Something special at the event horizon

Abstract

We calculate the free-fall energy density of scalar fields semi-classically by employing the trace anomaly on a two-dimensional Schwarzschild black hole with respect to various black hole states in order to clarify whether something special at the horizon happens or not. For the Boulware state, the energy density at the horizon is always negative divergent, which is independent of initial free-fall positions. However, in the Unruh state the initial free-fall position is responsible for the energy density at the horizon and there is a critical point to determine the sign of the energy density at the horizon. In particular, a huge negative energy density appears when the freely falling observer is dropped just near the horizon. For the Hartle-Hawking state, it may also be positive or negative depending on the initial free-fall position, but it is always finite. Finally, we discuss physical consequences of these calculations.

11 pages, 3 figures, references added, version to appear in MPLA

Cited by in corpus (11)

• Hawking radiation, the Stefan-Boltzmann law, and unitarization
• The black hole quantum atmosphere
• Black hole quantum atmosphere for freely falling observers
• A Quantal Tolman Temperature
• Hawking versus Unruh effects, or the difficulty of slowly crossing a black hole horizon
• Origin of Hawking Radiation: Firewall or Atmosphere?
• The effective Tolman temperature in curved spacetimes
• Semiclassical approach for the evaporating black hole revisited
• Free-fall energy density and flux in the Schwarzschild black hole
• Observables in quantum field theory on a collapsing black hole background
• Thermal scalar field stress tensor on a two dimensional black hole and its near horizon properties