Dynamics of the four kinds of Trapping Horizons and Existence of Hawking Radiation

Abstract

We work with the notion of apparent/trapping horizons for spherically symmetric, dynamical spacetimes: these are quasi-locally defined, simply based on the behaviour of congruence of light rays. We show that the sign of the dynamical Hayward-Kodama surface gravity is dictated by the inner/outer nature of the horizon. Using the tunneling method to compute Hawking Radiation, this surface gravity is then linked to a notion of temperature, up to a sign that is dictated by the future/past nature of the horizon. Therefore two sign effects are conspiring to give a positive temperature for the black hole case and the expanding cosmology, whereas the same quantity is negative for white holes and contracting cosmologies. This is consistent with the fact that, in the latter cases, the horizon does not act as a separating membrane, and Hawking emission should not occur.

arXiv comment22 pages, 4 figures

References in corpus (7)

• Hawking Radiation as Tunneling
• General Laws of Black-Hole Dynamics
• Introduction to Isolated Horizons in Numerical Relativity
• The 1965 Penrose singularity theorem
• Kodama time: Geometrically preferred foliations of spherically symmetric spacetimes
• The Apparent Universe
• Astrophysical black holes may radiate, but they do not evaporate

Cited by in corpus (4)

• Causal Nature and Dynamics of Trapping Horizons in Black Hole Collapse
• Temperature and entropy-area relation of quantum matter near spherically symmetric outer trapping horizons
• Trapping Horizons of the Evolving Charged Wormhole and Black Bounce
• Cosmological Solutions, a New Wick-Rotation, and the First Law of Thermodynamics