CERN-PH-TH/2006-076 hep-th/0605001 Higher–Derivative Corrected Black Holes: Perturbative Stability and Absorption Cross–Section in Heterotic String Theory

Abstract: This work addresses spherically symmetric, static black holes in higher–derivative stringy gravity. We focus on the curvature–squared correction to the Einstein–Hilbert action, present in both heterotic and bosonic string theory. The string theory low–energy effective action necessarily describes both a graviton and a dilaton, and we concentrate on the Callan–Myers–Perry solution in d–dimensions, describing stringy corrections to the Schwarzschild geometry. We develop the perturbation theory for the higher–derivative corrected action, along the guidelines of the Ishibashi–Kodama framework, focusing on tensor type gravitational perturbations. The potential obtained allows us to address the perturbative stability of the black hole solution, where we prove stability in any dimension. The equation describing gravitational perturbations to the Callan–Myers–Perry geometry also allows for a study of greybody factors and quasinormal frequencies. We address gravitational scattering at low frequencies, computing corrections arising from the curvature–squared term in the stringy action. We find that the absorption cross–section receives α ′ corrections, even though it is still proportional to the area of the black hole event–horizon. W