Related papers: On the existence of Killing vector fields
In the search for exact solutions to Einstein's field equations the main simplification tool is the introduction of spacetime symmetries. Motivated by this fact we develop a method to write the field equations for general matter in a form…
Starting with the most general four-dimensional spacetime possessing two commuting Killing vectors and a nontrivial Killing tensor, we analytically integrate Einstein-Yang-Mills equations for a completely arbitrary gauge group. It is…
General $\mathcal{N}=(1,0)$ supergravity-matter systems in six dimensions may be described using one of the two fully fledged superspace formulations for conformal supergravity: (i) $\mathsf{SU}(2)$ superspace; and (ii) conformal…
In this article, we continue the program started in our previous article of exploring an important class of thermodynamic systems from a geometric point of view. In order to model the time evolution of systems verifying the two laws of…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
Evolution of a physical quantum state vector is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. In previous literature, it was concluded that a…
The geometric intrinsic approach to Hojman symmetry is developed and use is made of the theory of the Jacobi last multipliers to find the corresponding conserved quantity for non divergence-free vector fields. The particular cases of…
In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely…
An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting…
We address two problems concerning the ADM mass-minimizing initial data sets. First, we show that the equality case of the positive mass theorem embeds into a pp-wave spacetime. Second, we show that positive Bartnik mass minimizers embed…
We construct the Killing superalgebra of supersymmetric backgrounds of ten-dimensional heterotic and type II supergravities and prove that it is a Lie superalgebra. We also show that if the fraction of supersymmetry preserved by the…
A very general class of Lagrangians which couple scalar fields to gravitation and matter in two spacetime dimensions is investigated. It is shown that a vector field exists along whose flow lines the stress-energy tensor is conserved,…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective…
We study invariant systems of PDEs defining Killing vector-valued forms, and then we specialize to Killing spinor-valued forms. We give a detailed treatment of their prolongation and integrability conditions by relating the point-wise…
In this paper, Killing vectors of spherically spacetimes have been evaluated in the context of teleparallel theory of gravitation. Further, we investigate the Killing vectors of the Friedmann metrics. It is found that for static spherically…
A vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected…
A detailed examination of the Killing equations in Robertson-Walker coordinates shows how the addition of matter and/or radiation to a de Sitter Universe breaks the symmetry generated by four of its Killing fields. The product U =…
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the constraint and Hamiltonian…
For a symmetric system, we want to study the problem of crossing an hypersurface in the neighborhood of a given point, when we suppose that all of the available vector fields are tangent to the hypersurface at the point. Classically one…