Scalar charge of black holes in Einstein-Maxwell-dilaton theory

TL;DR

This paper derives a relationship between scalar charge and electric potential for black holes in Einstein-Maxwell-dilaton theory, revealing it is independent of spin in weak charge limits, aiding gravitational wave tests.

Contribution

It provides a novel analytical expression linking scalar charge to electric potential, simplifying tests of the theory with gravitational wave data.

Findings

Scalar charge proportional to electric potential at the horizon.

Scalar charge independent of black hole spin in weak charge limit.

Facilitates testing Einstein-Maxwell-dilaton theory with gravitational waves.

Abstract

We show that the monopole scalar charge of black holes in Einstein--Maxwell--dilaton theory is proportional to the electric potential at the event horizon, with a proportionality factor given by (minus) the scalar coupling constant. We also show that the scalar charge, in the weak electric charge limit, does not depend on the black hole spin. This result can be very useful to circumvent spin degeneracy issues when testing the theory against gravitational waves observations.