Weak Gravitational lensing by phantom black holes and phantom wormholes using the Gauss-Bonnet theorem

TL;DR

This paper investigates how phantom black holes and wormholes influence light deflection in the weak gravitational field, using the Gauss-Bonnet theorem, and explores observational signatures like Einstein rings.

Contribution

It applies the Gauss-Bonnet theorem to analyze light deflection by phantom black holes and wormholes, highlighting the effects of phantom scalar fields and shape functions.

Findings

Gravitational lensing is affected by phantom scalar fields.

Shape and mass functions significantly influence light deflection.

Results are verified through geodesic equations and Einstein ring analysis.

Abstract

In this paper, we study the deflection of light by a class of phantom black hole and wormhole solutions in the weak limit approximation. More specifically, in the first part of this work, we study the deflection of light by Garfinkle-Horowitz-Str\"{o}minger black hole and Einstein-Maxwell anti-dilaton black hole using the optical geometry and the Gauss-Bonnet theorem. Our calculations show that gravitational lensing is affected by the phantom scalar field (phantom dilaton). In the second part of this work, we explore the deflection of light by a class of asymptotically flat phantom wormholes. In particular, we have used three types of wormholes: wormhole with a bounded/unbounded mass function, and a wormhole with a vanishing redshift function. We show that the particular choice of the shape function and mass function plays a crucial role in the final expression for the deflection angle of light. In the third part of the paper, we verify our findings with the help of standard geodesics equations. Finally, in the fourth part of this paper, we consider the problem for the observational relevance of our results studying the creation of the weak field Einstein rings.