Enhanced asymptotic symmetry algebra of ( 2 + 1 ) -dimensional flat space

In this paper we present a new set of asymptotic boundary conditions for Einstein gravity in (2+1)-dimensions with a vanishing cosmological constant that are a generalization of the Barnich-Compère boundary conditions [G. Barnich and G. Compere, Classical Quantum Gravity 24, F15 (2007)]. These new boundary conditions lead to an asymptotic symmetry algebra that is generated by a bms3 algebra and two affine u^(1) current algebras. We then apply these boundary conditions to topologically massive gravity (TMG) and determine how the presence of the gravitational Chern-Simons term affects the central extensions of the asymptotic symmetry algebra. We furthermore determine the thermal entropy of solutions obeying our new boundary conditions for both Einstein gravity and TMG.