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UID:20251121T140806EST-4453h48jaA@132.216.98.100
DTSTAMP:20251121T190806Z
DESCRIPTION:\n	Seminar Geometric Analysis\n\nOn Gravitational Collapse in Ge
 neral Relativity\n\nXinliang An\, University of Toronto\n\nIn the process 
 of gravitational collapse\, singularities may form\, which are either cove
 red by trapped surfaces (black holes) or visible to faraway observers (nak
 ed singularities). In this talk\, I will present four results with regard 
 to gravitational collapse for Einstein vacuum equation. The first is a sim
 plified approach to Christodoulou’s monumental result which showed that tr
 apped surfaces can form dynamically by the focusing of gravitational waves
  from past null infinity. We extend the methods of Klainerman-Rodnianski\,
  who gave a simplified proof of this result in a finite region. The second
  result extends the theorem of Christodoulou by allowing for weaker initia
 l data but still guaranteeing that a trapped surface forms in the causal d
 omain. In particular\, we show that a trapped surface can form dynamically
  from initial data which is merely large in a scale-invariant way. The sec
 ond result is obtained jointly with Jonathan Luk. The third result answere
 d the following questions: Can a ``black hole’’ emerge from a point? Can w
 e find the boundary (apparent horizon) of a ``black hole’’ region? The fou
 rth result extends Christodoulou’s famous example on formation of naked si
 ngularity for Einstein-scalar field system under spherical symmetry. With 
 numerical and analytic tools\, we generalize Christodoulou’s result and co
 nstruct an example of naked singularity formation for Einstein vacuum equa
 tion in higher dimension. The fourth result is obtained jointly with Xuefe
 ng Zhang.\n
DTSTART:20170407T173000Z
DTEND:20170407T173000Z
LOCATION:BURN 920\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue 
 Sherbrooke Ouest
SUMMARY:Xinliang An\, University of Toronto
URL:/mathstat/channels/event/xinliang-university-toron
 to-267432
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