Black Holes with Quantum Massive Spin-2 Hair

TL;DR

This work shows that classical no-hair theorems do not preclude quantum mechanical hair for black holes coupled to a massive spin-2 field or a massive Kalb-Ramond two-form. By employing a Stückelberg decomposition, the author reveals topologically nontrivial configurations where h_mu_nu vanishes outside the horizon while a detectable, long-range hair remains via a stringy Aharonov-Bohm effect, with the effect persisting for arbitrarily large masses. A parallel analysis for massive U(1) gauge theory demonstrates how boundary couplings and gauge-invariant reparametrizations preserve AB-type interference, even for massive photons. The results imply that black holes can carry new quantum charges detectable through string-like probes, with potential relevance for string theory, early-universe dynamics, and TeV-scale gravity phenomenology.

Abstract

We show that black holes can posses a long range quantum mechanical hair associated with a massive spin-2 field, which can be detected by a stringy generalization of the Aharovon-Bohm effect, in which a string loop lassoes the black hole. The long distance effect persist for arbitrarily high mass of the spin-2 field. An analogous effect is exhibited by a massive antisymmetric two-form field. We make a close parallel between the two and the ordinary Aharonov-Bohm phenomenon, and also show that in the latter case the effect can be experienced even by the electrically-neutral particles, provided some boundary terms are added to the action.