Particle production rate for a dynamical system using the path integral approach

TL;DR

This paper studies particle creation in a dynamical Vaidya spacetime using path integral formalism, analyzing different mass functions and their thermodynamic implications, revealing a high initial particle production rate that declines over time.

Contribution

It introduces a novel application of path integral methods to analyze particle production in non-stationary Vaidya geometries with various mass functions.

Findings

Particle production rate is initially high and then rapidly declines.

Surface gravity and temperature vary over time, indicating dynamic thermodynamic behavior.

The background geometry significantly influences the particle creation process.

Abstract

In this work, we investigate the particle creation rate in a dynamical (Vaidya) spacetime using Feynman's path integral formalism within the framework of the effective action approach. We examine three distinct cases involving the following mass functions, each representing dynamical geometries: (i) $m(v,r)=\mu v$, (ii) $m(v,r)=\mu v +\nu r$, and (iii) $m(v,r)=\mu v -\frac{\mu^2 v^2}{2r}$, where $\mu$ and $\nu$ are positive constants that satisfy all known energy conditions. We analyze particle production rates in the region of dynamical horizons, revealing an initial high rate followed by a rapid decline in all cases. Additionally, we explore the thermodynamic properties by calculating the surface gravity and corresponding Hayward-Kodama temperatures for each scenario. Graphical representations show the variation of surface gravity over time for the three cases, offering insights into the system's thermodynamic evolution. Our research investigates the connection between background geometry and the particle creation process, placing it within the broader context of quantum field theory in curved spacetime. The non-stationary nature of Vaidya geometry is highlighted as a valuable framework for examining the dynamic aspects of particle creation. This in-depth analysis enhances our understanding of quantum processes in curved spacetime and may offer insights relevant to thermodynamics and studies of gravitational collapse.