带电球体的一种Reissner-Nordstrm内解

AN INTERIOR REISSNER-NORDSTROM SOLUTION FOR A CHARGED SPHERE

一、引言Einstein 重力场方程的求解,是广义相对论的一个重要问题.但自从 Reissner-Nord-°trm 外解确定以后,至今没有找到一个相应内解的简洁表示.本文采用一般的球对称度规,对场方程进行严格求解.在假设理想气体球的电荷密度ρe=ρ0rβeλ/2,物质密度ρm=μr-

In this paper,the Einstein-Maxwell field equations are solved for a sphe- rically symmetric static charged sphere.Let pressure P=kp_m,matter density P_m=μr^a and charge density p_=P_or~βe^(λ/2),we have proved that there is a rational solution only when the matter density p_m is negative,and obtained a simpler metric form which our solution is matched with the exterior Rei- ssner-Nordstrm solution at the boundary r=R.Though the matter density is negative,the energy density is positive everywhere.So this has a real physical meaning and may provide the Poincare stress for the stability of the electron.