Related papers: The Poisson brackets of free null initial data for…
An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric…
A set of consistent Poisson brackets for an open string in generic spacetime background and NS-NS $B$-field is constructed. Upon quantization, this set of Poisson brackets lead to spacial \emph{commutative} $D$-branes at the string ends,…
A general framework for a systematic quasi-localization of canonical general relativity and a new ingredient, the requirement of the gauge invariance of the boundary terms appearing in the calculation of Poisson brackets, are given. As a…
Based on scale critical initial data, we construct smooth asymptotically flat Cauchy initial data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surfaces (MOTS) but whose future evolution contains a trapped…
The goal of this paper is to present the physics behind Brill initial data sets as an excellent tool for numerical experiments of axisymmetric spacetimes, data sets which are practical applications of HPC for numerical solutions of…
The coupling of gravity to dust helps to discover simple quadratic combinations of the gravitational super-Hamiltonian and supermomentum whose Poisson brackets strongly vanish. This leads to a new form of vacuum constraints which generate a…
We consider the Cauchy problem for the barotropic Euler system coupled to Helmholtz or Poisson equations, in the whole space. We assume that the initial density is small enough, and that the initial velocity is close to some reference…
We study a generalization of free Poisson random measure by replacing the intensity measure with a n.s.f. weight $\varphi$ on a von Neumann algebra $M$. We give an explicit construction of the free Poisson random weight using full Fock…
The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown…
Four-dimensional spacetimes foliated by a two-parameter family of homologous two-surfaces are considered in Einstein's theory of gravity. By combining a 1+(1+2) decomposition, the canonical form of the spacetime metric and a suitable…
In a recent article, we propose a general geometric notion of initial data on big bang singularities. This notion is of interest in its own right. However, it also serves the purpose of giving a unified perspective on many of the results in…
Wolpert's cosine formula on Teichm\"uller space gives the Weil-Petersson Poisson bracket $\{l_\alpha, l_\beta\}$ for geodesic length functions $l_\alpha,l_\beta$ of closed curves $\alpha,\beta$ as the sum of the cosines of the angle of…
For a Dirac theory of quantum gravity obtained from the refined algebraic quantization procedure, we propose a quantum notion of Cauchy surfaces. In such a theory, there is a kernel projector for the quantized scalar and momentum…
We demonstrated that classical mechanics have, besides the well known quantum deformation, another deformation -- so called hyperbolic quantum mechanics. The classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the…
The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…
We construct a Leibniz bracket on the space $\Omega^\bullet (J^k (\pi))$ of all differential forms over the finite-dimensional jet bundle $J^k (\pi)$. As an example, we write Maxwell equations with sources in the covariant…
It is shown that the new Poisson brackets proposed in Part I of this work (J. Math. Phys. 34, 5747(hep-th/9305133)) arise naturally in an extension of the formal variational calculus incorporating divergences. The linear spaces of local…
We show that the second accelerating expansion of the universe appears smoothly from the decelerating universe remarkably after the initial inflation in the two-dimensional soluble semi-classical dilaton gravity along with the modified…
Motivated by the work of previous authors on vortex sheets and their applications, the intrinsic inviscid evolution equations of a closed vortex sheet in a plane, separating two piecewise constant density fluids, and their Hamiltonian form…
Recently it has been suggested by S. Carlip that black hole entropy can be derived from a central charge of the Virasoro algebra arising as a subalgebra in the surface deformations of General Relativity in any dimension. Here it is shown…