2016/04/02 by Gonçalo M. Quinta, Antonino Flachi, José P. S. Lemos · 7 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Black hole (networking) #Classical mechanics #Cosmology and Gravitation Theories #Dual polyhedron #Geometry #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Theoretical physics #Vacuum polarization #gr-qc
paper · pdf · doi:10.1103/physrevd.93.124073
published in Physical review. D/Physical review. D. 93(12) (American Physical Society)
arxiv created 2016/04/02 · openalex publication_date 2016/06/29 · arxiv updated 2016/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
There has been considerable interest in applying the gauge-gravity duality to condensed matter theories with particular attention being devoted to gravity duals (Lifshitz spacetimes) of theories that exhibit anisotropic scaling. In this context, black hole solutions with Lifshitz asymptotics have also been constructed, focused on incorporating finite temperature effects. The goal here is to look at quantum polarization effects in these spacetimes and, to this aim, we develop a way to compute the coincidence limit of the Green's function for massive, nonminimally coupled scalar fields, adapting to the present situation the analysis developed for the case of asymptotically anti--de Sitter black holes. The basics are similar to previous calculations; however, in the Lifshitz case, one needs to extend the previous results to include a more general form for the metric and dependence on the dynamical exponent. All formulas are shown to reduce to the anti--de Sitter (AdS) case studied before once the value of the dynamical exponent is set to unity and the metric functions are accordingly chosen. The analytical results we present are general and can be applied to a variety of cases, in fact, to all spherically symmetric Lifshitz black hole solutions. We also implement the numerical analysis choosing some known Lifshitz black hole solutions as illustration.