# Curvature invariant characterization of event horizons of four-dimensional black holes conformal to stationary black holes

## TL;DR

This paper develops methods to create curvature invariants that identify event horizons of four-dimensional black holes conformally related to stationary solutions, with applications to rotating dynamical black holes and conditions for conformal relations.

## Contribution

It introduces three approaches for generating conformally covariant curvature invariants and applies them to specific black hole solutions, extending horizon detection techniques.

## Key findings

- Constructed invariants that detect conformal Killing horizons.
- Derived conditions for dynamical black holes to be conformally related to stationary ones.
- Discussed limitations and extensions of invariants to higher dimensions.

## Abstract

We introduce three approaches to generate curvature invariants that transform covariantly under a conformal transformation of a four dimensional spacetime. For any black hole conformally related to a stationary black hole, we show how a set of conformally covariant invariants can be combined to produce a conformally covariant invariant that detects the event horizon of the conformally related black hole. As an application we consider the rotating dynamical black holes conformally related to the Kerr-NUT-(Anti)-de Sitter spacetimes and construct an invariant that detects the conformal Killing horizon along with a second invariant that detects the conformal stationary limit surface. In addition, we present necessary conditions for a dynamical black hole to be conformally related to a stationary black hole and apply these conditions to the ingoing Kerr-Vaidya and Vaidya black hole solutions to determine if they are conformally related to stationary black holes for particular choices of the mass function. While two of the three approaches cannot be generalized to higher dimensions, we discuss the existence of a conformally covariant invariant that will detect the event horizon for any higher dimensional black hole conformally related to a stationary black hole which admits at least two conformally covariant invariants, including all vacuum spacetimes.