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DTSTART;TZID=America/New_York:20250204T110000
DTEND;TZID=America/New_York:20250204T120000
DTSTAMP:20260506T231153
CREATED:20240903T192049Z
LAST-MODIFIED:20250130T190257Z
UID:10003428-1738666800-1738670400@cmsa.fas.harvard.edu
SUMMARY:The mass angular momentum inequality
DESCRIPTION:General Relativity Seminar \nSpeaker: Gilbert Weinstein\, Ariel University \nTitle: The mass angular momentum inequality \nAbstract: We show that either there is a counterexample to black hole uniqueness\, in the form of a regular axisymmetric stationary vacuum spacetime with an asymptotically flat end and multiple degenerate horizons which is ‘ADM stable’\, or the following statement holds. Complete\, simply connected\, maximal initial data sets for the Einstein equations with multiple ends that are either asymptotically flat or asymptotically cylindrical\, admit an ADM mass lower bound given by the square root of total angular momentum\, under the assumption of nonnegative energy density and axisymmetry. Moreover\, equality is achieved bound only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target\, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-2425/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-2.4.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250211T110000
DTEND;TZID=America/New_York:20250211T120000
DTSTAMP:20260506T231153
CREATED:20250128T211214Z
LAST-MODIFIED:20250210T141458Z
UID:10003698-1739271600-1739275200@cmsa.fas.harvard.edu
SUMMARY:On the past maximal development of near-FLRW data for the  Einstein scalar-field Vlasov system
DESCRIPTION:General Relativity Seminar \nSpeaker: Liam Urban (University of Vienna) \n\nTitle: On the past maximal development of near-FLRW data for the Einstein scalar-field Vlasov system \nAbstract: In recent years\, the formation of Big Bang singularities has been increasingly well understood in presence of scalar-field matter\, which suppresses the geometric oscillations that one generically expects otherwise. From a cosmological perspective\, however\, one would like to understand whether this feature persists when coupled to further models that more closely resemble the matter content in our universe. \nIn this talk\, I will discuss the past nonlinear stability of FLRW solutions to the Einstein scalar-field Vlasov system in three and four spacetime dimensions without symmetry assumptions. The latter is based on joint work with David Fajman. In both works\, near-FLRW solutions are\nshown to be asymptotically velocity term dominated toward the past\,  resulting in a quiescent Big Bang singularity with stable Kretschmann scalar blow-up. The Vlasov distribution\, however\, becomes highly anisotropic towards the Big Bang singularity\, concentrating in preferred momentum directions associated with eigendirections of the shear. To ensure that the scalar field sufficiently mitigates this behaviour\, one crucially exploits a scaling hierarchy between horizontal and vertical derivatives in the expansion normalized Vlasov equation. In four\nspacetime dimensions\, this analysis is paired with a Bel-Robinson energy formalism to control the spacetime and scalar field evolution\, while one finds a significantly more direct proof in three dimensions since the spatial Riemann curvature is pure trace. \nAs a corollary\, one also obtains that the Strong Cosmic Censorship conjecture holds for four-dimensional polarized $U(1)$-symmetric solutions to the Einstein vacuum equations with spatial topology $M\times\S^1$ and isotropic quotient.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-21125/
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/1738856087821-8bd46bd5-9d75-4777-80dd-59b2ca5dc8d52025_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250218T110000
DTEND;TZID=America/New_York:20250218T120000
DTSTAMP:20260506T231153
CREATED:20240903T191953Z
LAST-MODIFIED:20250219T144101Z
UID:10003426-1739876400-1739880000@cmsa.fas.harvard.edu
SUMMARY:General Relativity Seminar
DESCRIPTION:General Relativity Seminar \nSpeaker: Maximilian Ofner\, University of Vienna \nTitle: Stability and Instability of Relativistic Fluids in Slowly Expanding Spacetimes \nAbstract: Homogeneous and isotropic solutions to the relativistic Euler equations are known to be unstable on a Minkowski background. However\, for FLRW models with a fast expansion rate\, relativistic fluids stabilize. This scenario suggests a transition between stable and unstable behavior\, somewhere along a family of spacetimes parametrized by their expansion rate. In this talk we will discuss this phase transition for various equations of state\, focusing on the regime of linear and decelerated expansion. This is based on recent analytical results\, complemented by numerical analysis.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-21825/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-2.18.25.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250225T110000
DTEND;TZID=America/New_York:20250225T120000
DTSTAMP:20260506T231153
CREATED:20240903T183821Z
LAST-MODIFIED:20250228T212719Z
UID:10003420-1740481200-1740484800@cmsa.fas.harvard.edu
SUMMARY:BKL bounces outside homogeneity
DESCRIPTION:General Relativity Seminar \nSpeaker: Warren Li ( Princeton University) \nTitle: BKL bounces outside homogeneity \nAbstract: In work spanning the late 20th century\, physicists Belinski\, Khalatnikov and Lifshitz (BKL) proposed a general ansatz for solutions to the Einstein (vacuum) equations near singularities. They suggest that the spacetime dynamics at different spatial points on the singularity decouple and are well-approximated by a system of autonomous nonlinear ODEs\, whose orbits are governed by a chaotic cascade of “BKL bounces”. In this talk\, we present recent work verifying BKL’s heuristics in a large class of symmetric\, but spatially inhomogeneous\, spacetimes. In particular\, we prove decoupling even in the presence of (up to one) BKL bounce. The proof uses nonlinear ODE analysis coupled to hyperbolic energy estimates\, and one hopes our methods may be applied more generally.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-22525/
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/1740157873632-2128c0f1-4416-42e5-a58b-0475ecffb3852025-1_1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250311T110000
DTEND;TZID=America/New_York:20250311T120000
DTSTAMP:20260506T231153
CREATED:20250128T213420Z
LAST-MODIFIED:20250312T191855Z
UID:10003700-1741690800-1741694400@cmsa.fas.harvard.edu
SUMMARY:Positive scalar curvature with point singularities
DESCRIPTION:General Relativity Seminar \nSpeaker: Rudolf Zeidler\, Mathematical Institute\, University of Münster \nTitle: Positive scalar curvature with point singularities \nAbstract: I will explain a certain topological construction of positive scalar curvature metrics with uniformly Euclidean ($L^\infty$) point singularities. This provides counterexamples to a conjecture of Schoen. It also shows that there are metrics with uniformly Euclidean point singularities which cannot be smoothed via a geometric flow while simultaneously preserving non-negativity of the scalar curvature. Based on recent joint work with Simone Cecchini and Georg Frenck.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-31125/
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-3.11.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250325T160000
DTEND;TZID=America/New_York:20250325T170000
DTSTAMP:20260506T231153
CREATED:20250128T213506Z
LAST-MODIFIED:20250326T194012Z
UID:10003701-1742918400-1742922000@cmsa.fas.harvard.edu
SUMMARY:Unstable Fluids in Expanding Cosmologies
DESCRIPTION:General Relativity Seminar \nSpeaker: Elliot Marshal\, School of Mathematics at Monash University \nTitle: Unstable Fluids in Expanding Cosmologies \nAbstract: The FLRW solution is the simplest cosmological model in general relativity\, describing a fluid-filled\, spatially homogeneous universe. While there is extensive literature in the physics community on cosmological models with a linear equation of state \, rigorous stability results have\, until recently\, been limited to FLRW models with accelerated expansion and small sound speeds. In this talk\, I will discuss numerical work on two types of instabilities which can occur in non-linearly perturbed FLRW models outside of this regime. The first concerns a longstanding conjecture of Alan Rendall on FLRW models with positive cosmological constant and super-radiative (K>1/3) equations of state. Our numerical work\, in collaboration with F. Beyer and T.A. Oliynyk\, supports Rendall’s conjecture and highlights the underlying mechanism for the instability. In the second case\, I will discuss evidence that perturbations of slowly expanding (decelerated) FLRW models generically form shocks in finite time. This contrasts with known results for accelerated models where shock formation is suppressed for suitably small perturbations.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-32525/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-3.25.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250401T110000
DTEND;TZID=America/New_York:20250401T120000
DTSTAMP:20260506T231153
CREATED:20250128T213541Z
LAST-MODIFIED:20250331T195936Z
UID:10003702-1743505200-1743508800@cmsa.fas.harvard.edu
SUMMARY:Low-regularity Local Well-posedness of the Elastic Wave System
DESCRIPTION:General Relativity Seminar \nSpeaker: Sifan Yu\, National University of Singapore \nTitle: Low-regularity Local Well-posedness of the Elastic Wave System \nAbstract: In this talk\, I will present a recent work on the elastic wave system in three spatial dimensions. For admissible harmonic elastic materials\, we prove a low-regularity local well-posedness result for the corresponding elastic wave equations. For such materials\, we can split the dynamics into the “divergence-part” and the “curl-part\,” and each part satisfies a distinct coupled quasilinear wave system with respect to different acoustical metrics. Our main result is that the Sobolev norm H^{3+} of the “divergence-part” (the “faster-wave part”) and the H^{4+} of the “curl-part” (the “slower-wave part”) can be controlled in terms of initial data for short times. We note that the Sobolev norm assumption H^{3+} is optimal for the “divergence-part.” This is a joint work with Xinliang An and Haoyang Chen.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-4125/
LOCATION:Virtual
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-4.1.2025.docx_11-am.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250415T110000
DTEND;TZID=America/New_York:20250415T120000
DTSTAMP:20260506T231153
CREATED:20250128T213613Z
LAST-MODIFIED:20250409T142345Z
UID:10003703-1744714800-1744718400@cmsa.fas.harvard.edu
SUMMARY:Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds
DESCRIPTION:General Relativity Seminar \nSpeaker: Aghil Alaee\, Clark University \nTitle: Positive mass theorem for ALE(AE) and ALF(AF) Toric 4-Manifolds \nAbstract: One of the fundamental conjectures in mathematical relativity is the positivity of total mass (if it is defined!) for complete non-compact Riemannian manifolds assuming appropriate lower bounds on scalar curvature. This conjecture has been proved for AE manifolds using several techniques\, starting with the celebrated results of Schoen-Yau and Witten. There are counter-examples to this conjecture in the AF\, ALF\, and ALE cases. In this talk\, we will refine this conjecture and prove it for toric 4-manifolds. The proof is robust and can be extended to higher dimensions if additional assumptions are added. This is a joint work with Marcus Khuri and Hari Kunduri.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-41525/
LOCATION:CMSA G102\, 20 Garden Street\, Cambridge\, MA\, 02138
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-4.15.2025.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20250422T110000
DTEND;TZID=America/New_York:20250422T120000
DTSTAMP:20260506T231153
CREATED:20250128T213711Z
LAST-MODIFIED:20250418T204712Z
UID:10003704-1745319600-1745323200@cmsa.fas.harvard.edu
SUMMARY:Hyperbolic equations in a double null gauge
DESCRIPTION:General Relativity Seminar \nSpeaker: Christopher Stith\, University of Michigan \nTitle: Hyperbolic equations in a double null gauge \nAbstract: The hyperbolic nature of the Einstein equations is well-known and has been used in many different contexts. More recently\, the double null gauge has proven to be a powerful tool for quantitative analysis of the Einstein equations. It has the advantage of reducing the equations for many dynamical quantities to ODEs along null curves\, and the Bianchi equations to a first-order hyperbolic system. The double null gauge has been used extensively and to great effect in analyzing the structure of spacetime for many purposes\, including (for instance) stability problems and trapped surface formation. However\, the local existence problem for the Einstein equations in a double null gauge has never been treated in full in its own right. In this talk\, we discuss how to formulate a general procedure for solving the linearized problem\, namely\, the local existence theory for systems of first-order hyperbolic equations in a double null gauge.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-42225/
LOCATION:CMSA G102\, 20 Garden Street\, Cambridge\, MA\, 02138
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-4.22.2025.png
END:VEVENT
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