Current Research on BMS-Like Transformations and Charges of Black Holes

Abstract

The BMS-like charges we consider here are also referred to as BMS soft hair, since they correspond to soft gravitons and extend the notion of black hole hair. Today we will focus on the classical picture, the next lecture will focus on the quantum model. Consider Schwarzschild geometry in Eddington–Finkelstein coordinates in advanced time $v=t+r^*$. The only difference of this form of the metric with that of the Bondi coordinates the fact that we use $r^*$ instead of r

$$ds^2 = - \left( 1- \frac{r_s}{r} \right) ^2 dv^2 + 2 dv dr^* + r^2 \gamma _{z \bar{z}}dz d\bar{z} ~.$$