
Physics 2008
Local Hawking temperature for dynamical black holesAbstract: A local Hawking temperature is derived for any future outer trapping horizon in spherical symmetry, using a HamiltonJacobi variant of the ParikhWilczek 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 quasistationary picture of blackhole evaporation in early stages. However, the geometrical surface gravity is generally not the surface gravity of a static black hole with the same parameters.
