"No hair" theorem for black holes in the Mansouri-Chang theory of gravitation

Abstract

We show that a static, spherically symmetric black hole in Mansouri-Chang (MC) gravity theory (where the Lagrangian contains up to fourth derivatives of the metric) will "swallow" all effects due to the higher derivatives, so that outside the event horizon the metric necessarily reduces to a Schwarzschild metric. Hence Pavelle's recent proof of the equivalence of MC and standard Einstein theory should be reinterpreted as a proof of a "no hair" theorem for MC black holes. For normal stars, MC and standard theory need not be equivalent. Our results apply to a wide class of higher-derivative theories in addition to MC theory. We also derive the "oscillator variable" decomposition for these theories.