Understand
The theory of isolated horizon provides a quasi-local framework to study the spacetime geometry in the neighbourhood of the horizon of a black hole in equilibrium without any reference to structures far away from the horizon.
- While the geometric properties of the Kerr-(A)dS and more general algebraically special solutions have drawn substantial interest recently in the isolated horizon formalism, their horizon metrics have never been written down explicitly in the adapted Bondi-like coordinate system.
- Following the approach by Krishnan and assuming that the horizon symmetry extends to certain order in the bulk, we present in this note a general method to compute the metric functions order by order radially in Bondi-like coordinates in 4-dimensions from a small set of intrinsic data -- the connection and the Newman-Penrose spin coefficient $\pi$ specified on the horizon cross-section.
- Applying this general method, we then present the horizon metric of non-extremal Kerr-dS in Bondi-like coordinates.