Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2508.17253

Rigorous calculation of scalar scattering in Schwarzschild background: the convergence of partial-wave series and Poisson spot

Zhao Li·Wen Zhao
View original source ↗Read source document ↗Export metadata ↓

Abstract

Black hole (BH) perturbation theory and the scattering models provide a powerful framework for studying gravitational lensing at the wave-optics level. However, conventional calculations encountered two issues: the divergence of the partial-wave series and the divergence of the Poisson spot near the optical axis. These issues hinder the accurate calculation of lensed waveforms and the study of polarization and wave characteristics in the lensing process, especially near the optical axis. This work demonstrates that both divergences stem from the asymptotic expansion of the radial wave function. By computing the scattered wave function at finite radii and avoiding the asymptotic expansion, we naturally obtain convergent results. We compute scalar waves scattered by (1) a weak-gravity body with Newtonian potential and (2) a Schwarzschild BH with Regge-Wheeler potential. In both cases, we analyze the convergence of the partial-wave series and present finite-luminosity diffraction patterns, with a bright Poisson spot. The above calculations are compared with the Kirchhoff diffraction integral in the near-axis regions and give consistent results. Our investigations provide a foundation for studying gravitational wave scattering by BHs and understanding lensing at the wave-optics level.

Explore related subjects

gr-qc

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zhao Li, Wen Zhao. 2025-12-01. Rigorous calculation of scalar scattering in Schwarzschild background: the convergence of partial-wave series and Poisson spot. https://doi.org/10.1103/xsxj-9vdw

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

An upper bound on the minimum orbital period of black holes

Previous research has focused on establishing lower bounds on the minimum orbital period of black holes. In this work, we explore the complementary question of whether an upper bound exists for the minimum orbital period of black holes. We investigate the minimum orbital periods of three types of black holes: Schwarzschild, Reissner-Nordström and Kerr-Newman black holes. We find that the minimum orbital period of these black holes is bounded by an upper limit $T_{min} \leqslant 6\sqrt{3}πM$, where $M$ is the black hole mass. Our results suggest that this upper bound on the minimum orbital period may be a general property in black hole spacetimes.

gr-qc↗
arXiv2026

Dirac Observables for Gowdy Cosmologies regular at the Big Bang

Gowdy cosmologies are exact, spatially inhomogeneous solutions of the vacuum Einstein equations which describe nonlinear gravitational waves coalescing at the Big Bang singularity. With toroidal spatial sections they provenly have the Asymptotic Velocity Domination property, in that close to the Big Bang dynamical spatial gradients fade out and the dynamics is governed by a Carroll-type gravity theory. Here we construct an infinite set of Dirac observables for Gowdy cosmologies, valid off-shell, strongly, and without gauge fixing. These observables stay regular at the Big Bang and can be matched to much simpler Dirac observables of the Carroll-type gravity theory. Conversely, in an adapted foliation there is a systematic anti-Newtonian expansion (in inverse powers of the reduced Newton constant) of the full Dirac observables whose leading terms are the Carroll ones. In particular, this provides an off-shell generalization of the Asymptotic Velocity Domination property.

gr-qc↗
arXiv2026

Global causality constraints in rotating scalar-tensor spacetimes

Modified gravity is often formulated as an effective field theory (EFT), where higher-order corrections parametrize departures from General Relativity. We argue that such corrections should be constrained by the global causal structure of curved spacetime, in addition to the usual flat-space requirements such as positivity and unitarity. We propose that within the domain of validity of the EFT, the onset of closed timelike curves should not happen in a parametrically more accessible region than in the corresponding GR background. We test this diagnostic in the quadratic k-essence sector of scalar-tensor gravity. For stationary and axisymmetric spacetimes, the invariant test for closed axial orbits is the sign of the azimuthal component of the metric \(g_{φφ}\). We supplement this test by requiring a local time function in the space of Killing vectors. We apply these conditions to quadratic k-essence on Kerr--(A)dS backgrounds, with and without scalar charge. The zero-charge branch is exact Kerr--(A)dS, and we treat the charged branch perturbatively in scalar charge and in Hartle--Thorne slow rotation. Expanding for small spin \(χ=a/(GM)\ll1\), frame dragging begins at \(\mathcal O(χ)\), while the quadrupolar backreaction relevant for circular closed timelike curves enters at second order in both rotation and charge. We find that, in the truncation used here, any occurrence of \(g_{φφ}<0\) also lies outside EFT control. A higher-order calculation or a fully nonlinear treatment is therefore needed. Finally, we discuss how quasinormal modes and black-hole echoes could probe such causal structure.

gr-qc↗