Compact anisotropic stars with membrane - a new class of exact solutions to the Einstein field equations
Abstract
A new class of solutions to Einstein's classical field equations of general relativity is presented. The solutions describe a non-rotating, spherically symmetric, compact self gravitating object, residing in a static electro-vacuum space time. The solutions generally have an interior non-zero matter-distribution. A wide class of interior solutions can be constructed for any specific set of exterior parameters (mass, charge). The original Schwarzschild and Reissner-Nordstroem solutions constitute special cases within the variety of interior solutions. An outstanding feature of the new solutions is a non-continuous boundary of the matter-distribution, accompanied by a two dimensional membrane at the boundary. The membrane consists of an infinitesimally thin spherical shell of tangential pressure (surface tension/stress). The interior matter state generally has a locally anisotropic pressure. A general procedure for generating the new solutions is given. A few solutions are derived and discussed briefly. In order to identify the physically most promising solutions, a selection principle is formulated, based on the holographic principle. One solution of particular interest emerges. It is characterized by the property, that the "stress-energy content" of the membrane is equal to the gravitating mass of the object.
Keywords
Cite
@article{arxiv.gr-qc/0306063,
title = {Compact anisotropic stars with membrane - a new class of exact solutions to the Einstein field equations},
author = {Michael Petri},
journal= {arXiv preprint arXiv:gr-qc/0306063},
year = {2007}
}
Comments
34 pages, no figures; revised v2: references and typos corrected, references added, changed Introduction to acknowledge relevent papers that were overlooked; v3: moved equations of motion to Appendix