Scalar hairy black holes and scalarons in the isolated horizons formalism

TL;DR

This paper tests and extends the Isolated Horizons formalism to spherically symmetric Einstein-Higgs black hole solutions, confirming mass relations and proposing an empirical formula for their ADM mass.

Contribution

It demonstrates the applicability of the IH formalism to new hairy black hole solutions and extends the model to account for their horizon properties.

Findings

Mass formulae hold for Einstein-Higgs hairy black holes.

An empirical formula approximates the ADM mass of these solutions.

The extended model captures the behavior of horizon properties.

Abstract

The Isolated Horizons (IH) formalism, together with a simple phenomenological model for colored black holes has been used to predict non-trivial formulae that relate the ADM mass of the solitons and hairy Black Holes of Gravity-Matter system on the one hand, and several horizon properties of the black holes in the other. In this article, the IH formalism is tested numerically for spherically symmetric solutions to an Einstein-Higgs system where hairy black holes were recently found to exist. It is shown that the mass formulae still hold and that, by appropriately extending the current model, one can account for the behavior of the horizon properties of these new solutions. An empirical formula that approximates the ADM mass of hairy solutions is put forward, and some of its properties are analyzed.