On the analytic generalization of particle deflection in the weak field regime and shadow size in light of EHT constraints for Schwarzschild-like black hole solutions

TL;DR

This paper derives an analytic formula for particle deflection and shadow size in Schwarzschild-like spacetimes, incorporating EHT observational constraints, with applications to various black hole models including dark matter and modified gravity theories.

Contribution

It provides a generalized weak field deflection angle formula valid for Schwarzschild-like spacetimes and relates shadow size to metric parameters, extending analysis to diverse black hole solutions.

Findings

Derived a simple, general deflection angle formula applicable to multiple black hole models.

Showed shadow size depends only on specific metric parameters, enabling constraints from EHT data.

Applied the formulas to examples in modified gravity and dark matter contexts, finding new and consistent results.

Abstract

In this paper, an analytic generalization of the weak field deflection angle (WDA) is derived by utilizing the current non-asymptotically flat generalization of the Gauss-Bonnet theorem. The derived formula is valid for any Schwarzschild-like spacetime, which deviates from the classical Schwarzschild case through some constant parameters. This work provided four examples in the context of bumblebee gravity theory, and one example from a black hole surrounded with soliton dark matter, where some results are new, and some agreed with existing literature. The WDA formula provided a simple calculation, where approximations based on some conditions can be done directly on it, skipping the preliminary steps. For the shadow size analysis, it is shown how it depends solely on the parameter associated with the metric coefficient in the time coordinate. A general formula for the constrained parameter is also derived based on the Event Horizon Collaboration (EHT) observational results. Finally, the work realized further possible generalizations on other black hole models, such as RN-like, dS/AdS-like black hole solutions, and even black hole solutions in higher dimensions.