Optical Images of Mini Boson Stars in Palatini $f(R)$ Gravity

TL;DR

This paper explores the optical signatures of mini boson stars in Palatini $f(R)$ gravity, revealing distinctive features that could help differentiate them from black holes through astronomical imaging.

Contribution

It introduces a numerical analysis of photon trajectories and images of boson stars in Palatini $f(R)$ gravity, highlighting differences from black holes due to the absence of stable photon rings.

Findings

Boson stars lack stable photon rings unlike black holes.

Optical images are dominated by direct photon emissions.

Optical properties depend on scalar field and coupling parameter.

Abstract

We investigate the optical properties of mini boson stars within the framework of Palatini $f(R)$ gravity, adopting a quadratic form $f(R) = R + \xi R^2$, where $\xi$ is the gravitational coupling constant. By deriving the modified scalar Lagrangian and solving the field equations numerically, we explore photon trajectories and the resulting optical images under spherical light sources and thin accretion disks. Unlike Schwarzschild black holes (BHs), boson stars lack stable photon rings due to the positive second derivative of their effective potential. Consequently, their images are dominated by direct emissions from photons completing a single orbit. The study examines the dependence of the optical characteristics on the initial scalar field $\psi_0$ and the coupling parameter $\xi$. Numerical results include effective potentials, redshift maps, and detailed imaging of boson stars, providing insights into distinguishing boson stars from black holes using high-resolution astronomical observations.