Abstract
We compute the quasinormal frequencies of d-dimensional spherically symmetric black holes with leading string α′ corrections in the eikonal limit for tensorial gravitational perturbations and scalar test fields. We find that, differently than in Einstein gravity, the real parts of the frequency are no longer equal for these two cases. The corresponding imaginary parts remain equal to the principal Lyapunov exponent corresponding to circular null geodesics, to first order in α′. We also compute the radius of the shadow cast by these black holes.
Highlights
Black holes in the ringdown phase resulting from a black hole collision form a dissipative system which can be described by black hole perturbation theory: they lose energy by emitting gravitational radiation
The article is organized as follows: in section 2 we will review the stringcorrected black hole solution we will consider, the master equation and the corresponding potentials for minimally coupled test scalar fields and tensorial gravitational perturbations; in section 3 we analyze how to compute the corresponding quasinormal frequencies in the eikonal limit in this context, and we obtain such frequencies; in section 4 we review how to obtain the black hole shadow from the quasinormal modes and we compute it for the black hole we consider
We must point out that, because the equation for the maximization of VTeik does not coincide with the one defining a circular null geodesic, the identifications of ΩT with the angular velocity at such geodesic and ΛT as the principal Lyapunov exponent corresponding to such orbit are not expected to be valid for these perturbations
Summary
Black holes in the ringdown phase resulting from a black hole collision form a dissipative system which can be described by black hole perturbation theory: they lose energy by emitting gravitational radiation Those decaying oscillations are called quasinormal modes, and they are given in terms of complex frequencies. In this article we will consider d-dimensional asymptotically flat spherically symmetric black holes in string theory and compute their quasinormal frequencies in the eikonal limit and the radius of the black hole shadow. In the presence of higher order corrections in the lagrangian, one can still have spherically symmetric black holes of the form (1), but the master equation obeyed by each perturbation variable is expected to change. It is enough to just quote here the explicit expression for the temperature of this black hole, given by
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