Properties of space-time in the vicinity of trapped regions

TL;DR

This paper analyzes the near-horizon geometry of Kerr Vaidya metrics, revealing unique properties of the energy-momentum tensor, horizon location, and violations of energy conditions, with implications for black hole physics.

Contribution

It provides a detailed characterization of Kerr Vaidya metrics' properties, including energy-momentum tensor classification and horizon behavior, extending understanding of dynamical black hole geometries.

Findings

Energy-momentum tensor is of Segre type 3 with zero eigenvalues.

Apparent horizon location for quasi-stationary Kerr Vaidya black holes identified.

Infalling observers experience diverging energy density and flux, indicating a firewall.

Abstract

We investigate the near horizon geometry of the simplest representative of the class of axisymmetric space-times: the Kerr Vaidya metrics. Kerr Vaidya metrics can be derived from the Vaidya metric by the complex coordinate transformation suggested by Newman and Janis. We show that the energy momentum tensor belongs to type 3 in the Segre Hawking Ellis classification but has a special form with all Lorentz invariant eigenvalues belonging to zero. We find a location of the apparent horizon for quasi-stationary Kerr Vaidya black holes. The energy-momentum tensor of the Kerr Vaidya geometries violates the null energy condition. We show that energy density, pressure, and flux for an infalling observer are diverging in the outgoing Kerr Vaidya metric. This firewall leads to the violation of a specific quantum energy inequality.