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Stability of Big Bang singularity for the Einstein-Maxwell-scalar field-Vlasov system in the full strong sub-critical regime
Xinliang An, Taoran He, Dawei Shen
In dimensions, we study the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system. This system incorporates gravity, electromagnetic, weak and str…
On Kerr black hole formation with complete apparent horizon and a new approach toward Penrose inequality
Xinliang An, Taoran He
Arising from admissible extended scale-critical short-pulse initial data, we show that 3+1 dimensional Einstein vacuum equations admit dynamical Kerr black hole formation solutions…
Angular Momentum Memory Effect
Xinliang An, Taoran He, Dawei Shen
Utilizing recent mathematical advances in proving stability of Minkowski spacetime with minimal decay rates and nonlinear stability of Kerr black holes with small angular momentum,…
Dynamics of Apparent Horizon and a Null Comparison Principle
Xinliang An, Taoran He
This paper investigates the global dynamics of the apparent horizon. We present an approach to establish its existence and its long-term behaviors. Our apparent horizon is construc…
Quantitative blow-up estimates for spacelike singularities in gravitational-collapse cosmological spacetimes
Xinliang An, Haoyang Chen, Taoran He
Under spherical symmetry, with double-null coordinates , we study the gravitational collapse of the Einstein--scalar field system with a positive cosmological constant. The…