Quantum Behaviors on an Excreting Black Hole

TL;DR

This paper investigates quantum behaviors on a dynamic black hole background, analyzing particle trajectories, quantum field dynamics, and a generic approach for mutual gravitation of quanta to better understand quantum effects in curved spacetime.

Contribution

It introduces a novel algebraic framework for modeling mutually gravitating quantum fields on a dynamic black hole background, incorporating invariant densities and Einstein's equations.

Findings

Calculated trajectories of classical particles near an excreting black hole

Examined dynamics of massless and massive quantum fields on the spacetime

Developed a generic algebraic approach for quantum mutual gravitation

Abstract

Often, geometries with horizons offer insights into the intricate relationships between general relativity and quantum physics. However, some subtle aspects of gravitating quantum systems might be difficult to ascertain using static backgrounds, since quantum mechanics incorporates dynamic measurability constraints (such as the uncertainty principle, etc.). For this reason, the behaviors of quantum systems on a dynamic black hole background are explored in this paper. The velocities and trajectories of representative outgoing, ingoing, and stationary classical particles are calculated and contrasted, and the dynamics of simple quantum fields (both massless and massive) on the space-time are examined. Invariant densities associated with the quantum fields are exhibited on the Penrose diagram that represents the excreting black hole. Furthermore, a generic approach for the consistent mutual gravitation of quanta in a manner that reproduces the given geometry is developed. The dynamics of the mutually gravitating quantum fields are expressed in terms of the affine parameter that describes local motions of a given quantum type on the space-time. Algebraic equations that relate the energy-momentum densities of the quantum fields to Einstein's tensor can then be developed. An example mutually gravitating system of macroscopically coherent quanta along with a core gravitating field is demonstrated. Since the approach is generic and algebraic, it can be used to represent a variety of systems with specified boundary conditions.