Related papers: Generalised hyperbolicity in conical space-times
We study a class of time functions called uniform temporal functions in the general context of globally hyperbolic closed cone fields. We prove some existence results for uniform temporal functions, and prove the density of uniform temporal…
We introduce the (2+1)-spacetimes with compact space of genus g and with r gravitating particles which arise by ``Minkowskian suspensions of flat or hyperbolic cone surfaces'', by ``distinguished deformations'' of hyperbolic suspensions and…
This paper investigates wave-equations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the non-characteristic Cauchy problem to show that a solution to a wave-equation vanishing in…
We present recent developments concerning Lorentzian geometry in algebras of generalized functions. These have, in particular, raised a new interest in refined regularity theory for the wave equation on singular space-times.
We provide a bound for $m$ such that the zero locus of a very general section of an $m$-multiple of some ample line bundle on a weighted projective space with isolated singularities is algebraically hyperbolic.
We study string theory in supersymmetric time-dependent backgrounds. In the framework of general relativity, supersymmetry for spacetimes without flux implies the existence of a covariantly constant null vector, and a relatively simple form…
The Ablowitz-Ladik equation is a very important model in the nonlinear mathematical physics. In this paper, the hyperbolic function solitary wave solutions, the trigonometric function periodic wave solutions and the rational wave solutions…
In this article, existence results concerning temporal functions with additional properties on a globally hyperbolic manifold are obtained. These properties are certain bounds on geometric quantities as lapse and shift. The results are…
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on…
A new general class of solutions of ungauged four-dimensional Supegravity, in one-to-one correspondence with spherically symmetric, static black-hole solutions and Lifshitz solutions with Hyperscaling violation (\emph{hvLif}) is studied.…
We prove small-data global existence to semi-linear wave equations on hyperbolic space of dimension greater than or equal to three, for nonlinearities that have the form of a sufficiently high integer power of the solution. We also prove…
We propose that cosmological time is {\it effectively} the conjugate of the constants of nature. Different definitions of time arise, with the most relevant related to the constant controlling the dynamics in each epoch. The Hamiltonian…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
In this paper we propose a unified approach to (topological) string theory on certain singular spaces in their large volume limit. The approach exploits the non-commutative structure of D-branes, so the space is described by an algebraic…
We believe that the difference between time scale systems and ordinary differential equations is not as big as people use to think. We consider linear operators that correspond to linear dynamic systems on time scales. We study solvability…
We study the porous medium equation on manifolds with conical singularities. Given strictly positive initial values, we show that the solution exists in the maximal $L^{q}$-regularity space for all times and is instantaneously smooth in…
In these notes we address the canonical quantization of the cosmological models which appear as solutions of the low energy effective action of closed bosonic string theory (dilaton models). The analysis is restricted to the quantization of…
We consider maximal globally hyperbolic flat (2+1) spacetimes with compact space S of genus g>1. For any spacetime M of this type, the length of time that the events have been in existence is M defines a global time, called the cosmological…
We consider the generalised space-time introduced by the author in 2003 in the context of the non-linear realisation of the semi-direct product of E11 and its first fundamental representation. For all the fields we propose gauge…
The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing…