Black hole equations of motion in the null gauge with back reaction due to radiation

OSVALDO M. MORESCHI; EMANUEL GALLO

Valencia

Conferencia; GR22/13th Edoardo Amaldi; 2019

International Society of General Relativity and Gravitation

We here develop further the general framework for modeling the dynamics of themotion of black holes, presented in \cite{Gallo:2019},by employing a convenient null gauge, in general relativity, for the construction of thebalanced equations of motion.This null gauge has the property thatthe asymptotic structure is intimately related tothe interior one; in particular there is a strongconnexion between the field equation and thebalanced equations of motion. We will present the balanced equations of motion in second orderof the acceleration.We will show how to solve the required componentsof the field equation at their respective required orders,$G^2$ and $G^3$, in terms of the gravitational constant.We will indicate how this approach can be extended to higher orders.