Related papers: A note on proper conformal vector fields in cylind…
The existence of symmetries in asymptotically flat space-times are studied from the point of view of initial value problems. General necessary and sufficient (implicit) conditions are given for the existence of Killing vector fields in the…
We study the conformal classes of 2-dimensional Lorentzian tori with (non zero) Killing fields. We define a map that associate to such a class a vector field on the circle (up to a scalar factor). This map is not injective but has finite…
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the…
By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a…
We study the compatibility between the conformal symmetry together with the unitarity and the continuous higher-form symmetries. We show that the d-dimensional unitary conformal field theories are not consistent with continuous p-form…
Fayos and Sopuerta have recently set up a formalism for studying vacuum spacetimes with an isometry, a formalism that is centred around the bivector corresponding to the Killing vector and that adapts the tetrad to the bivector. Steele has…
The usual ambient space approach to conformal fields is based on identifying the d-dimensional conformal space as the Dirac projective hypercone in a flat d+2-dimensional ambient space. In this work, we explicitly concentrate on singletons…
In this paper, we use less topological restrictions and more geometric and analytic conditions to obtain some sufficient conditions on Yamabe solitons such that their metrics are Yamabe metrics, that is, metrics of constant scalar…
Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. They describe continuous phase transitions in fluids, magnets, and numerous other materials, while at the same…
Using the quasi-Maxwell formalism, we derive the necessary and sufficient conditions for the matching of two stationary spacetimes along a stationary timelike hypersurface, expressed in terms of the gravitational and gravitomagnetic fields…
We establish normal forms for conformal vector fields on pseudo-Riemannian manifolds in the neighborhood of a singularity. For real-analytic Lorentzian manifolds, we show that the vector field is analytically linearizable or the manifold is…
In this paper, we study the correspondence between a field theory in de Sitter space in $D$-dimensions and a dual conformal field theory in a euclidean space in $(D-1)$-dimensions. In particular, we investigate the form in which this…
We develop a technique relating scalar fields with different masses in different conformally flat space-times. We apply this technique to the case of FRW space-times, with $k=\pm 1,0$, and discuss several examples. We also study various…
$Vect(N)$, the algebra of vector fields in $N$ dimensions, is studied. Some aspects of local differential geometry are formulated as $Vect(N)$ representation theory. There is a new class of modules, {\it conformal fields}, whose…
We present a new approach to the study of vacuum spacetimes with a Killing symmetry. The central quantity in this approach is the exterior derivative of the Killing vector field, which is a test electromagnetic field. Considering the…
It is argued that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semi-direct sum of supertranslations with infinitesimal local conformal transformations and not, as usually…
We present a maximally symmetric vacuum spacetime, which is locally isometric anti- de Sitter, admitting closed timelike curves appear after a definite instant of time i.e., a time-machine spacetime. The spacetime is regular, free-from…
The drift method, introduced by the second author, provides a new formulation of the Einstein constraint equations, either in vacuum or with matter fields. The natural of the geometry underlying this method compensates for its slightly…
The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. Harmonic conformal gradient fields on pseudo-Euclidean hyperquadrics are classified up to congruence, as are harmonic Killing fields…
We classify, up to a natural equivalence relation, vector fields of the plane which belong to the kernel of a 1--form. This form can be closed, in which case the vector fields are integrable, or not, in which case the differential of the…