Galactic microlensing by Lobo-Parsaei-Riazi phantom wormhole: Paczy\'{n}ski light curves and probabilistic features

Abstract

Gravitational microlensing can provide a possible observational method for distinguishing between the signatures of massive and massless phantom wormholes. In this work, we consider Galactic microlensing by the bounded Lobo-Parsaei-Riazi phantom wormhole (LPR), assuming source stars located in the Galactic Bulge and in the Large Magellanic Cloud (LMC). We derive the weak-field deflection angle up to fourth post-Newtonian order and compute the Einstein radius, Einstein-radius crossing time, and idealized point-source Paczy\'{n}ski-type light curves. We also estimate the optical depth and event rate in a simplified model in which the wormhole lenses are assumed to be gravitationally bound to the Galaxy. The LPR parameter $\gamma$, which is related to the radial equation-of-state parameter by $\omega = 1/ \gamma$, affects the ADM mass, the Einstein radius, and the microlensing timescale. In the massive phantom branch $-1 < \gamma < 0$, the leading deflection term is proportional to $1/r$, and the resulting point-source light curves are Paczy\'{n}ski-like. The massless comparison case $\gamma = 1$ is qualitatively different because the leading $1/r$ term vanishes and gutters may appear. The idealized observational predictions are compared with those for a Schwarzschild black hole.