Holography in three-dimensional Kerr–de Sitter space with a gravitational Chern–Simons term

Abstract

The holographic description of the three-dimensional Kerr–de Sitter space with a gravitational Chern–Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy–momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the conventional Hawking temperature, and it is found that the usual Gibbons–Hawking entropy is modified. It is remarked that, due to the gravitational Chern–Simons term, (a) the results go beyond the analytic continuation from AdS, (b) the maximum-mass/N-bound conjecture may be violated and (c) the three-dimensional cosmology is chiral. A statistical mechanical computation of the entropy, from a Cardy-like formula for a dual CFT at the asymptotic boundary, is discussed. Some remarks on the technical differences in the Chern–Simons energy–momentum tensor, from the literature, are also made.