Scalar Quasi-Normal Modes in Black Hole Gravitational Lensing

Abstract

We investigate the excitation of quasi-normal modes (QNMs) in gravitational lensing by a Schwarzschild black hole using a scalar field model. By employing a time-domain mode-sum method, we analyze the complex interplay between an incident burst signal and the black hole spacetime. We find that the incident waves can non-resonantly excite a substantial number of high-$l$ modes, with amplitudes for modes as high as l=20 remaining significant compared to the fundamental l=0 mode. We confirm through QNM template fitting that the late-time behaviors of these excited modes are indeed QNMs. After passing through the black hole, we find that the lensed waves form a highly directional and coherent Gaussian beam whose cross-sectional intensity profile is well-described by a Gaussian profile. Unlike spherical waves, this beam's amplitude does not decrease with distance from the black hole but remains nearly constant in the near-field region. Moreover, due to the superposition of numerous QNMs, oscillations largely cancel each other out. The lensed temporal waves do not exhibit typical oscillatory patterns.

13 pages, 10 figures, accepted for publication in PRD

References in corpus (5)

• Extraction of Gravitational Waves in Numerical Relativity
• Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques
• The wave nature of continuous gravitational waves from microlensing
• Absorbing boundary conditions for Einstein's field equations
• Rigorous calculation of scalar scattering in Schwarzschild background: the convergence of partial-wave series and Poisson spot