Estimates the mass of a spacetime in terms of the total area of its black holes
In mathematical general relativity, the Penrose inequality, first conjectured by Sir Roger Penrose, estimates the mass of a spacetime in terms of the total area of its black holes and is a generalization of the positive mass theorem. The Riemannian Penrose inequality is an important special case. Specifically, if (M, g) is an asymptotically flat Riemannian 3-manifold with nonnegative scalar curvature and ADM mass m, and A is the area of the outermost minimal surface (possibly with multiple connected components), then the Riemannian Penrose inequality asserts
This is purely a geometrical fact, and it corresponds to the case of a complete three-dimensional, space-like, totally geodesic submanifold
of a (3 + 1)-dimensional spacetime. Such a submanifold is often called a time-symmetric initial data set for a spacetime. The condition of (M, g) having nonnegative scalar curvature is equivalent to the spacetime obeying the dominant energy condition.
This inequality was first proved by Gerhard Huisken and Tom Ilmanen in 1997 in the case where A is the area of the largest component of the outermost minimal surface. Their proof relied on the machinery of weakly defined inverse mean curvature flow, which they developed. In 1999, Hubert Bray gave the first complete proof of the above inequality using a conformal flow of metrics. Both of the papers were published in 2001.
and 28 Related for: Riemannian Penrose inequality information
mass theorem. The RiemannianPenroseinequality is an important special case. Specifically, if (M, g) is an asymptotically flat Riemannian 3-manifold with...
graph Riemannian group Riemannian holonomy Riemannian manifold also called Riemannian space Riemannian metric tensor RiemannianPenroseinequality Riemannian...
Ilmanen, he proved a version of the RiemannianPenroseinequality, which is a special case of the more general Penrose conjecture in general relativity....
and differential geometer. He is known for having proved the RiemannianPenroseinequality. He works as professor of mathematics and physics at Duke University...
Sir Roger Penrose, OM, FRS, HonFInstP (born 8 August 1931) is a British mathematician, mathematical physicist, philosopher of science and Nobel Laureate...
the RiemannianPenroseinequality. J. Differential Geom. 59 (2001), no. 3, 353–437. A more general version of the RiemannianPenroseinequality was found...
submanifolds of a Riemannian or pseudo-Riemannian manifold. It has been used to prove a certain case of the RiemannianPenroseinequality, which is of interest...
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an...
analysis of Willmore flow and in Hubert Bray's proof of the RiemannianPenroseinequality. Simon himself was able to apply his analysis to establish the...
positive mass theorem was used in Hubert Bray's proof of the RiemannianPenroseinequality. In local coordinates, this says gijkij = 0 In local coordinates...
shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. The term also has meaning in any differentiable manifold with...
also sometimes referred to as the Penrose–Terrell effect, the Terrell–Penrose effect or the Lampa–Terrell–Penrose effect, but not the Lampa effect. By...
theory Hubert Bray, mathematician, known for having proved the RiemannianPenroseinequality David Brooks, columnist for The New York Times Thomas Brothers...
Imbedding Problem for Riemannian Manifolds". Annals of Mathematics. 63 (1): 20–63. doi:10.2307/1969989. JSTOR 1969989. MR 0075639. Penrose, Roger (2005). "18...
is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure...
of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:...
Mathematics at Stony Brook University. Much of his research concerns the Riemannian geometry of 4-manifolds, or related topics in complex and differential...
and Euclidean wormholes (named after Euclidean manifold, a structure of Riemannian manifold). The Casimir effect shows that quantum field theory allows the...
late 1960s Roger Penrose and Stephen Hawking used global techniques to prove that singularities appear generically. For this work, Penrose received half...
bits of matter. The equation is important as a fundamental lemma for the Penrose–Hawking singularity theorems and for the study of exact solutions in general...
Number 1, 39–104, 2013 "Near-equality in the PenroseInequality for Rotationally Symmetric Riemannian Manifolds" by Dan Lee and Christina Sormani Annales...
blueshifts for P+ region particles. Pfenning, Michael John (1998). "Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes". p. 1692...
Global Information