PDE Seminar Abstracts

Some mathematical problems in gravitational waves

Xiao Zhang
Chinese Academy of Sciences, China
Mon 28th Aug 2017, 2-3pm, Carslaw Room 829 (AGR)


On 11 February 2016, the LIGO Scientific Collaboration announced that they detected gravitational waves on 14 September 2015 from a 1.3 billion light years distant merger of two black holes.

The nonlinear effects of gravitational waves are described by Bondi-Sachs spacetimes. In the case of zero cosmological constant, they were originally introduced by Bondi for axi-symmetric spacetimes, and generalized by Sachs to general asymptotically flat spacetimes over 50 years ago. Bondi also 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 - 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? As 1998s cosmological observation indicated our universe has a positive cosmological constant, the Bondi-Sachs spacetimes for positive cosmological constant gain much attention currently. We shall also discuss the natural boundary condition and the surprising peeling property for the Bondi-Sachs spacetimes in this case.