Search results for "Mathematical physics"
showing 10 items of 2687 documents
Null conformal Killing-Yano tensors and Birkhoff theorem
2015
We study the space-times admitting a null conformal Killing-Yano tensor whose divergence defines a Killing vector. We analyze the similitudes and differences with the recently studied non null case (Gen. Relativ. Grav. (2015) {\bf 47} 1911). The results by Barnes concerning the Birkhoff theorem for the case of null orbits are analyzed and generalized.
On Weyl-electric and Weyl-magnetic spacetimes
2002
The concepts of purely electric and purely magnetic Weyl tensors are extended and the intrinsic characterization of the new wider classes is given. The solutions v to the equations W(v; v) = 0 or *W(v; v) = 0 are determined for every Petrov type, and the new electric or magnetic type I cases are studied in more detail.
PainlevéGullstrand synchronizations in spherical symmetry
2010
A Painlev\'e-Gullstrand synchronization is a slicing of the space-time by a family of flat spacelike 3-surfaces. For spherically symmetric space-times, we show that a Painlev\'e-Gullstrand synchronization only exists in the region where $(dr)^2 \leq 1$, $r$ being the curvature radius of the isometry group orbits ($2$-spheres). This condition says that the Misner-Sharp gravitational energy of these 2-spheres is not negative and has an intrinsic meaning in terms of the norm of the mean extrinsic curvature vector. It also provides an algebraic inequality involving the Weyl curvature scalar and the Ricci eigenvalues. We prove that the energy and momentum densities associated with the Weinberg c…
A note on the Pais-Uhlenbeck model and its coherent states
2011
In some recent papers many quantum aspects of the Pais-Uhlenbeck model were discussed. In particular, several inequivalent hamiltonians have been proposed, with different features, giving rise, at a quantum level, to the fourth-order differential equation of the model. Here we propose two new possible hamiltonians which also produce the same differential equation. In particular our first hamiltonian is self-adjoint and positive. Our second proposal is written in terms of pseudo-bosonic operators. We discuss in details the ground states of these hamiltonians and the (bi-)coherent states of the models.
On the convexity of Relativistic Hydrodynamics
2013
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\it Rev. Mod. Phys.} {\bf 61} 75). The classical limit is recovered.
Rainich theory for type D aligned Einstein–Maxwell solutions
2007
The original Rainich theory for the non-null Einstein-Maxwell solutions consists of a set of algebraic conditions and the Rainich (differential) equation. We show here that the subclass of type D aligned solutions can be characterized just by algebraic restrictions.
Large Time Behavior for Inhomogeneous Damped Wave Equations with Nonlinear Memory
2020
We investigate the large time behavior for the inhomogeneous damped wave equation with nonlinear memory ϕtt(t,&omega
𝒟 $\mathcal {D}$ -Deformed Harmonic Oscillators
2015
We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms of $\cal{D}$-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint hamiltonians whose eigenvalues and eigenvectors can be found adopting the quite general framework of the so-called $\cal{D}$-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.
A Rainich-like approach to the Killing-Yano tensors
2002
The Rainich problem for the Killing-Yano tensors posed by Collinson \cite{col} is solved. In intermediate steps, we first obtain the necessary and sufficient conditions for a 2+2 almost-product structure to determine the principal 2--planes of a skew-symmetric Killing-Yano tensor and then we give the additional conditions on a symmetric Killing tensor for it to be the square of a Killing-Yano tensor.We also analyze a similar problem for the conformal Killing-Yano and the conformal Killing tensors. Our results show that, in both cases, the principal 2--planes define a maxwellian structure. The associated Maxwell fields are obtained and we outline how this approach is of interest in studying …
Non-Perturbative Renormalization of Lattice Four-Fermion Operators without Power Subtractions
1999
A general non-perturbative analysis of the renormalization properties of $\Delta I=3/2$ four-fermion operators in the framework of lattice regularization with Wilson fermions is presented. We discuss the non-perturbative determination of the operator renormalization constants in the lattice Regularization Independent (RI or MOM) scheme. We also discuss the determination of the finite lattice subtraction coefficients from Ward Identities. We prove that, at large external virtualities, the determination of the lattice mixing coefficients, obtained using the RI renormalization scheme, is equivalent to that based on Ward Identities, in the continuum and chiral limits. As a feasibility study of …