國立清華大學 數學系

Abstract The nonlinear effects of gravitational waves can be described by Bondi-Sachs spacetimes. They were originally introduced by Bondi for axi-symmetric spacetimes, and generalized by Sachs to general asymptotically flat spacetimes over 50 years ago for the zero cosmological constant. In this framework, Bondi defined the Bondi energy-momentum at null infinity, which represents the rest energy of spacetimes after the loss due to gravitational radiation. In this talk, we shall discuss some basic problems in gravitational waves for zero cosmological constant: Whether the Bondi energy is nonnegative? i.e., whether the gravitational waves can carry away more energy than they initially have? How the Bondi energy-momentum relates to the ADM energy-momentum defined at spatial infinity? We shall also discuss the natural boundary condition and the peeling property when the cosmological constant is nonzero.