Some inequalities among curvature invariants
Abstract
Abstract We prove an infinite sequence of inequalities among scalar polynomial invariants of symmetric rank-2 tensors of Segre types A 1, A 3, and B . In particular, these inequalities apply to the Ricci tensor and the energy-momentum tensor. If at least one of them is violated by the Ricci tensor, then the Einstein equations force violation of all classical energy conditions. In addition, we use one of the inequalities to generalize the known relation between the second Ricci invariant and the Kretschmann scalar.
Fields of Study & Subjects
Relativity and Gravitational Theory
Advanced Differential Geometry Research
Cosmology and Gravitation Theories
Publication details
- Journal / source
- The European Physical Journal C
- Volume
- 86
- Issue
- 3
- Publication date
- 1 March 2026
- Language
- EN