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

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.

16 pages, 6 figures, Accepted from Physical Review D

References in corpus (28)

• Heat kernel expansion: user's manual
• Isolated and dynamical horizons and their applications
• Advances in QED with intense background fields
• Dynamical Horizons and their Properties
• Dynamical Horizons: Energy, Angular Momentum, Fluxes and Balance Laws
• Essential and inessential features of Hawking radiation
• Hawking temperature from tunnelling formalism
• On the Hawking radiation as tunneling for a class of dynamical black holes
• Classical collapse to black holes and quantum bounces: A review
• Cosmological Particle Production: A Review
• The Heisenberg-Euler Effective Action: 75 years on
• Gravitational collapse of null fluid on the brane
• Out-of-equilibrium criticalities in graphene superlattices
• Testing Quantum Electrodynamics with Exotic Atoms
• Gravitational Pair Production and Black Hole Evaporation
• Gravitational Collapse for the K-essence Emergent Vaidya Spacetime
• Euler - Heisenberg effective action and magnetoelectric effect in multilayer graphene
• K-essence Emergent Spacetime as Generalized Vaidya Geometry
• Generalized Vaidya spacetime: horizons, conformal symmetries, surface gravity and diagonalization
• Evaporation of dynamical horizon with the Hawking temparature in the {\bf K-}essence emergent Vaidya spacetime
• Dynamical horizon of evaporating black hole in Vaidya spacetime
• Unruh effect in vacua with anisotropic scaling: Applications to multilayer graphene
• Particle creation rate for dynamical black holes
• The Negative Energy in Generalized Vaidya Spacetime
• Thermodynamics with conformal Killing vector in the charged Vaidya metric
• R-summed form of adiabatic expansions in curved spacetime
• Two physical characteristics of numerical apparent horizons
• Naked Singularity Explosion in Higher Dimensions