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SUMMARY:The conformal field equations\, black holes\, gravitational waves 
 and the Newman-Penrose constants - Chris Stevens (University of Canterbury
 )
DTSTART:20230515T130000Z
DTEND:20230515T140000Z
UID:TALK200131@talks.cam.ac.uk
CONTACT:Dr Greg Taujanskas
DESCRIPTION:The conformal field equations\, black holes\, gravitational wa
 ves and the Newman-Penrose constants\n\nIn recent years\, a (numerically) 
 wellposed Initial Boundary Value Problem (IBVP) for the generalized confor
 mal field equations has been put forward. These equations regularly extend
  the Einstein equations to include "infinity" and the associated IBVP has 
 been used to successfully evolve\, in the fully non-linear regime\, a blac
 k hole space-time perturbed with a gravitational wave. This framework allo
 ws for direct calculations of global quantities defined at infinity\, such
  as the Bondi-Sachs energy-momentum\, and we have used it to successfully 
 reproduce the Bondi-Sachs mass loss.\n\nIn this talk\, two applications wi
 ll be discussed:\n\nLinear perturbations of black holes are well known and
  the associated oscillations in the Weyl curvature are known as quasinorma
 l modes. In recent work\, we investigated the analogous non-linear curvatu
 re oscillations and how they decay to the linear regime. In doing so\, we 
 have observed that only a short amount of physical proper time can be reso
 lved numerically in the conformal representation. Ideas to alleviate this 
 problem will be put forward.\n\nAnother recent application was the calcula
 tion of the Newman-Penrose Constants (NPC). These are five complex quantit
 ies defined on null infinity that are absolutely conserved if it is smooth
 . In stationary space-times\, they can be written terms of mass and angula
 r momentum moments\, but their physical interpretation in non-stationary s
 pace-times is still lacking. We compute\, for the first time\, the NPC in 
 a general setting and show that they remain constant\, implying smoothness
  of null infinity to at least the level of our numerical precision.
LOCATION:MR13
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