Noncommutative fields in Reissner-Nordstr\"{o}m black hole background

TL;DR

This paper explores the behavior of noncommutative matter and gravitational fields in a Reissner-Nordström black hole background, deriving equations for their propagation and dual descriptions in effective metrics.

Contribution

It introduces equations governing noncommutative electromagnetic, scalar, spinor, and gravitational perturbations in the RN background, including two models of NC gravity with quadratic corrections.

Findings

Derivation of NC scalar and spinor field propagation equations.

Formulation of NC electromagnetic perturbation equations.

Development of NC gravity equations in two models.

Abstract

In this short paper we discuss dynamics of noncommutative (NC) matter fields in the Reissner-Nordstr\"{o}m (RN) black hole background. After reviewing the propagation of charged NC scalar and spinor fields, we derive the equation governing the propagation of NC electromagnetic (EM) perturbation in the RN background. The propagation of NC scalar and spinor perturbation have a dual description in terms of the propagation of commutative fields in the effective/dual metric. Finally, we turn to the gravitational perturbations. We present equations of motion for the NC gravitational field obtained in two different models: $SO(2,3)_\star$ NC gravity and braided NC gravity. Typically for NC gravity models, the first nontrivial corrections are quadratic in the NC parameter. The obtained NC gravity equations are the starting point to discuss the propagation of NC gravitational perturbations and the validity of the dual description in terms of the effective metric.