Thursday, 11 May 2017

homework and exercises - Gibbons-Hawking-York (GHY) boundary term for Schwarzschild metric


What is the simplest way to calculate Gibbons-Hawking-York boundary term for Schwarzschild metric?


\begin{align} \int Kd\Sigma&=-32\pi^2m\left(1-2Mr^{-1}\right)^{1/2}\times\frac{d}{dr}\left[ir^2\left(1-2Mr^{-1}\right)^{1/2}\right]\\ &=-32\pi^2iM\left(2r-3M\right). \end{align}




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