https://doi.org/10.1140/epjc/s10052-026-15421-9
Regular Article - Theoretical Physics
Some inequalities among curvature invariants
1
Astronomical Observatory, Jagiellonian University, Kraków, Poland
2
Institute of Theoretical Physics, Jagiellonian University, Kraków, Poland
a
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Received:
23
October
2025
Accepted:
5
February
2026
Published online:
1
March
2026
Abstract
We prove an infinite sequence of inequalities among scalar polynomial invariants of symmetric rank-2 tensors of Segre types A1, A3, 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.
© The Author(s) 2026
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