# Scalar Polynomial Curvature Invariant Vanishing on the Event Horizon of Any Black Hole Metric Conformal to a Static Spherical Metric

## TL;DR

This paper introduces a scalar polynomial curvature invariant that remains covariant under conformal transformations and uniquely vanishes on the event horizon of any black hole conformal to a static spherical metric, aiding horizon detection.

## Contribution

The authors develop a new conformally covariant scalar invariant that vanishes precisely at black hole horizons in conformally related static spherical spacetimes.

## Key findings

- Invariant vanishes on the event horizon of conformally related static spherical black holes
- Invariant transforms covariantly under conformal transformations
- Provides a geometric tool for horizon identification in complex spacetimes

## Abstract

We construct a scalar polynomial curvature invariant that transforms covariantly under a conformal transformation from any spherically symmetric metric. This invariant has the additional property that it vanishes on the event horizon of any black hole that is conformal to a static spherical metric.