Dynamical evolution of electromagnetic perturbation in the background of a scalar hairy black hole in Horndeski theory

We have investigated dynamical evolution of electromagnetic perturbation in a scalar hairy black hole spacetime, which belongs to solutions in Horndeski theory with a logarithmic cubic term. Our results show that the parameter [Formula: see text] affects the existence of event horizon and modifies the asymptotical structure of spacetime at spatial infinity, which imprints on the quasinormal frequency of electromagnetic perturbation. Moreover, we find that the late-time tail of electromagnetic perturbation in this background depends also on the parameter [Formula: see text] due to the existence of solid angle deficit. These imply that the spacetime properties arising from the logarithmic cubic term in the action play important roles in the dynamical evolutions of the electromagnetic perturbation in the background of a scalar hairy black hole.

ON THE TIME TIMES TEMPERATURE BOUND

Recently Hod proposed a lower bound on the relaxation time of a perturbed thermodynamic system. For gravitational systems this bound transforms into a condition on the fundamental quasinormal frequency. We test the bound in some space–times whose quasinormal frequencies are calculated exactly, as the three-dimensional BTZ black hole, the D-dimensional de Sitter space–time, and the D-dimensional Nariai space–time. We find that for some of these space–times their fundamental quasinormal frequencies do not satisfy the bound proposed by Hod.

ASYMPTOTIC QUASINORMAL MODES OF A NONCOMMUTATIVE GEOMETRY INSPIRED SCHWARZSCHILD BLACK HOLE

We study the asymptotic quasinormal modes for the scalar perturbation of the noncommutative geometry inspired Schwarzschild black hole in 3+1 dimensions. We have considered M ≥ M0, which effectively correspond to a single horizon Schwarzschild black hole with correction due to noncommutativity. We have shown that for this situation the real part of the asymptotic quasinormal frequency is proportional to ln (3). The effect of noncommutativity of space–time on quasinormal frequency arises through the constant of proportionality, which is Hawking temperature TH(θ). We also consider the two-horizons case and show that in this case also the real part of the asymptotic quasinormal frequency is proportional to ln (3).