Related papers: Particle Number and 3D Schroedinger Holography

A numerical algorithm to solve the spectral problem for arbitrary self-adjoint extensions of 1D regular Schroedinger operators is presented. It is shown that the set of all self-adjoint extensions of 1D regular Schroedinger operators is in…

We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We…

Generalizing Riemannian theorems of Anderson-Herzlich and Biquard, we show that two $(n+1)$-dimensional stationary vacuum space-times (possibly with cosmological constant $\Lambda \in \R$) that coincide up to order one along a timelike…

We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schr\"{o}dinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of…

An asymptotically planar AdS spacetimes is characterized by its ADM mass and tensions. We define an additional ADM charge Q associated with the scaling Killing vector of AdS, show that Q is given by a certain sum over the ADM mass and…

We characterize a general solution to the vacuum Einstein equations which admits isolated horizons. We show it is a non-linear superposition -- in precise sense -- of the Schwarzschild metric with a certain free data set propagating…

For the Schr\"odinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global solutions are asymptotically given by the sum of a free wave and…

This thesis is dedicated to the study of quasi-local boundary in quantum gravity in the 3D space-time case. This research takes root in the holographic principle, which conjectures that the geometry and the dynamic of a space-time region…

In this paper we construct asymptotically locally AdS and flat black holes in the presence of a scalar field whose kinetic term is constructed out from a linear combination of the metric and the Einstein tensor. The field equations as well…

We show that for non-relativistic free particles, the (bosonic) many particle equations can be rewritten in geometric fashion in terms of a classical theory of conformally stretched spacetime. We further generalize the results for the…

We construct time-periodic solutions for a system of self-gravitating massless scalar field, with negative cosmological constant, in d+1 spacetime dimensions at spherical symmetry, both perturbatively and numerically. We estimate the…

We consider the Schroedinger equation with a general interaction term, which is localized in space. The interaction may be x, t dependent and non-linear. Purely non-linear parts of the interaction are localized via the radial Sobolev…

Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…

Finsler geometry is just riemannian geometry without the quadratic restriction[1]. In this paper, we study the motion of massive(non-zero rest mass) and massless particles for schwarzschild metric in finsler spacetime in the case of two…

The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…

We study the asymptotic behaviour of solutions to the linear wave equation on cosmological spacetimes with Big Bang singularities and show that appropriately rescaled waves converge against a blow-up profile. Our class of spacetimes…

We consider the massive wave equation on asymptotically AdS spaces. We show that the timelike scri behaves like a finite timelike boundary, on which one may impose the equivalent of Dirichlet, Neumann or Robin conditions for a range of…

Motivated by the gauge/gravity duality, we introduce a numerical scheme based on generalized harmonic evolution to solve the Einstein field equations on asymptotically anti-de Sitter (AdS) spacetimes. We work in global AdS5, which can be…

We study the global geometry of a general class of spacetimes of relevance to the supersymmetric $AdS_3/CFT_2$ correspondence in eleven-dimensional supergravity. Specifically, we study spacetimes admitting a globally-defined…

This talk reports on recent progress toward the semiglobal study of asymptotically flat spacetimes within numerical relativity. The development of a 3D solver for asymptotically Minkowski-like hyperboloidal initial data has rendered…