Eric Woolgar
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View article: Extreme 5-dimensional black holes with SU(2)-symmetric horizons
Extreme 5-dimensional black holes with SU(2)-symmetric horizons Open
A bstract We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit SU(2) symmetry must be that of a Berger sphere.
View article: Extreme 5-dimensional black holes with SU(2)-symmetric horizons
Extreme 5-dimensional black holes with SU(2)-symmetric horizons Open
We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit $\SU(2)$ symmetry must be that of a Berger sphere.
View article: Deformations of the Kerr-(A)dS near horizon geometry
Deformations of the Kerr-(A)dS near horizon geometry Open
We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński (2013 Gen. Rel. Grav. 45 9…
View article: Deformations of the Kerr-(A)dS Near Horizon Geometry
Deformations of the Kerr-(A)dS Near Horizon Geometry Open
We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kamiński [Gen Rel Grav 45 (2013) 98…
View article: Rigidity of quasi-Einstein metrics: The incompressible case
Rigidity of quasi-Einstein metrics: The incompressible case Open
As part of a programme to classify quasi-Einstein metrics $(M,g,X)$ on closed manifolds and near-horizon geometries of extreme black holes, we study such spaces when the vector field $X$ is divergence-free but not identically zero. This co…
View article: Static near horizon geometries and rigidity of quasi-Einstein manifolds
Static near horizon geometries and rigidity of quasi-Einstein manifolds Open
Static vacuum near horizon geometries are solutions $(M,g,X)$ of a certain quasi-Einstein equation on a closed manifold $M$, where $g$ is a Riemannian metric and $X$ is a closed 1-form. It is known that when the cosmological constant vanis…
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: Bakry-Émery Ricci Curvature Bounds on Manifolds with Boundary
Bakry-Émery Ricci Curvature Bounds on Manifolds with Boundary Open
We prove a Bakry-Émery generalization of a theorem of Petersen and Wilhelm, itself a generalization of a theorem of Frankel, that closed minimal hypersurfaces in a complete manifold with a suitable curvature bound must intersect. We then p…
View article: Self-similar curve shortening flow in hyperbolic 2-space
Self-similar curve shortening flow in hyperbolic 2-space Open
We find and classify self-similar solutions of the curve shortening flow in standard hyperbolic 2-space. Together with earlier work of Halldórsson on curve shortening flow in the plane and Santos dos Reis and Tenenblat in the 2-sphere, thi…
View article: Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary
Inscribed Radius Bounds for Lower Ricci Bounded Metric Measure Spaces with Mean Convex Boundary Open
Consider an essentially nonbranching metric measure space with the measure contraction property of Ohta and Sturm, or with a Ricci curvature lower bound in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the inscribed…
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: Diameter bounds for metric measure spaces with almost positive Ricci curvature and mean convex boundary
Diameter bounds for metric measure spaces with almost positive Ricci curvature and mean convex boundary Open
Consider a metric measure space with non-negative Ricci curvature in the sense of Lott, Sturm and Villani. We prove a sharp upper bound on the diameter of any subset whose boundary has a positive lower bound on its generalized mean curvatu…
View article: Ricci Flow and Volume Renormalizability
Ricci Flow and Volume Renormalizability Open
With respect to any special boundary defining function, a conformally compact asymptotically hyperbolic metric has an asymptotic expansion near its conformal infinity. If this expansion is even to a certain order and satisfies one extra co…
View article: Asymptotically hyperbolic normalized Ricci flow and rotational symmetry
Asymptotically hyperbolic normalized Ricci flow and rotational symmetry Open
We consider the normalized Ricci flow evolving from an initial metric which is conformally compactifiable and asymptotically hyperbolic. We show that there is a unique evolving metric which remains in this class, and that the flow exists u…
View article: Nonexistence of degenerate horizons in static vacua and black hole uniqueness
Nonexistence of degenerate horizons in static vacua and black hole uniqueness Open
We show that in any spacetime dimension $D\\ge 4$, degenerate components of\nthe event horizon do not exist in static vacuum configurations with positive\ncosmological constant. We also show that without a cosmological constant\nasymptotic…
View article: Nonexistence of extremal de Sitter black rings
Nonexistence of extremal de Sitter black rings Open
We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathem…
View article: Nonexistence of de Sitter Black Rings
Nonexistence of de Sitter Black Rings Open
We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathem…
View article: Cosmological singularity theorems and splitting theorems for <i>N</i>-Bakry-Émery spacetimes
Cosmological singularity theorems and splitting theorems for <i>N</i>-Bakry-Émery spacetimes Open
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein …