arXiv subjects

Juan B. Sancho

Publications and source records attributed to Juan B. Sancho.

3 recordsLinked to original sources

arXiv2025

Uniqueness of the torsion-curvature pair

On smooth manifolds of dimension $n \ge 4$, we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that satisfy both the linear and differential Bianchi identities. This result extends to arbitrary linear connections a recent characterisation of the curvature tensor of a symmetric linear connection obtained in the paper "On the uniqueness of the torsion and curvature operators", Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM, 114, 2020.

math.DG↗

arXiv2014

Noether's Second Theorem on natural bundles

Following work by I. Anderson, in this note we present a formulation of Noether's Second Theorem that is valid on any natural bundle.

math-ph↗

arXiv2007

On the naturalness of Einstein's equation

We compute all 2-covariant tensors naturally constructed from a semiriemannian metric which are divergence-free and have weight greater than -2. As a consequence, it follows a characterization of the Einstein tensor as the only, up to a constant factor, 2-covariant tensor naturally constructed from a semiriemannian metric which is divergence-free and has weight 0 (i.e., is independent of the unit of scale). Since these two conditions are also satisfied by the energy-momentum tensor of a relativistic space-time, we discuss in detail how these theorems lead to the field equation of General Relativity.

gr-qc↗