Vacuum Polarization and Persistence on the Black Hole Horizon

Abstract

We find the exact one-loop effective action in a Schwarzschild black hole in the proper-time integral from the Schwinger variational principle, which has the same form up to number of states as the Heisenberg-Euler and Schwinger QED effective action in a constant electric field. The leading term for Hawking radiation comes from the first simple pole of the vacuum polarization and the sum of residues from all simple poles exactly leads to the vacuum persistence. We show that the vacuum persistence is the total flux of Hawking radiation for bosons and fermions and the vacuum polarization has an expression of thermal distribution and the propagator.

RevTex 5 pages, no figure

References in corpus (6)

• Hawking Radiation from Charged Black Holes via Gauge and Gravitational Anomalies
• Effective Action of QED in Electric Field Backgrounds
• Effective Action of QED in Electric Field Backgrounds II: Spatially Localized Fields
• Consistency restrictions on maximal electric field strength in QFT
• Vacuum Persistence and Inversion of Spin Statistics in Strong QED
• Probing the Vacuum Structure of Spacetime

Cited by in corpus (2)

• In-Out Formalism for One-Loop Effective Actions in QED and Gravity
• Lessons from Schwinger Effective Action for Black Holes