PROFESSOR ABHAY ASHTEKAR

Surprisingly, several basic questions in classical and quantum gravity, which were resolved some 40-50 years ago for zero $\Lambda$, still remain open in the $\Lambda >0$ case. In particular, we still do not have a satisfactory notion of gravitational radiation or Bondi 4-momentum in exact general relativity, nor a positive energy theorem. Similarly, the standard constructions of 'in' and 'out' Hilbert spaces that we routinely use (e.g. in the analysis of black hole evaporation) do not extend to the $\Lambda >0$ case. In this talk the speaker will present some illustrative examples of these quandaries and introduce a systematic approach to resolve the open issues.