Study on deflection angle, shadow, quasinormal modes, and greybody factor of the black hole surrounded by quintessence in Rastall gravity

TL;DR

This paper investigates the properties of a charged black hole surrounded by quintessence in Rastall gravity, analyzing deflection angles, shadow, quasinormal modes, and greybody factors, revealing how these features depend on charge, mass, and quintessence.

Contribution

It provides a comprehensive analysis of black hole characteristics in Rastall gravity with quintessence, including new calculations of deflection angles, shadow, quasinormal modes, and greybody bounds.

Findings

Deflection angle increases with black hole mass and quintessence presence.

Black hole shadow shrinks with increasing charge Q.

Greybody factor lower bound decreases with charge Q and increases with mass m.

Abstract

The present study focuses on investigating the deflection angle in the weak-field approximation, shadow, quasinormal modes using Lyapunov exponents, and lower bound of the greybody factor for a charged black hole surrounded by a quintessence field in Rastall gravity. The weak deflection angles are calculated using the Gauss-Bonnet method. They decrease with increasing impact parameter b and charge Q, but gradually increase with increasing black hole mass m. Notably, the presence of a surrounding quintessence field in Rastall gravity leads to a higher deflection angle compared to Schwarzschild or Reissner-Nordstrom black holes with positive Nq. The photon sphere and shadow of the black hole are analysed concerning the charge Q and mass m; they shrink as Q increases and expand with increasing m. We further analyse the quasinormal modes of the black hole, explicitly derive the coordinate time Lyapunov exponent {\lambda}c and the quasinormal frequency {\omega}. In the eikonal limit, the Lyapunov exponent ensures that the real and imaginary parts of the quasinormal modes can be expressed by the frequency and instability time scale of the unstable null circular geodesics. Additionally, we derive the lower bounds of the greybody factor Gb; it decreases for increasing charge Q, while the increasing mass m enhances it. Importantly, all the findings reduce to those of the Reissner-Nordstrom black hole for Nq=0 and to the Schwarzschild black hole for Nq=Q=0.