相关论文: Bowen-York Tensors

We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds $(M,g)$. The Cotton-York tensor linearized at $g$ maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution…

In the initial conditions of the $3 + 1$ formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point.…

We construct a family of finite element sub-complexes of the conformal complex on tetrahedral meshes and show their exactness on contractible domains. This complex includes vector fields and symmetric and traceless tensor fields, connected…

We present general formulas for transverse and transverse-traceless (TT) symmetric tensors in flat spaces. TT tensors in conformally flat spaces can be obtained by means of a conformal transformation.

The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the $3 + 1$ formalism. As such, it is part of the freely specifiable initial data for…

The Bel-Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov-Bel classification of the Weyl tensor. The new classes…

We reformulate the abelian tensor multiplet on a curved spacetime with at least two supercharges in a cohomological form where all the bosonic and fermionic fields become tensor fields. These tensor fields are rewritten as fields in loop…

We address the problem of how to characterise when a rank-two conformal Killing tensor is the trace-free part of a Killing tensor for a metric in the conformal class. We call such a metric a Killing scale. Our approach is via differential…

Vector algebra is a powerful and needful tool for Physics but unfortunately, due to lack of mathematical skills, it becomes misleading for first undergraduate courses of science and engineering studies. Standard vector identities are…

Braman [B08] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. This extends the familiar notion that matrices form the set of all linear…

Transverse-tracefree (TT-) tensors on $({\bf R}^3,g_{ab})$, with $g_{ab}$ an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at…

This paper deals with the problem of describing the vector spaces of divergence-free, natural tensors on a pseudo-Riemannian manifold that are second-order; i.e., that are defined using only second derivatives of the metric. The main result…

A vector field on a Riemannian manifold is called conformal Killing if it generates one-parameter group of conformal transformations. The class of conformal Killing symmetric tensor fields of an arbitrary rank is a natural generalization of…

Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly…

Random tensors are the natural generalization of random matrices to higher order objects. They provide generating functions for random geometries and, assuming some familiarity with random matrix theory and quantum field theory, we discuss…

We show that a tensor field of any rank integrates to zero over all broken rays if and only if it is a symmetrized covariant derivative of a lower order tensor which satisfies a symmetry condition at the reflecting part of the boundary and…

We find three families of twisting maps of K^m with K^n. One of them is related to truncated quiver algebras, the second one consists of deformations of the first and the third one requires m=n and yields algebras isomorphic to M_n(K).…

We show how the description of a shear-free ray congruence in Minkowski space as an evolving family of semi-conformal mappings can naturally be formulated on a finite graph. For this, we introduce the notion of holomorphic function on a…

In this paper we derive the projectors to all irreducible SO(d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors in d dimensions. These…

We show that Killing tensors on conformally flat $n$-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic…