| dc.description.abstract | Higher spin gauge theories are consistent interacting theories of higher spin fields in AdS spacetimes wherein they can evade the usual no-go theorems. With these theories one can study physics beyond the supergravity regime and it is believed that they belong to some parameter space corner of M-theory. Higher Spin gauge theory in (2+1)-dimensions is a toy model for Higher Spin theories in arbitrary dimensions in AdS. The advantage is that in three dimensions the theory becomes topological, due to the lack of propagating degrees of freedom. As a result, it is interesting to work out the details of this theory in the black hole regime. In this thesis, the basic aspects of three-dimensional Higher Spin theories are reviewed in both metric-like and gauge-like formulations. More emphasis is put on the Chern-Simons formulation, where the gauge connections are valued in $SL(N,\mathbb{R})$. Specifically, a discussion about asymptotic symmetries, proper and improper transformations is included, inspired by the original work on central charges by Brown and Henneaux, and later from application of their results in the Chern-Simons formulation. In addition, different proposals for higher spin black holes are reviewed and studied, including their thermodynamics. Also, an attempt to show that there is no ergosphere for the rotating cases has been made, but in a specific gauge. It is important to point out that higher spin theories are included in a specific family of theories that do not keep the metric invariant under diffeomorphisms, because these transformations ”braid” the spin-2 field with all the higher spin fields. Therefore, concepts such as geodesics and horizon of a black hole are not well defined or need refinement. However, a proposal to use Wilson lines and Wilson loops was made by A. Castro, M. Ammon and N. Iqbal, that allows the calculation of the entanglement entropy using the Ryu and Takayanagi formula, which has been revised in this thesis. Finally, an attempt to extract information about the horizon shape and radius, using the Wilson line approach, has been made and a comparison between different back holes regimes of the same temperature has been included. | |
