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Emergence of Black Holes in General Relativity
[2018 KAIST-HKUST-NUS Joint Workshop in Mathematics : Analysis, PDE and Probability]
Date: 2018-11-16
Speaker : An, Xinliang (NUS)
Abstract : Black holes are predicted by Einstein's theory of general relativity, and now we have ample observational evidence for their existence. However theoretically there are many unanswered questions about how black holes come into being. In this talk, with tools from hyperbolic PDE, quasilinear elliptic equations, geometric analysis and dynamical systems, we will prove that, through a nonlinear focusing effect, initially low-amplitude and diffused gravitational waves can give birth to a black hole region in our universe. This result extends the 1965 Penrose’s singularity theorem and it also proves a conjecture of Ashtekar on black-hole thermodynamics.
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