Higher Spin Black Holes

  • Alfredo Pérez
  • David Tempo
  • Ricardo TroncosoEmail author
Part of the Lecture Notes in Physics book series (LNP, volume 892)


We review some relevant results in the context of higher spin black holes in three-dimensional spacetimes, focusing on their asymptotic behaviour and thermodynamic properties. For simplicity, we mainly discuss the case of gravity nonminimally coupled to spin-three fields, being nonperturbatively described by a Chern–Simons theory of two independent \(\mathit{sl}\left (3, \mathbb{R}\right )\) gauge fields. Since the analysis is particularly transparent in the Hamiltonian formalism, we provide a concise discussion of their basic aspects in this context; and as a warming up exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well as the BTZ black hole and its thermodynamics, exclusively in terms of gauge fields. The discussion is then extended to the case of black holes endowed with higher spin fields, briefly signaling the agreements and discrepancies found through different approaches. We conclude explaining how the puzzles become resolved once the fall off of the fields is precisely specified and extended to include chemical potentials, in a way that it is compatible with the asymptotic symmetries. Hence, the global charges become completely identified in an unambiguous way, so that different sets of asymptotic conditions turn out to contain inequivalent classes of black hole solutions being characterized by a different set of global charges.


Black Hole High Spin Gauge Transformation Black Hole Solution Gauge Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank G. Barnich, X. Bekaert, E. Bergshoeff, C. Bunster, A. Campoleoni, R. Canto, D. Grumiller, M. Henneaux, J. Jottar, C. Martínez, J. Matulich, J. Ovalle, R. Rahman, S-J Rey, J. Rosseel, C. Troessaert and M. Vasiliev for stimulating discussions. R.T. also thanks E. Papantonopoulos and the organizers of the Seventh Aegean Summer School, “Beyond Einstein’s theory of gravity”, for the opportunity to give this lecture in a wonderful atmosphere. This work is partially funded by the Fondecyt grants N 1130658, 1121031, 11130260, 11130262. The Centro de Estudios Científicos (CECs) is funded by the Chilean Government through the Centers of Excellence Base Financing Program of Conicyt.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alfredo Pérez
    • 1
  • David Tempo
    • 1
  • Ricardo Troncoso
    • 1
    • 2
    Email author
  1. 1.Centro de Estudios Científicos (CECs)ValdiviaChile
  2. 2.Universidad Andrés BelloSantiagoChile

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