently for other tasks. Besides published results, their extensions and generalizations, the book contains completely new results which appear for the first time.

P. Tolman

Papers

Relativity, thermodynamics and cosmology.