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

TL;DR

This study demonstrates that quantum corrections to black hole metrics increase chaotic behavior in particle motion, lowering the energy threshold for chaos, as shown through numerical analysis of Poincaré sections and Lyapunov exponents.

Contribution

It provides the first detailed numerical analysis of how quantum corrections from noncommutative geometry and quantum field theory enhance chaos near black holes.

Findings

Quantum corrections lower the energy needed for chaos to occur.

Chaos is evidenced by breaking of KAM tori in Poincaré sections.

Positive Lyapunov exponents confirm increased chaos.

Abstract

The paper is devoted to a detailed study of the effects of quantum corrections on the chaotic behavior 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 behavior, namely chaos is attained for relatively lower particle energy. This is demonstrated numerically by exhibiting the breaking of the KAM tori in Poincar\'e sections of particle trajectories and also via explicit computation of the (positive) Lyapunov exponents of the trajectories.