Long-lived quasinormal modes, shadows and particle motion in four-dimensional quasi-topological gravity

TL;DR

This paper studies the behavior of scalar perturbations, particle motion, and black hole shadows in four-dimensional quasi-topological gravity, revealing long-lived modes and moderate deviations from Schwarzschild black holes.

Contribution

It provides detailed analysis of quasinormal modes, particle trajectories, and shadows in a novel four-dimensional quasi-topological gravity framework.

Findings

Long-lived quasinormal modes emerge at high scalar masses.

Photon sphere and shadow sizes show moderate deviations from Schwarzschild.

Late-time signals are dominated by power-law tails at large scalar masses.

Abstract

We investigate massive scalar perturbations and several characteristics of particle motion in the spacetime of regular black holes arising in four-dimensional quasi-topological gravity. Quasinormal modes are computed using high-order WKB approximations with Pad\'e resummation and verified through time-domain integration. For moderate values of the scalar-field mass, the time-domain profiles confirm the WKB results with excellent accuracy. As the mass increases, the damping rate decreases substantially, indicating the approach to the quasi-resonant regime of long-lived modes. For sufficiently large masses, the late-time signal becomes dominated by oscillatory power-law tails, which mask the quasi-resonant mode in the time-domain profile. In addition, we analyze photon motion and circular geodesics, including the photon-sphere radius, shadow size, Lyapunov exponent, and ISCO characteristics. These quantities exhibit only moderate deviations from their Schwarzschild values, unlike the Hawking temperature of the black hole.