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DTSTART;TZID=America/New_York:20240206T100000
DTEND;TZID=America/New_York:20240206T110000
DTSTAMP:20260420T034643
CREATED:20240202T170516Z
LAST-MODIFIED:20240209T200944Z
UID:10000823-1707213600-1707217200@cmsa.fas.harvard.edu
SUMMARY:Noncompact n-dimensional Einstein spaces as attractors for the Einstein flow
DESCRIPTION:General Relativity Seminar \nSpeaker: Jinhua Wang\, Xiamen University \nTitle: Noncompact n-dimensional Einstein spaces as attractors for the Einstein flow \nAbstract: We prove that along with the Einstein flow\, any small perturbations of an $n$($n\geq4$)-dimensional\, non-compact negative Einstein space with some “non-positive Weyl tensor” lead to a unique and global solution\, and the solution will be attracted to a noncompact Einstein space that is close to the background one. The $n=3$ case has been addressed by Wang-Yuan\, while in dimension $n\geq 4$\, as we know\, negative Einstein metrics in general have non-trivial moduli spaces. This fact is reflected on the structure of Einstein equations\, which further indicates no decay for the spatial Weyl tensor. Furthermore\, it is suggested in the proof that the mechanic preventing the metric from flowing back to the original Einstein metric lies in the non-decaying character of spatial Weyl tensor. In contrary to the compact case considered in Andersson-Moncrief\, our proof is independent of the theory of infinitesimal Einstein deformations. Instead\, we take advantage of the inherent geometric structures of Einstein equations and develop an approach of energy estimates for a hyperbolic system of Maxwell type. \nReferences – arXiv: 2209.15244\, 2309.15152\, 2311.00868
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-2624/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-02.06.2024.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240213T110000
DTEND;TZID=America/New_York:20240213T110000
DTSTAMP:20260420T034643
CREATED:20240212T161202Z
LAST-MODIFIED:20240212T181141Z
UID:10000824-1707822000-1707822000@cmsa.fas.harvard.edu
SUMMARY:Characteristic Initial Value Problem for the 3D Compressible Euler Equations
DESCRIPTION:General Relativity Seminar \nSpeaker: Sifan Yu\, NUS \nTitle: Characteristic Initial Value Problem for the 3D Compressible Euler Equations \nAbstract: We present the first result for the characteristic initial value problem of the compressible Euler equations in three space dimensions without any symmetry assumption. We allow presence of vorticity and consider any equation of state. Compared to the standard Cauchy problem\, where initial data can be freely prescribed on a constant-time hypersurface\, we formulate the problem by distinguishing between the “free-component” and the “constrained-component” of the initial data. The latter is to be solved by the “free-component” utilizing the properties of the compressible Euler equations on the initial null hypersurfaces. Then\, we establish a priori estimates\, followed by a local well-posedness and a continuation criterion argument. Moreover\, we prove a regularity theory in Sobolev norms. Our analysis critically relies on the vectorfield method due to the nature of the problem. This is a joint work with Jared Speck.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-21324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-02.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240220T093000
DTEND;TZID=America/New_York:20240220T103000
DTSTAMP:20260420T034643
CREATED:20240219T195817Z
LAST-MODIFIED:20240219T195829Z
UID:10000825-1708421400-1708425000@cmsa.fas.harvard.edu
SUMMARY:Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes
DESCRIPTION:General Relativity Seminar \nSpeaker: He Mei\, Shenzhen University \nTitle: Asymptotic decay for defocusing semilinear wave equations on Schwarzschild spacetimes \nAbstract: In this talk\, I will present a work on the long time dynamics of solutions to the defocusing semilinear wave equations on the Schwarzschild black hole spacetimes. For sufficiently smooth and localized initial data\, we show that the solution decays in the domain of outer communication. The proof relies on a vector field method of Dafermos-Rodnianski together with Strichartz estimates for linear waves by Marzuola-Metcalfe-Tataru-Tohaneanu.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-22024/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240227T110000
DTEND;TZID=America/New_York:20240227T120000
DTSTAMP:20260420T034643
CREATED:20240226T152845Z
LAST-MODIFIED:20240227T193918Z
UID:10000826-1709031600-1709035200@cmsa.fas.harvard.edu
SUMMARY:On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes
DESCRIPTION:General Relativity Seminar \nSpeaker: Nishanth Gudapati\, Clark University \nTitle: On Axially Symmetric Perturbations of Kerr Black Hole Spacetimes \nAbstract: The Kerr black hole stability problem is an important open problem in general relativity. In this talk\, I will focus on the role of energy methods in the axisymmetric stability of Kerr black hole spacetimes. In particular\, I will discuss the construction and the application of a positive Hamiltonian energy for axially symmetric Maxwell and Einstein perturbations of sub-extremal Kerr black hole spacetimes.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-22724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-02.27.2024.png
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