Thermodynamics and Geometrical Optics of Reissner Nordstrom de Sitter Black Holes in Noncommutative Geometry

TL;DR

This paper explores how noncommutative geometry affects the thermodynamics, optics, and stability of Reissner-Nordstrom-de Sitter black holes, revealing phase transitions and modifications in photon trajectories and quasinormal modes.

Contribution

It introduces a novel thermodynamic framework for noncommutative black holes and analyzes optical and dynamical properties within this context.

Findings

Identifies a noncommutativity-induced second-order phase transition.

Derives modified photon trajectories and lensing effects due to noncommutativity.

Connects noncommutative geometry with changes in quasinormal modes and orbital stability.

Abstract

We investigate the thermodynamic, optical, and dynamical properties of Reissner-Nordstrom-de Sitter black holes in a noncommutative spacetime with a minimal length scale Theta. Within a two-horizon framework, we formulate an effective first law of thermodynamics and introduce an entropy capturing correlations between the event and cosmological horizons. Imposing the lukewarm condition, where both horizons share a common temperature, uniquely determines the entropy correction and yields closed-form expressions for thermodynamic quantities. The analysis reveals a noncommutativity-induced second-order phase transition, emphasizing the role of short-distance structure. On the optical side, we study photon motion and weak gravitational lensing, showing that noncommutativity modifies the effective potential and critical impact parameter. Using the Gauss-Bonnet method, we derive the weak deflection angle and analyze the effects of charge and cosmological constant. We further connect geometry and dynamics through the Lyapunov exponent and quasinormal modes, showing systematic impacts on orbital instability and damping.