Marcus Khuri
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View article: Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes
Proof of the Spacetime Penrose Inequality With Suboptimal Constant in the Asymptotically Flat and Asymptotically Hyperboloidal Regimes Open
We establish mass lower bounds of Penrose-type in the setting of $3$-dimensional initial data sets for the Einstein equations satisfying the dominant energy condition, which are either asymptotically flat or asymptotically hyperboloidal. M…
View article: Boundary behavior of compact manifolds with scalar curvature lower bounds and static quasi-local mass of tori
Boundary behavior of compact manifolds with scalar curvature lower bounds and static quasi-local mass of tori Open
A classic result of Shi and Tam states that a 2-sphere of positive Gauss and mean curvature bounding a compact 3-manifold with nonnegative scalar curvature must have total mean curvature not greater than that of the isometric embedding int…
View article: The Mass-Angular Momentum Inequality for Multiple Black Holes
The Mass-Angular Momentum Inequality for Multiple Black Holes Open
This is the second in a series of two papers to establish the conjectured mass-angular momentum inequality for multiple black holes, modulo the extreme black hole 'no hair theorem'. More precisely it is shown that either there is a counter…
View article: The Spacetime Penrose Inequality for Cohomogeneity One Initial Data
The Spacetime Penrose Inequality for Cohomogeneity One Initial Data Open
We prove the spacetime Penrose inequality for asymptotically flat $2(n+1)$-dimensional initial data sets for the Einstein equations, which are invariant under a cohomogeneity one action of $\mathrm{SU}(n+1)$. Analogous results are obtained…
View article: Boundary Behavior of Compact Manifolds With Scalar Curvature Lower Bounds and Static Quasi-Local Mass of Tori
Boundary Behavior of Compact Manifolds With Scalar Curvature Lower Bounds and Static Quasi-Local Mass of Tori Open
A classic result of Shi and Tam states that a 2-sphere of positive Gauss and mean curvature bounding a compact 3-manifold with nonnegative scalar curvature, must have total mean curvature not greater than that of the isometric embedding in…
View article: A Quasi-Local Mass
A Quasi-Local Mass Open
We define a new gauge independent quasi-local mass and energy, and show its relation to the Brown-York Hamilton-Jacobi analysis. A quasi-local proof of the positivity, based on spacetime harmonic functions, is given for admissible closed s…
View article: Spectral Torical Band Inequalities and Generalizations of the Schoen–Yau Black Hole Existence Theorem
Spectral Torical Band Inequalities and Generalizations of the Schoen–Yau Black Hole Existence Theorem Open
Generalized torical band inequalities give precise upper bounds for the width of compact manifolds with boundary in terms of positive pointwise lower bounds for scalar curvature, assuming certain topological conditions. We extend several i…
View article: Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem
Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem Open
Generalized torical band inequalities give precise upper bounds for the width of compact manifolds with boundary in terms of positive pointwise lower bounds for scalar curvature, assuming certain topological conditions. We extend several i…
View article: Asymptotically hyperbolic Einstein constraint equations with apparent horizon boundary and the Penrose inequality for perturbations of Schwarzschild-AdS <sup>*</sup>
Asymptotically hyperbolic Einstein constraint equations with apparent horizon boundary and the Penrose inequality for perturbations of Schwarzschild-AdS <sup>*</sup> Open
We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an applic…
View article: Asymptotic Analysis of Harmonic Maps With Prescribed Singularities
Asymptotic Analysis of Harmonic Maps With Prescribed Singularities Open
This is the first in a series of two papers to establish the mass-angular momentum inequality for multiple black holes. We study singular harmonic maps from domains of 3-dimensional Euclidean space to the hyperbolic plane having bounded hy…
View article: Black Lenses in Kaluza-Klein Matter
Black Lenses in Kaluza-Klein Matter Open
We present the first examples of formally asymptotically flat black hole solutions with horizons of general lens space topology $L(p,q)$. These 5-dimensional static/stationary spacetimes are regular on and outside the event horizon for any…
View article: Rigid comparison geometry for Riemannian bands and open incomplete manifolds
Rigid comparison geometry for Riemannian bands and open incomplete manifolds Open
Comparison theorems are foundational to our understanding of the geometric features implied by various curvature constraints. This paper considers manifolds with a positive lower bound on either scalar, 2-Ricci, or Ricci curvature, and con…
View article: Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS
Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS Open
We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an applic…
View article: The topology of general cosmological models*
The topology of general cosmological models* Open
Is the Universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the Universe is assumed to…
View article: Gravitational Solitons and Complete Ricci Flat Riemannian Manifolds of Infinite Topological Type
Gravitational Solitons and Complete Ricci Flat Riemannian Manifolds of Infinite Topological Type Open
We present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These latter solutions are referred to as gravitational solitons. F…
View article: The Geometry and Topology of Stationary Multi-Axisymmetric Vacuum Black Holes in Higher Dimensions
The Geometry and Topology of Stationary Multi-Axisymmetric Vacuum Black Holes in Higher Dimensions Open
Extending recent work in 5 dimensions, we prove the existence and uniqueness of solutions to the reduced Einstein equations for vacuum black holes in $(n+3)$-dimensional spacetimes admitting the isometry group $\mathbb{R}\times U(1)^{n}$, …
View article: The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results
The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results Open
We establish the positive energy theorem and a Penrose-type inequality for 3-dimensional asymptotically hyperboloidal initial data sets with toroidal infinity, weakly trapped boundary, and satisfying the dominant energy condition. In the u…
View article: Stability of the positive mass theorem under Ricci curvature lower bounds
Stability of the positive mass theorem under Ricci curvature lower bounds Open
We establish Gromov-Hausdorff stability of the Riemannian positive mass theorem under the assumption of a Ricci curvature lower bound. More precisely, consider a class of orientable complete uniformly asymptotically flat Riemannian 3-manif…
View article: Cosmic cloaking of rich extra dimensions
Cosmic cloaking of rich extra dimensions Open
We present arguments that show why it is difficult to see rich extra dimensions in the universe. Conditions are found where significant size and variation of the extra dimensions in a Kaluza–Klein compactification lead to a black hole in t…
View article: Balancing static vacuum black holes with signed masses in four and five dimensions
Balancing static vacuum black holes with signed masses in four and five dimensions Open
We construct a new set of asymptotically flat, static vacuum solutions to the Einstein equations in dimensions 4 and 5, which may be interpreted as a superposition of positive and negative mass black holes. The resulting spacetimes are axi…
View article: Rich Extra Dimensions Are Hidden Inside Black Holes
Rich Extra Dimensions Are Hidden Inside Black Holes Open
We present arguments that show why it is difficult to see \emph{rich} extra dimensions in the Universe. More precisely, we study the conditions under which significant size and variation of the extra dimensions in a Kaluza-Klein compactifi…
View article: Spacetime Harmonic Functions and Applications to Mass
Spacetime Harmonic Functions and Applications to Mass Open
In the pioneering work of Stern, level sets of harmonic functions have been shown to be an effective tool in the study of scalar curvature in dimension 3. Generalizations of this idea, utilizing level sets of so called spacetime harmonic f…
View article: The Topology of General Cosmological Models
The Topology of General Cosmological Models Open
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
View article: Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations
Spacetime Harmonic Functions and the Mass of 3-Dimensional Asymptotically Flat Initial Data for the Einstein Equations Open
We give a lower bound for the Lorentz length of the ADM energy-momentum vector (ADM mass) of 3-dimensional asymptotically flat initial data sets for the Einstein equations. The bound is given in terms of linear growth `spacetime harmonic f…
View article: Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds
Harmonic Functions and The Mass of 3-Dimensional Asymptotically Flat Riemannian Manifolds Open
An explicit lower bound for the mass of an asymptotically flat Riemannian 3-manifold is given in terms of linear growth harmonic functions and scalar curvature. As a consequence, a new proof of the positive mass theorem is achieved in dime…