Eur. Phys. J. C (2019) 79: 627
https://doi.org/10.1140/epjc/s10052-019-7138-0

Regular Article - Theoretical Physics

Hawking radiation as instantons

¹ Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei, 10617, Taiwan
² Department of Physics, National Taiwan University, Taipei, 10617, Taiwan
³ Graduate Institute of Astrophysics, National Taiwan University, Taipei, 10617, Taiwan
⁴ Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Stanford University, Stanford, CA, 94305, USA
⁵ Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Chiba, 277-8583, Japan
⁶ Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan
⁷ Asia Pacific Center for Theoretical Physics, Pohang, 37673, Republic of Korea
⁸ Department of Physics, POSTECH, Pohang, 37673, Republic of Korea
⁹ Department of Physics Education, Pusan National University, Busan, 46241, Republic of Korea
¹⁰ Research Center for Dielectric and Advanced Matter Physics, Pusan National University, Busan, 46241, Republic of Korea

^* e-mail: innocent.yeom@gmail.com

Received: 6 January 2019
Accepted: 13 July 2019
Published online: 26 July 2019

Abstract

There have been various interpretations of Hawking radiation proposed based on the perturbative approach, and all have confirmed Hawking’s original finding. One major conceptual challenge of Hawking evaporation is the associated black hole information loss paradox, which remains unresolved. A key factor to the issue is the end-stage of the black hole evaporation. Unfortunately by then the evaporation process becomes non-perturbative. Aspired to provide a tool for the eventual solution to this problem, here we introduce a new interpretation of Hawking radiation as the tunneling of instantons. We study instantons of a massless scalar field in Einstein gravity. We consider a complex-valued instanton that connects an initial pure black hole state to a black hole with a scalar field that represents the Hawking radiation at future null infinity, where its action depends only on the areal entropy difference. By comparing it with several independent approaches to Hawking radiation in the perturbative limit, we conclude that Hawking radiation may indeed be described by a family of instantons. Since the instanton approach can describe non-perturbative processes, we hope that our new interpretation and holistic method may shed lights on the information loss problem.