A microscopic model of black hole evaporation in two dimensions

• Published in: The journal of high energy physics 2023-08, Vol.2023 (8), p.171-68, Article 171
• Main Authors: Gaikwad, Adwait, Kaushal, Anurag, Mandal, Gautam, Wadia, Spenta R.
• Format: Article
• Language: English
• Subjects: 2D Gravity; AdS-CFT Correspondence; Asymptotic methods; Black Holes; Classical and Quantum Gravitation; Couplings; Differential equations; Elementary Particles; Energy industry; Evaporation; Gravity; High energy physics; Operators (mathematics); Physics; Physics and Astronomy; Quantum Dissipative Systems; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Radiation; Random noise; Regular Article - Theoretical Physics; Relativity Theory; Scalars; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2023)171

A bstract We present a microscopic model of black hole (BH) ‘evaporation’ in asymptotically AdS 2 spacetimes dual to the low energy sector of the SYK model. To describe evaporation, the SYK model is coupled to a bath comprising of N f free scalar fields Φ i . We consider a linear combination of couplings of the form O SY K ( t )∑ i Φ i (0,  t ), where O SY K involves products of the Kourkoulou-Maldacena operator iJ / N ∑ k = 1 N / 2 s k ′ ψ 2 k − 1 t ψ 2 k t specified by a spin vector s ′ . We discuss the time evolution of a product of (i) a pure state of the SYK system, namely a BH microstate characterized by a spin vector s and an effective BH temperature T BH , and (ii) a Calabrese-Cardy state of the bath characterized by an effective temperature T bath . We take T bath ≪ T BH , and T BH much lower than the characteristic UV scale J of the SYK model, allowing a description in terms of the time reparameterization mode. Tracing over the bath degrees of freedom leads to a Feynman-Vernon type effective action for the SYK model, which we study in the low energy limit. The leading large N behaviour of the time reparameterization mode is found, as well as the O 1 / N fluctuations. The latter are characterized by a non-Markovian non-linear stochastic differential equation with non-local Gaussian noise. In a restricted range of couplings, we find two classes of solutions which asymptotically approach (a) a BH at a lower temperature, and (b) a horizonless geometry. We identify these with partial and complete BH evaporation, respectively. Importantly, the asymptotic solution in both cases involves the scalar product of the spin vectors s.s ′ , which carries some information about the initial state. By repeating the dynamical process O ( N 2 ) times with different choices of the spin vector s ′ , one can in principle reconstruct the initial BH microstate.