Near-horizon radiation and self-dual loop quantum gravity

¹ Institute for Gravitation and the Cosmos & Physics Department, Penn State - University Park, PA 16802, USA
² Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais - Parc de Grandmont, 37200 Tours, France
³ Laboratoire APC – Astroparticule et Cosmologie, Université Paris Diderot Paris 7 - 75013 Paris, France

Received: 6 March 2014
Accepted: 11 March 2014

Abstract

We compute the near-horizon radiation of quantum black holes in the context of self-dual loop quantum gravity. For this, we first use the unitary spinor basis of to decompose states of Lorentzian spin foam models into their self-dual and anti–self-dual parts, and show that the reduced density matrix obtained by tracing over one chiral component describes a thermal state at Unruh temperature. Then, we show that the analytically-continued dimension of the SU(2) Chern-Simons Hilbert space, which reproduces the Bekenstein-Hawking entropy in the large spin limit in agreement with the large spin effective action, takes the form of a partition function for states thermalized at Unruh temperature, with discrete energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with a degenerate ground state which is holographic and responsible for the entropy.