Deflection Angle and Shadow Behaviors of Quintessential Black Holes in arbitrary Dimensions

TL;DR

This paper analyzes how dark energy parameters and higher dimensions influence the deflection angle and shadow shapes of quintessential black holes, revealing that increased dark energy enhances these optical effects while higher dimensions diminish them.

Contribution

It provides a detailed study of photon trajectories and optical properties of higher-dimensional quintessential black holes with varying dark energy parameters, extending known four-dimensional results.

Findings

Deflection angle and shadow size increase with dark energy field intensity c.

Higher dimensions decrease deflection angle and shadow size for similar dark energy models.

Black hole charge also affects the optical properties of the black holes.

Abstract

Motivated by M-theory/superstring inspired models, we investigate certain behaviors of the deflection angle and the shadow geometrical shapes of higher dimensional quintessential black holes associated with two values of the dark energy (DE) state parameter, being \omega=-\frac{1}{3} and \omega=-\frac{2}{3}. Concretely, we derive the geodesic equation of photons on such backgrounds. Thanks to the Gauss-Bonnet theorem corresponding to the optical metric, we compute the leading terms of the deflection angle in the so-called weak-limit approximation. After that, we inspect the effect of DE and the space-time dimension d on the calculated optical quantities. Introducing DE via the field intensity c and the state parameter \omega, we find that the shadow size and the deflection angle increase by increasing values of the field intensity c. However, we observe that the high dimensions decrease such quantities for \omega-models exhibiting similar behaviors. Then, we consider the effect of the black hole charge, on these optical quantities, by discussing the associated behaviors. The present investigation recovers certain known results appearing in ordinary four dimensional models.