球面引力波的精确解

Exact solution of spherical gravitational wave

场源物体以角速度Ω自转时,拖动外场时空产生运动。在黎曼空间内察看旋转坐标系的线元,即Papapetrou线元,其度规函数不但跟空间坐标(Z、ρ)有关,还跟时间坐标(t)有关。再考虑谐和坐标条件,爱因斯坦场方程Rμυ=0被变形为带有度规函数的新场方程fgμυfμυ-gμυfμfυ+f4ρ-2gμυωμωυ+ω-1ρgμυ(f2ρ-1ωμ)υ=0。对时间宗量引进新的变换,球面引力波是新方程的0阶精确解。波函数表示:场源转动物质塌缩后变为旋转黑洞,黑洞视界存在周期性径向脉动,脉动振幅收敛于奇点,最远扩散至黑洞边界r=2GM/(kc2),小于史瓦西半径;黑洞旋转减慢趋于静止时,0阶球面波解的静场极限跟史瓦西解趋同。

Space-time take place wave motion of gravitational outfield when the field source body is rotating with angular velocity Ω. Metrics functions of Papapetrou line element relate to that, not only space coordinates but also time. If it is introduced from harmonic conditions, Einstein's field equations R_(μυ)=0 is turn into a new metrics equation fg^(μυ)f_(μυ)-g^(μυ)f_μf_υ+f^4ρ^(-2)g^(μυ)ω_μω_υ+ω^(-1)ρg^(μυ)(f^2ρ^(-1)ω_μ)_υ=0. This equation there is wave solutions when a new time parameter is used. Spherical gravitational wave function is zero-order solution of new equation. This solution show, rotating body is collapsed into black hole and it remain rotation too. Horizon of rotating black hole is periodicity pulsation follow a radial, pulse amplitude draw into a strageness point and enlarge to its boundary of black hole, r=2 GM/(kc^2). This boundary is smaller Schwarzschild radius. Static limit of spherical wave solution is Schwarzschild solution when black hole rotating slow down and incline to static stat.