Brown Bag Seminar | Hyperbolic Mass in 2+1 Dimensions

Solutions to general relativity with a negative cosmological constant have received significant attention due to the conjectured AdS/CFT correspondence, a particularly well-understood example of which is exhibited in 2• 1 dimensions. After reviewing known vacuum solutions to general relativity with a negative cosmological constant in 21 dimensions, I will present a gluing theorem for the corresponding vacuum general-relativistic initial data sets. By gluing two given vacuum initial data sets at infinity, we obtain new vacuum initial data sets. I will sketch the derivation of the mass formulae of the resulting manifolds. For the case of the BTZ black hole, by invoking usual black hole thermodynamics, our mass formulae may be interpreted as entropy formulae. Our gluing theorem yields complete manifolds with any mass aspect function, which are smooth except for one conical singularity.