# Scalar resonant frequencies and Hawking effect of an $f(R)$ global monopole

## TL;DR

This paper investigates the behavior of massive scalar fields around a Schwarzschild black hole with a global monopole in $f(R)$ gravity, deriving exact solutions and analyzing Hawking radiation and resonant frequencies using Heun functions.

## Contribution

It provides the first exact solutions for scalar fields in this specific $f(R)$ gravity black hole background and explores their resonant frequencies and Hawking radiation.

## Key findings

- Exact solutions for scalar fields obtained in terms of Heun functions.
- Analysis of Hawking radiation in the $f(R)$ gravity context.
- Determination of scalar resonant frequencies.

## Abstract

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in $f(R)$ gravity. The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions. We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles.