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  • Letter
  • Open Access

Holographic dictionary for Lifshitz and hyperscaling violating black holes

Wan Cong1,*, David Kubizňák2,†, Robert B. Mann3,‡, and Manus R. Visser4,§

  • 1University of Vienna, Faculty of Physics, Boltzmanngasse 5, A 1090 Vienna, Austria
  • 2Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, Prague, V Holešovičkách 2, 180 00 Prague 8, Czech Republic
  • 3Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
  • 4Institute for Mathematics, Astrophysics and Particle Physics, and Radboud Center for Natural Philosophy, Radboud University, 6525 AJ Nijmegen, The Netherlands

  • *Contact author: wan.cong@univie.ac.at
  • †Contact author: david.kubiznak@matfyz.cuni.cz
  • ‡Contact author: rbmann@uwaterloo.ca
  • §Contact author: manus.visser@ru.nl
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Phys. Rev. D 112, L061901 – Published 9 September, 2025

DOI: https://doi.org/10.1103/kx5q-xk8y

Abstract

We develop a novel holographic dictionary for the thermodynamics of black holes with Lifshitz and hyperscaling violating asymptotics, generalizing the dictionary for anti—de Sitter black holes. Using our dictionary we show that the holographic Euler equation is dual to a generalized Smarr formula for these black holes, and we find a precise match between the extended bulk and boundary first law. Notably, the dictionary for the central charge appearing in the Euler relation depends on the hyperscaling violating parameter, but not on the Lifshitz dynamical exponent.

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References (45)

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Phys. Rev. D 112, L061901– Published 9 September, 2025
  • Received 15 November 2024
  • Accepted 20 August 2025
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