Null infinity as SU(2) Chern–Simons theories and its quantization

Abstract This paper studies the quantization of the future null infinity (I^+ I +) of an asymptotically flat spacetime. Based on the observation by Ashtekar and Speziale that I^+ I + can be regarded as an extremal weakly isolated horizon, we extend the quantization framework developed for weakly isolated horizon to quantize I^+ I +. We first show that the symplectic structure of I^+ I + is equivalent to the sum of the symplectic structures of two SU (2) Chern–Simons theories with opposite levels. Based on this observation, we apply Chern–Simons quantization approach to quantize I^+ I +. Finally, we compute the entropy of I^+ I + by counting the microstates, showing that it is proportional to the area of Δ ~, a spacelike cross-section of I^+ I +. Our result is consistent with the universal entropy formula in the framework of (weakly) isolated horizon.