Static spherically-symmetric scalar-field theory in general relativity |
| |
Authors: | Demetrios D Dionysiou |
| |
Institution: | 1. Department of Mathematics, Hellenic Air Force Academy, Dekelia, Attica, Greece
|
| |
Abstract: | A spherically-symmetric static scalar field in general relativity is considered. The field equations are defined by $$\begin{gathered} R_{ik} = - \mu \varphi _i \varphi _k ,\varphi _i = \frac{{\partial \varphi }}{{\partial x^i }}, \varphi ^i = g^{ik} \varphi _k , \hfill \\ \hfill \\ \end{gathered} $$ where ?=?(r,t) is a scalar field. In the past, the same problem was considered by Bergmann and Leipnik (1957) and Buchdahl (1959) with the assumption that ?=?(r) be independent oft and recently by Wyman (1981) with the assumption ?=?(r, t). The object of this paper is to give explicit results with a different approach and under a more general condition $$\phi _{;i}^i = ( - g)^{ - 1/2} \frac{\partial }{{\partial x^i }}\left {( - g)^{1/2} g^{ik} \frac{\partial }{{\partial x^k }}} \right] = - 4\pi ( -g )^{ - 1/2} \rho $$ where ?=?(r, t) is the mass or the charge density of the sources of the field. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|