Local scale symmetry and black holes

Abstract

We derive solutions for a black hole coupled to a real scalar field under considerations of local scale symmetry. Starting with the simple case $(λ=0)$, we find the solutions and derive the black hole's temperature, entropy, and its effective mass, and observe an adiabatic accretion of the scalar field onto the black hole. As a result, the effective mass of the black hole grows. In the general case $(λ\ne 0)$, the situation becomes more intricate; The horizons (the vanishing points of $g_{tt}$) depend on the mass of the black hole, scalar field strength, $λ$ and other positive parameter $R_ϕ$. In this case, we propose two possible behaviors: When the black hole's mass is small enough, the field is mostly concentrated far from the black hole, whereas when the black hole's mass is sufficiently large, it is mostly concentrated inside the black hole.