Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes

TL;DR

This paper analyzes how massless scalar waves are absorbed and scattered in spherically symmetric spacetimes with a cosmological constant, providing analytical expressions and exploring effects in both low-energy and high-energy regimes.

Contribution

It offers new analytical solutions for scalar wave absorption and scattering in spacetimes with a cosmological constant across different energy regimes.

Findings

Absorption probability increases with cosmological constant in low-energy regime.

High-energy greybody factor also increases with cosmological constant.

Results reduce to Schwarzschild case when cosmological constant is zero.

Abstract

We study the absorption and scattering of massless scalar waves propagating in spherically symmetric spacetimes with dynamical cosmological constant both in low-energy and high-energy zones. In the former low-energy regime, we solve analytically the Regge-Wheeler wave equation and obtain an analytic absorption probability expression which varies with $M\sqrt{\Lambda}$, where $M$ is the central mass and $\Lambda$ is cosmological constant. The low-energy absorption probability, which is in the range of $[0, 0.986701]$, increases monotonically with increase in $\Lambda$. In the latter high-energy regime, the scalar particles adopt their geometric optics limit value. The trajectory equation with effective potential emerges and the analytic high-energy greybody factor, which is relevant with the area of classically accessible regime, also increases monotonically with increase in $\Lambda$, as long $\Lambda$ is less than or of the order of $10^4$. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value $27\pi r_g^2/4$.