# Absorption and scattering of a noncommutative black hole

## TL;DR

This paper investigates how noncommutative geometry affects the scattering and absorption of scalar waves by a Schwarzschild black hole, revealing decreased cross sections with increased noncommutativity, supported by analytical and numerical methods.

## Contribution

It introduces a detailed analysis of scalar wave scattering by a noncommutative black hole using the partial wave method, highlighting modifications in cross sections due to noncommutativity.

## Key findings

- Decreased scattering and absorption cross sections with higher noncommutativity parameter.
- Analytical phase shift derived in low-frequency limit.
- Numerical confirmation of cross section modifications across frequencies.

## Abstract

In this paper we focus on the partial wave method with the aim of exploring the scattering of massless scalar waves due to the noncommutative Schwarzschild black hole via Lorentzian smeared mass distribution. We determine the phase shift analytically in low-frequency limit and we show that the scattering and absorption cross section is modified. Specially, we show that in the low-frequency limit the scattering/absorption cross section has its value decreased when we increase the value of the non-commutativity parameter. In addition, we have confirmed this result by solving the problem numerically for arbitrary frequencies. Such modifications found for the scattering and absorption cross section present similarities with the Reissner-Nordstr\"{o}m black hole.