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

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.

5 pages, minor corrections to two equations and references

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• On the Definition of Black Holes: Bridging the Gap Between Black Holes and Singularities
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• Alternative characterization of a black hole boundary