SCHWARZSCHILD SOLUTION OF THE MODIFIED EINSTEIN FIELD EQUATIONS

A reformulation of the Schwarzschild solution of the linearized Einstein field equations in post-Riemannian Finsler spacetime is derived. The solution is constructed in three stages: the exterior solution, the event-horizon solution and the interior solution. It is shown that the exterior solution is asymptotically similar to Newtonian gravity at large distances implying that Newtonian gravity is a low energy approximation of the solution. Application of Eddington-Finklestein coordinates is shown to reproduce the results obtained from standard general relativity at the event horizon. Further application of Kruskal-Szekeres coordinates reveals that the interior solution contains maximally extensible geodesics.

NONUNIFORM BRANEWORLD STARS: AN EXACT SOLUTION

In this paper the first exact interior solution to Einstein's field equations for a static and nonuniform braneworld star with local and nonlocal bulk terms is presented. It is shown that the bulk Weyl scalar [Formula: see text] is always negative inside the stellar distribution, and in consequence it reduces both the effective density and the effective pressure. It is found that the anisotropy generated by bulk gravity effect has an acceptable physical behavior inside the distribution. Using a Reissner–Nördstrom-like exterior solution, the effects of bulk gravity on pressure and density are found through matching conditions.

EMBEDDING VERSUS IMMERSION IN GENERAL RELATIVITY

We briefly discuss the concepts of immersion and embedding of space-times in higher-dimensional spaces. We revisit the classical work by Kasner in which he constructs a model of immersion of the Schwarzschild exterior solution into a six-dimensional pseudo-Euclidean manifold. We show that, from a physical point of view, this model is not entirely satisfactory, since the causal structure of the immersed space-time is not preserved by the immersion.

Behaviour of the Kramer Radiating Star

We study the behaviour of the model for a radiating star proposed by Kramer. The evolution of the model is governed by a second order nonlinear differential equation. The general solution of this equation is expressed in terms of elementary and special functions. This completes the solution of the Einstein field equations for the interior of the star. The model matches smoothly to the Vaidya exterior solution and the condition p = qB is satisfied at the boundary. We briefly study the thermodynamics of the model and indicate the difficulty in specifying the temperature explicitly.

An Exact Model of an Anisotropic Relativistic Sphere

In this paper the field equations of general relativity are solved to obtain an exact solution for a static anisotropic fluid sphere. The solution is free from singularity and satisfies the necessary physical requirements. The physical 3-space of the solution is pseudo-spheroidal. The solution is matched at the boundary with the Schwarzschild exterior solution. Numerical estimates of various physical parameters are briefly discussed.

SPECTRAL SHIFT FROM AN EVOLVING DUST SPHERE

Following O’brien-Synge’s junction conditions we find an exterior solution for a (n+2)-dimensional spherically symmetric distribution in comoving coordinates and match it with the zero-pressure dust interior. An expression for Schwarzschild-like mass is also obtained from the conditions of fit at the boundary. The relevant transformation relations which recast the comoving exterior into the static Schwarzschild-like form are also obtained. This generalizes to higher dimensions an earlier work of Raychaudhuri in 4D spacetime. Utilizing the transformation relations, an expression for frequency shift of radiation emitted from the surface of the sphere is also obtained.