AdS3 to dS3 transition in the near horizon of asymptotically de Sitter solutions

Abstract

We consider two solutions of Einstein-$\mathrm{\ensuremath{\Lambda}}$ theory which admit the extremal vanishing horizon (EVH) limit, odd-dimensional multispinning Kerr black hole (in the presence of cosmological constant) and cosmological soliton. We show that the near horizon EVH geometry of Kerr has a three-dimensional maximally symmetric subspace whose curvature depends on rotational parameters and the cosmological constant. In the Kerr-dS case, this subspace interpolates between ${\mathrm{AdS}}_{3}$, three-dimensional flat and ${\mathrm{dS}}_{3}$ by varying rotational parameters, while the near horizon of the EVH cosmological soliton always has a ${\mathrm{dS}}_{3}$. The feature of the EVH cosmological soliton is that it is regular everywhere on the horizon. In the near EVH case, these three-dimensional parts turn into the corresponding locally maximally symmetric spacetimes with a horizon: Kerr-${\mathrm{dS}}_{3}$, flat space cosmology or BTZ black hole. We show that their thermodynamics match with the thermodynamics of the original near EVH black holes. We also briefly discuss the holographic two-dimensional CFT dual to the near horizon of EVH solutions.