Related papers: Sachs Equations and Plane Waves VI: Penrose Limits
In various areas of modern physics and in particular in quantum gravity or foundational space-time physics it is of great importance to be in the possession of a systematic procedure by which a macroscopic or continuum limit can be…
We study properties of Sobolev-type metrics on the space of immersed plane curves. We show that the geodesic equation for Sobolev-type metrics with constant coefficients of order 2 and higher is globally well-posed for smooth initial data…
We develop the theory of lattice point counting on connected and simply connected nilpotent Lie groups of step-two, endowed with the parabolic type dilation and a family of homogeneous norms $ \mathcal{N}_{\alpha,M}(x,…
We apply the Lunin--Maldacena construction of gravity duals to beta-deformed gauge theories to a class of Type IIB backgrounds with U(1)^3 global symmetry, which include the multicenter D3-brane backgrounds dual to the Coulomb branch of N=4…
Green functions for the scalar, spinor and vector fields in a plane wave geometry arising as a Penrose limit of $AdS\times S$ are obtained. The Schwinger-DeWitt technique directly gives the results in the plane wave background, which turns…
This paper concerns the elastic structures which exhibit non-zero strain at free equilibria. Many growing tissues (leaves, flowers or marine invertebrates) attain complicated configurations during their free growth. Our study departs from…
We derive the Penrose data for half-flat pp-waves and extend his original construction for the Weyl spinor of plane waves in terms of this data.
We show that the complex saddle points of the no-boundary wave function with a positive cosmological constant and a positive scalar potential have a representation in which the geometry consists of a regular Euclidean AdS domain wall that…
We find a regular analytic 1st order deformation of the Klebanov-Strassler background. From the dual gauge theory point of view the deformation describes supersymmetry soft breaking gaugino mass terms. We calculate the difference in vacuum…
We show that the index of a lightlike geodesic in a conformally standard stationary spacetime is equal to the index of its spatial projection as a geodesic of a Finsler metric associated to the spacetime. Moreover we obtain the Morse…
Motivated by the rigidity case in the localized Riemannian Penrose inequality, we show that suitable singular metrics attaining the optimal value in the Riemannian Penrose inequality is necessarily smooth in properly specified coordinates.…
Penrose et al. investigated the physical incoherence of the spacetime with negative mass via the bending of light. Precise estimates of time-delay of null geodesics were needed and played a pivotal role in their proof. In this paper, we…
It is shown that the Lorentz transformations can be derived for a non-orthogonal Euclidean space. In this geometry one finds the same relations of special relativity as the ones known from the orthogonal Minkowski space. In order to…
We study the a.s. convergence of a sequence of random embeddings of a fixed manifold into Euclidean spaces of increasing dimensions. We show that the limit is deterministic. As a consequence, we show that many intrinsic functionals of the…
We study isometric embeddings of a Euclidean space or a Heisenberg group into a higher dimensional Heisenberg group, where both the source and target space are equipped with an arbitrary left-invariant homogeneous distance that is not…
We present an exact mapping between the staggered six-vertex model and an integrable model constructed from the twisted affine $D_2^2$ Lie algebra. Using the known relations between the staggered six-vertex model and the antiferromagnetic…
Since the late1950s, almost all discussions of Asymptotically Flat (Einstein-Maxwell) Space-Times have taken place in the context of Penrose's Null Infinity, $\mathcal{I}^{+}.$\ $\ $In addition,\ almost all calculations have used the Bondi…
Expansions of the gravitational field arising from the development of asymptotically Euclidean, time symmetric, conformally flat initial data are calculated in a neighbourhood of spatial and null infinities up to order 6. To this ends a…
In models of modified gravity, extra degrees of freedom usually appear. They must be removed from the spectrum because they may indicate the presence of instabilities and because otherwise the model might not agree with observation. In the…
A class of non-local non-linear Schrodinger equations(NLSE) is considered in an external potential with space-time modulated coefficient of the nonlinear interaction term as well as confining and/or loss-gain terms. This is a generalization…