Retrolensing by a spherically symmetric naked singularity

TL;DR

This paper studies how a scalar field affects retrolensing near a naked singularity, revealing that scalar fields increase brightness but decrease angular separation of images compared to non-scalar cases.

Contribution

It provides analytic expressions for lensing coefficients in a scalar field context and compares the effects on observable properties with Schwarzschild black holes.

Findings

Brightness increases with scalar field presence.

Lensing coefficients and angular positions decrease with scalar field.

Scalar field effects differ from non-scalar gravity scenarios.

Abstract

Considering a strong field limit, we investigate the retrolensing phenomenon in the vicinity of a Janis-Newman-Winicour (JNW) naked singularity embedded in a scalar field. We assume that the light rays from a nearby source are reflected by the photon sphere of the naked singularity, acting as a lens, to create a pair of images. The analytic expressions of the lensing coefficients $\bar{a}$ and $\bar{b}$ are obtained, which are scalar dependent and discordant with \cite{Bozza:2002b}. Moreover, considering the powerful supermassive black hole candidates Sgr A* and M87*, we examined the influence of the scalar field on the apparent brightness and angular positions of the parity images. Our results are highlighted in correspondence with a non-scalar field gravity, specifically the Schwarzschild gravity. We have found that the brightness increases in the presence of the scalar field, while, the lensing coefficients $\bar{a}$, $\bar{b}$, the angular positions and the angular separation of the relativistic images experience a reverse effect.