JHEP, 11, 066 (2025)
Black hole mass/charge relation and weak no-hair theorem conjecture
Guan-Yi Lu1，Meng-Nan Yang1 and Hong Lu2,1,3
1 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.
2 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.
3 Peng Huanwu Center for Fundamental Theory, Hefei, Anhui 230026, China.
* mrhonglu@gmail.com
Abstract
We consider Einstein gravity minimally coupled to two Maxwell fields and one (real) dilaton scalar. We study the electrically-charged spherically-symmetric and static solutions that are asymptotic to Minkowski spacetime. General solutions are described by four independent parameters: mass M, two electric charges (Q1,Q2) and the scalar charge Σ. For black holes, the scalar charge is not independent, but a function of (M,Q1,Q2). We provide a set of formulae relating the mass to the charges, which allows us to determine Σ(M,Q1,Q2) without having to solve the black hole equations. Our results confirm the weaker version of the no-hair theorem conjecture involving one real scalar: it can be turned on in a black hole, but it does not have a continuous independent hairy parameter.
