维迪雅度规

维迪雅度规描述了具有球对称的辐射引力场，是史瓦西度规在非静态情况下的推广，是维迪雅于1951年提出来的^[1]。其数学表示为：

${\displaystyle \mathrm {d} \tau ^{2}={\bigg (}{\frac {\dot {M}}{f(M)}}{\bigg )}^{2}{\bigg (}1-{\frac {2GM}{r}}{\bigg )}\mathrm {d} t^{2}-{\bigg (}1-{\frac {2GM}{r}}{\bigg )}^{-1}\mathrm {d} r^{2}-r^{2}\mathrm {d} \Omega ^{2}}$

其中

${\displaystyle \mathrm {d} \Omega ^{2}=\mathrm {d} \theta ^{2}+\sin ^{2}\theta \mathrm {d} \varphi ^{2}}$

${\displaystyle M=M(r,t)}$

${\displaystyle f(M)=M'(1-{\frac {2GM}{r}})}$

${\displaystyle {\dot {M}}=\partial M/\partial t}$

${\displaystyle M'=\partial M/\partial r}$

参考文献

1. Vaidya, P.C., 1951, Proceedings of the Indian Academy of Sciences, A33, 264