Quantum corrections enhance chaos: Study of particle motion near a generalized Schwarzschild black hole

Abstract

The paper is devoted to a detailed study of the effects of quantum corrections on the chaotic behaviour in the dynamics of a (massless) probe particle near the horizon of a generalized Schwarzschild black hole. Two possible origins inducing the modification of black hole metric are considered separately; the noncommutative geometry inspired metric (suggested by Nicolini, Smailagic and Spallucci) and the metric with quantum field theoretic corrections (derived by Donoghue). Our results clearly show that in both cases, the metric extensions favour chaotic behaviour, namely chaos is attained for relatively lower particle energy. This is demonstrated numerically by exhibiting the breaking of the KAM tori in Poincaré sections of particle trajectories and also via explicit computation of the (positive) Lyapunov exponents of the trajectories.