Local Hawking temperature for dynamical black holes

Abstract

A local Hawking temperature is derived for any future outer trapping horizon in spherical symmetry, using a Hamilton-Jacobi variant of the Parikh-Wilczek tunneling method. It is given by a dynamical surface gravity as defined geometrically. The operational meaning of the temperature is that Kodama observers just outside the horizon measure an invariantly redshifted temperature, diverging at the horizon itself. In static, asymptotically flat cases, the Hawking temperature as usually defined by the Killing vector agrees in standard cases, but generally differs by a relative redshift factor between the horizon and infinity, being the temperature measured by static observers at infinity. Likewise, the geometrical surface gravity reduces to the Newtonian surface gravity in the Newtonian limit, while the Killing definition instead reflects measurements at infinity. This may resolve a longstanding puzzle concerning the Hawking temperature for the extremal limit of the charged stringy black hole, namely that it is the local temperature which vanishes. In general, this confirms the quasi-stationary picture of black-hole evaporation in early stages. However, the geometrical surface gravity is generally not the surface gravity of a static black hole with the same parameters.

9 pages

References in corpus (1)

• The black hole information paradox

Cited by in corpus (6)

• Hawking Radiation of Apparent Horizon in a FRW Universe
• Hawking Radiation from a Vaidya Black Hole: A Semi-Classical Approach and Beyond
• Radiation from Einstein-Gauss-Bonnet de Sitter Black Hole via Tunneling Process
• Some results on dynamical black holes
• Hawking temperature and the emergent cosmic space
• Gravitational thermodynamics and universal holographic duality in dynamical spacetimes