Demagnifying gravitational lenses toward hunting a clue of exotic matter and energy

TL;DR

This paper explores a modified gravity lens model that predicts demagnification effects, potentially revealing the presence of exotic matter or energy, and provides analytical and numerical insights into these phenomena.

Contribution

It introduces a new gravitational lens model based on modified gravity theories with exotic matter, analyzing conditions for demagnification and its implications for detecting exotic matter.

Findings

Demagnification occurs when source position exceeds a threshold related to the power n.

Total amplification can be less than unity despite gravitational influence.

Numerical results show significant light depletion for specific source positions and n values.

Abstract

We examine a gravitational lens model inspired by modified gravity theories and exotic matter and energy. We study an asymptotically flat, static, and spherically symmetric spacetime that is modified in such a way that the spacetime metric depends on the inverse distance to the power of positive $n$ in the weak-field approximation. It is shown analytically and numerically that there is a lower limit on the source angular displacement from the lens object to get demagnification. Demagnifying gravitational lenses could appear, provided the source position $\beta$ and the power $n$ satisfy $\beta > 2/(n+1)$ in the units of the Einstein ring radius under a large-$n$ approximation. Unusually, the total amplification of the lensed images, though they are caused by the gravitational pull, could be less than unity. Therefore, time-symmetric demagnification parts in numerical light curves by gravitational microlensing (F.Abe, Astrophys. J. 725, 787, 2010) may be evidence of an Ellis wormhole (being an example of traversable wormholes), but they do not always prove it. Such a gravitational demagnification of the light might be used for hunting a clue of exotic matter and energy that are described by an equation of state more general than the Ellis wormhole case. Numerical calculations for the $n=3$ and 10 cases show maximally $\sim 10$ and $\sim 60$ percent depletion of the light, when the source position is $\beta \sim 1.1$ and $\beta \sim 0.7$, respectively.