相关论文: Spherically symmetric self-similar solutions and t…
We classify all spherically symmetric perfect fluid solutions of Einstein's equations with equation of state p/mu=a which are self-similar in the sense that all dimensionless variables depend only upon z=r/t. For a given value of a, such…
The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1<alpha<1) are described. We prove that for large and small values of the similarity variable, z=r/t, all such…
We classify all spherically symmetric dust solutions of Einstein's equations which are self-similar in the sense that all dimensionless variables depend only upon $z\equiv r/t$. We show that the equations can be reduced to a special case of…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
Static spherically symmetric solutions to the Einstein-Euler equations with prescribed central densities are known to exist, be unique and smooth for reasonable equations of state. Some criteria are also available to decide whether…
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantised gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically…
We consider the self-similar solutions associated with the critical behavior observed in the gravitational collapse of spherically symmetric perfect fluids with equation of state $p=\alpha\mu$. We identify for the first time the global…
We investigate self-similar solutions which are asymptotic to the Friedmann universe at spatial infinity and contain a scalar field with potential. The potential is required to be exponential by self-similarity. It is found that there are…
We look for "static" spherically symmetric solutions of Einstein's Equations for perfect fluid source with equation of state $p=w\rho$. In order to include the possibilities of recently popularized dark energy and phantom energy possibly…
The time independent spherically symmetric solutions of General Relativity (GR) coupled to a dynamical unit timelike vector are studied. We find there is a three-parameter family of solutions with this symmetry. Imposing asymptotic flatness…
We present two classes of inhomogeneous, spherically symmetric solutions of the Einstein-Maxwell-Perfect Fluid field equations with cosmological constant generalizing the Vaidya-Shah solution. Some special limits of our solution reduce to…
In Newton's and in Einstein's theory we give criteria on the equation of state of a barotropic perfect fluid which guarantee that the corresponding one-parameter family of static, spherically symmetric solutions has finite extent. These…
In this article, a special static spherically symmetric perfect fluid solution of Einstein's equations is provided. Though pressure and density both diverge at the origin, their ratio remains constant. The solution presented here fails to…
We analyze the 3-parameter family of exact, regular, static, spherically symmetric perfect fluid solutions of Einstein's equations (corresponding to a 2-parameter family of equations of state) due to Pant and Sah and "rediscovered" by…
We investigate the gravitational collapse of a spherically symmetric, perfect fluid with equation of state P = (Gamma -1)rho. We restrict attention to the ultrarelativistic (``kinetic-energy-dominated'', ``scale-free'') limit where black…
We use a combination of numerical and analytical methods, exploiting the equations derived in a preceding paper, to classify all spherically symmetric self-similar solutions which are asymptotically Friedmann at large distances and contain…
The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the…
Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
The self-similarity hypothesis claims that in classical general relativity, spherically symmetric solutions may naturally evolve to a self-similar form in certain circumstances. In this context, the validity of the corresponding hypothesis…