Causal global structure of Kerr spacetime through a double null foliation

OSVALDO M. MORESCHI

Otro; José Plínio Baptista School of Cosmology, Compact Objects; 2021

Causal structure in spherically symmetric spacetimes:In spherically symmetric spacetimes, it is natural to considerdiagrams in which each point corresponds to one of the spheresof symmetries, and one arrives at the usual causal diagramsof the spacetime, as for example\cite{Carter73}:Let us note that each point can be characterized as $r=$constant,or $r_*=$constant, where $r_*=r + 2 m\ln(\frac{r}{2 m}-1)$ is the tortoise coordinate.This diagram is the main tool for understanding the global causalstructure of Schwarzschild spacetime.The symbol $\mathscr{I}^+$ denotes \blue{future null infinity};which is the asymptotic region reached by outgoing future directed null geodesics.Causal diagrams for Kerr spacetime:From Carter's work\cite{Carter:1966zza} and text books\cite{Chandrasekhar:1983este}one is accustomed to see the diagram:%\begin{figure}[H]%\centering%\includegraphics[clip,width=0.24\textwidth]{graficos/carter66-conformal-%kerr.png}%%\caption{%%}%%\label{fig:ASD-raw}%\end{figure}which is constructed \red{only for the points on the axis $\theta=0$ or $\theta=\pi$}, of the spacetime.Global causal diagrams for Kerr spacetime:We will present the necessary tools to construct global causal diagrams forthe Kerr spacetime.