Related papers: Generalized harmonic spatial coordinates and hyper…
We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
To compare two space-times on large domains, and in particular the global structure of their manifolds, requires using identical frames of reference and associated coordinate conditions. In this paper we use and compare two classes of…
In this work, the quantization of the most general Bianchi Type I geometry, with and without a cosmological constant, is considered. In the spirit of identifying and subsequently removing as many gauge degrees of freedom as possible, a…
We analize the relational quantum evolution of generally covariant systems in terms of Rovelli's evolving constants of motion and the generalized Heisenberg picture. In order to have a well defined evolution, and a consistent quantum…
We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…
We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators…
Formulating a perfect fluid filled spherically symmetric metric utilizing the 3+1 formalism for general relativity, we show that the metric coefficients are completely determined by the mass-energy distribution, and its time rate of change…
The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal boundary constructions by R. Penrose. Our study covers: (1) adaptive…
We investigate the general relativistic phase of an electromagnetic wave as it propagates in the gravitational field of the Earth, which is modeled as an isolated, weakly aspherical gravitating body. We introduce coordinate systems to…
With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools…
Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data.…
In Horava's theory of gravity, Lorentz symmetry is broken in exchange for renormalizability, but the original theory has been argued to be plagued with problems associated with a new scalar mode stemming from the very breaking of Lorentz…
The spherically symmetric Einstein-Vlasov system in Schwarzschild coordinates (i.e. polar slicing and areal radial coordinate) is considered. An improved continuation criterion for global existence of classical solutions is given. Two other…
General relativity is a covariant theory of two transverse, traceless graviton degrees of freedom. According to a theorem of Hojman, Kuchar, and Teitelboim, modifications of general relativity must either introduce new degrees of freedom or…
We investigate consequences of allowing the Hilbert space of a quantum system to have a time-dependent metric. For a given possibly nonstationary quantum system, we show that the requirement of having a unitary Schreodinger time-evolution…
An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is…
We consider Fock's fundamental theory of the hydrogen atom in momentum space which allows a realization of the previously predicted rotation group of a three-dimensional (3D) sphere in four-dimensional (4D) space. We then modify Fock's…
In this article we study generalizations of the inhomogeneous Burgers equation. First at the operator level, in the sense that we replace classical differential derivations by operators with certain properties, and then we increase the…