A5077003224- Geometric Analysis and Curvature Flows
- Cosmology and Gravitation Theories
- Black Holes and Theoretical Physics
- Advanced Differential Geometry Research
- Geometry and complex manifolds
- Relativity and Gravitational Theory
- Nonlinear Partial Differential Equations
- Advanced Operator Algebra Research
- Geometric and Algebraic Topology
- Mathematical Dynamics and Fractals
- Noncommutative and Quantum Gravity Theories
- Galaxies: Formation, Evolution, Phenomena
- Astrophysical Phenomena and Observations
- Geophysics and Gravity Measurements
- Theoretical and Computational Physics
- Advanced Mathematical Modeling in Engineering
- Numerical methods in inverse problems
- Markov Chains and Monte Carlo Methods
- International Science and Diplomacy
- Stochastic processes and statistical mechanics
- Space Science and Extraterrestrial Life
- advanced mathematical theories
- Algebraic and Geometric Analysis
- Advanced Mathematical Physics Problems
- History and Developments in Astronomy
Harvard University
2022-2024
Woodwell Climate Research Center
2020-2024
Harvard University Press
2021
University of Oxford
2018-2019
We prove a Riemannian positive mass theorem for manifolds with single asymptotically flat end, but otherwise arbitrary other ends, which can be incomplete and contain negative scalar curvature. The incompleteness negativity is compensated by large curvature on an annulus, in quantitative fashion. In the complete noncompact case nonnegative curvature, we have no extra assumption hence long-standing conjecture of Schoen Yau.
Abstract We prove a positive mass theorem for spin initial data sets $(M,g,k)$ that contain an asymptotically flat end and shield of dominant energy (a subset $M$ on which the scalar $\mu -|J|$ has lower bound). In similar vein, we show $\mathcal{E}$ violates (i.e., $\textrm{E} < |\textrm{P}|$), there exists constant $R>0$, depending only $\mathcal{E}$, such any set containing must violate hypotheses Witten’s proof in $R$-neighborhood $\mathcal{E}$. This implies with arbitrary...
This white paper outlines the plans of History Philosophy Culture Working Group Next Generation Event Horizon Telescope Collaboration.
For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between theWang/Liu–Yau quasi-local mass the boundary and Hawking strictly minimizing hulls in Jang graphs domain. Using this, Penrose inequality that involves these masses area outermost marginally outer trapped surface (MOTS) domain or minimal within graphs. Moreover, obtain sufficient conditions for (non)existence MOTS domain, spirit folklore hoop conjecture.
For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass boundary and Hawking strictly minimizing hulls in Jang graphs domain. Using this, Penrose inequality that involves these masses area outermost marginally outer trapped surface (MOTS) domain or minimal within graphs. Moreover, obtain sufficient conditions for (non)existence MOTS domain, spirit folklore hoop conjecture.
We offer a mathematically rigorous basis for the widely held suspicion that full black hole evaporation is in tension with predictability.Based on conditions expressing global causal structure of evaporating spacetimes, we prove two theorems Lorentzian geometry showing such spacetimes either fail to be causally simple or continuous.These theorems, when combined recent results [1] timelike boundary, bear significantly question whether these permit predictable evolution.
We prove a Riemannian positive mass theorem for manifolds with single asymptotically flat end, but otherwise arbitrary other ends, which can be incomplete and contain negative scalar curvature. The incompleteness negativity is compensated by large curvature on an annulus, in quantitative fashion. In the complete noncompact case nonnegative curvature, we have no extra assumption hence long-standing conjecture of Schoen Yau.
Using minimal hypersurfaces, we obtain topological obstructions to admitting complete metrics with positive scalar curvature on a given class of non-compact n-manifolds n less than 8. We show that the Liouville theorem for locally conformally flat n-manifold non-negative follows from impossibility there being metric its connect sum n-torus. With recent work Chodosh-Li, is now proved in all remaining cases. Finally, using MOTS instead an Initial Data Set version these results Dominant Energy...
Chruściel, Isenberg, and Pollack constructed a class of vacuum cosmological spacetimes that do not admit Cauchy surfaces with constant mean curvature. We prove that, for sufficiently large values the gluing parameter, these examples are both future past null geodesically incomplete. The authors honored to dedicate this paper Robert Bartnik on occasion his 60th birthday.
Hawking's area theorem is a fundamental result in black hole theory that universally associated with the null energy condition. That this condition can be weakened illustrated by formulation of strengthened version based on an allows for violations With semi-classical context mind, some brief remarks pertaining to suitability and its are made.
Let $X$ be a closed $3$-manifold, $\mathcal{M}_{R>0}$ the space of metrics on with positive scalar curvature, and $\text{Diff}(X)$ group diffeomorphisms $X$. Marques proves fundamental result that $\mathcal{M}_{R>0}/ \text{Diff}(X)$ is path connected. Using this theorem Cerf in differential topology, shows asymptotically flat nonnegative curvature $\mathbb{R}^3$ Based Carlotto-Li's generalization Marques' to case compact manifold boundary, we show mean convex boundary...
The interior of the Kerr solution is singular and achronological. classic singularity theorem by Hawking Penrose relies on chronology, thus does not apply to solution. An improvement their Kriele partially removes requirement chronology. However, both these theorems fail give any information type or location incomplete geodesics. Here, using recent results Minguzzi, we prove a new theorem, specifically designed black holes, which enables locating null geodesics within hole interior, all...
Abstract We prove that if in a C 0 spacetime complete partial Cauchy hypersurface has non-empty horizon, then the horizon is caused by presence of almost closed causal curves behind it or influence points at infinity. This statement related to strong cosmic censorship and conjecture Wald. In this light, Wald’s can be formulated as PDE problem about location horizons inside black hole interiors.
We generalize Y. Shi and L.-F.\ Tam's \cite{ShiTam} nonnegativity result for the Brown-York mass, by considering nonnegative scalar curvature (NNSC) fill-ins that need only be complete rather than compact. Moreover, NNSC not even as long incompleteness is ``shielded'' a region with positive occurs sufficiently far away. accomplish this generalizing P.~Miao's~\cite{Miao02} mass theorem corners to asymptotically flat manifolds may have other ends, or possibly incomplete ends are appropriately...
Based on scale critical initial data, we construct smooth asymptotically flat Cauchy data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surfaces (MOTS) but whose future evolution contains a trapped region, which itself is bounded by an apparent horizon (a hypersurface foliated MOTS). Although long time behaviour of these solutions unknown, statement Kerr Stability would yield dynamical, critical, non-spherically symmetric class examples conjectures Weak Cosmic...
Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions well global ones like the existence a compact (achronal) slice. Here, we prove new theorem for chronological spacetimes satisfy what call ‘past null focusing’ condition. Such condition forces all geodesics $$\gamma :[0,a)\rightarrow M$$ with future endpoint (0)$$ to develop pair conjugate points if past complete. By Einstein field equations, will be satisfied density matter fields remains...