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Holographic Phase Transitions in \((2+1)\)-Dimensional Black Hole Spacetimes in NMG

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Abstract

In this work, we aim at the question of holographic phase transitions in two-dimensional systems with Lifshitz scaling. We consider the gravity side candidate for a dual description as the black hole solution of new massive gravity (NMG) with Lifshitz scaling. We discuss the effects due to the Lifshitz scaling in the AGGH (Ayon-Beato-Garbarz-Giribet-Hassaïne) solution in comparison with the BTZ (Bañados-Teitelboim-Zanelli) black hole. Likewise, we compute the order parameter and it indicates a second-order phase transition in a \((1+1)\) dimension Lifshitz boundary.

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Data Availability

No datasets were generated or analyzed during the current study.

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Notes

  1. We omit the hat notation.

  2. We started varying \(E_+\) from 0 to 10 and later, we changed in order to see at least five curves.

  3. We noticed that we needed smaller steps in \(\Psi _+\) for the \(<O_1>\) and \(<O_2>\) curves to be smooth.

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Acknowledgements

We would like to thank Bin Wang and Eleftherios Papantonopoulos for useful discussions.

Funding

This work has been supported by FAPESP, FAPEMIG, and CNPq, Brazil.

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Author notes

  1. Elcio Abdalla, Jeferson de Oliveira, Alan Bendasoli Pavan, and Carlos Eduardo Pellicer contributed equally to this work.

Authors and Affiliations

  1. Instituto de Física, Universidade de São Paulo, São Paulo, 05315-970, SP, Brazil

    Elcio Abdalla

  2. Instituto de Física, Universidade Federal de Mato Grosso, Cuiabá, 78060-900, MT, Brazil

    Jeferson de Oliveira

  3. Instituto de Física e Química, Universidade Federal de Itajubá, Itajubá, 37500-903, MG, Brazil

    Alan Bendasoli Pavan

  4. Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, Natal, 59072-970, RN, Brazil

    Carlos Eduardo Pellicer

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  1. Elcio Abdalla
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Contributions

J.O., E.A., and A.B.P. proposed the idea of the work; J.O., E.A., and A.B.P. wrote the main manuscript text, J.O. and A.B.P. did the analytic calculations, C.E.P. did the numerical calculations and prepared figures. All authors reviewed the manuscript.

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Correspondence to Alan Bendasoli Pavan.

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Abdalla, E., de Oliveira, J., Pavan, A.B. et al. Holographic Phase Transitions in \((2+1)\)-Dimensional Black Hole Spacetimes in NMG. Braz J Phys 54, 50 (2024). https://doi.org/10.1007/s13538-024-01429-7

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