2+1 black hole with SU(2) hair (and the theory where it grows)

Spanish Relativity Meeting: almost 100 years after Einstein's revolution

Zanelli, Jorge^1,2

Centro de Estudios Científicos, CECs, Valdivia, Chile^1

Universidad Andres Bello, Av. Republica 440, Santiago, Chile^2

关键词: Black hole solutions;    Covering spaces;    Dirac point;    Gauge symmetries;    Long-wavelength limits;    Minkowski space;    Spin quantization;    Three dimensions;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/600/1/012005/pdf
DOI  :  10.1088/1742-6596/600/1/012005

来源: IOP

【 摘 要 】

A black hole solution in three spacetime dimensions, endowed with an SU(2) charge is presented. The construction is based on two main features of three dimensions: i) AdS3spacetime is locally Lorentz-flat, that is, it can be covered with a congruence of local inertial observers, just like flat Minkowski space; ii) The SO(2,1) and SU(2) groups are isomorphic, so that a flat connection of the first can be mapped to a flat connection of the second. The global nontrivial nature of the solution is a consequence of the topology produced by the identification in the covering space that gives rise to the 2+1 black hole. It can be seen that this solution belongs to the vacuum (matter-free) sector of a supersymmetric theory based on the Chern-Simons action for the su(1, 2|2) superalgebra. The action for this system matches that of graphene in the long wavelength limit near the Dirac point. The SU(2) gauge symmetry is interpreted as the freedom to choose locally the definition of spin quantization axis for the electrons.