Related papers: Sachs Equations and Plane Waves VI: Penrose Limits

Utilizing the covariant formulation of Penrose's plane wave limit by Blau et~al., we construct for any semi-Riemannian metric $g$ a family of "plane wave limits." These limits are taken along any geodesic of $g$, yield simpler metrics of…

We propose a formulation of the Penrose plane wave limit in terms of null Fermi coordinates. This provides a physically intuitive (Fermi coordinates are direct measures of geodesic distance in space-time) and manifestly covariant…

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic,…

We initiate the construction of integrable $\lambda$-deformed WZW models based on non-semisimple groups. We focus on the four-dimensional case whose underlying symmetries are based on the non-semisimple group $E_2^c$. The corresponding…

We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We…

We consider versions of the Penrose singularity theorem and the Hawking horizon topology theorem in weighted spacetimes that contain weighted versions of trapped surfaces, for arbitrary spacetime dimension and synthetic dimension. We find…

We show that the conformal Penrose limit is an ordinary plane wave limit in a higher dimensional framework which resolves the spacetime singularity. The higher dimensional framework is provided by Ricci-flat manifolds which are of the form…

We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic…

For the AdS/CFT duality, considerations of plane wave metric which is obtained as Penrose limit of $AdS_5 \times S^5$ proved to be quite useful and interesting. In this work, we obtain Penrose limit metrics for Lifshitz, Schrodinger,…

We study locally conformally homogeneous Lorentzian manifolds of dimension at least $3$, admitting an essential pseudo-group of local conformal transformations. Generalizing a recent result of Alekseevsky and Galaev, we show that any such…

We give a simplified approach to Kunzinger & Saemann's theory of Lorentzian length spaces in the globally hyperbolic case; these provide a nonsmooth framework for general relativity. We close a gap in the regularly localizable setting, by…

In a recent letter, Stenull and Lubensky claim that periodic approximants of Penrose tilings, which are generically isostatic, have a nonzero bulk modulus B when disordered, and, therefore, Penrose tilings are good models of jammed…

As a footnote to arXiv:1909.07756, I show that, given a (time-like) umbilic 3-surface $\Sigma$ in a 4-dimensional space-time $M$, the Penrose limit taken along any null geodesic $\Gamma$ which lies in $\Sigma$ is a diagonalisable…

The Riemannian Penrose inequality is a fundamental result in mathematical relativity. It has been a long-standing conjecture of G. Huisken that an analogous result should hold in the context of extrinsic geometry. In this paper, we resolve…

A certain conformally invariant N=1 supersymmetric SU(n) gauge theory has a description as an infra-red fixed point obtained by deforming the N=4 supersymmetric Yang-Mills theory by giving a mass to one of its N=1 chiral multiplets. We…

We establish a lower bound on the total mass of the time slices of (n + 1)-dimensional asymptotically flat standard static spacetimes under the timelike convergence condition. The inequality can be viewed equivalently as a Minkowski-type…

In an earlier paper, we showed that the causal boundary of any homogeneous plane wave satisfying the null convergence condition consists of a single null curve. In Einstein-Hilbert gravity, this would include any homogeneous plane wave…

We generalize the classical junction conditions for constructing impulsive gravitational waves by the Penrose "cut and paste" method. Specifically, we study nonexpanding impulses which propagate in spaces of constant curvature with any…

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.…

We investigate various aspects of the plane wave geometries obtained from D1/D5-brane system. We study the effect of Hopf-duality on the supersymmetries preserved by the Penrose limit of $AdS_3\times S^3\times T^4$ geometry. In type-IIB…