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Stability of Schwarzschild black holes in fourth-order gravity
Phys. Rev. D 32, 379 – Published 15 July, 1985
DOI: https://doi.org/10.1103/PhysRevD.32.379
Abstract
Both the classical and quantum stability of the Schwarzschild metric in fourth-order theories of gravity are investigated. Characterizing the theories by the mass squared of the two massive particles present in the linearized theory, we find that, provided both particles are nontachyonic, the black hole is classically stable; arbitrary initial perturbations which are regular at infinity and on the future event horizon cannot grow without bound. In the quantum case, where the Schwarzschild metric is unstable when in equilibrium with thermal radiation in the Einstein theory, we find that it is catastrophically unstable when the spin-two particle is tachyonic, but that when nontachyonic the fourth-order terms stabilize low-mass black holes; black holes do not evaporate away completely in these theories (an effect due to Hawking radiation of the negative-energy spin-two particle of the theory). We conclude that black holes appear well behaved in a quarter of the parameter space available to the fourth-order theories.
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