# Fundamental oscillation modes of scalar bosonic dark stars

## TL;DR

This paper analyzes the fundamental oscillation modes of nonrotating boson stars in general relativity, exploring how their frequencies and damping times depend on microscopic properties like self-coupling and scalar particle mass.

## Contribution

It provides a detailed calculation of $f$-mode frequencies and damping times, reexamines empirical relations, and suggests how observations could constrain the boson star equation of state.

## Key findings

- Empirical relations between $f$-mode parameters and star properties are refined.
- Oscillation modes depend on self-coupling and scalar mass parameters.
- Potential to constrain the equation of state from mode observations.

## Abstract

We perform a detailed analysis of the fundamental $f$-mode frequencies and damping times of nonrotating boson stars in general relativity by solving the nonradial perturbation equations. Two parameters which govern the microscopic properties of the bosonic condensates, namely the self-coupling strength and the mass of scalar particle, are explored. These two quantities characterize oscillations of boson star. Specifically, we reexamine some empirical relations that describe the $f$-mode parameters in terms of mass and radius of the boson stars. We found it is possible to constrain the equation of state if the fundamental oscillation mode is observed.