arXiv subjects

Kornelia Nikiel

Publications and source records attributed to Kornelia Nikiel.

2 recordsLinked to original sources

arXiv2026

Some inequalities among curvature invariants

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.

gr-qc↗

arXiv2025

Halilsoy and Chandrasekhar standing gravitational waves in the linear approximation

Halilsoy and Chandrasekhar cylindrical standing gravitational waves correspond to two different classes of solutions to the vacuum Einstein equations. Both families satisfy the definition of standing gravitational waves proposed by Stephani, but only the latter class fulfills the stricter definition introduced by Chandrasekhar. The aim of this research is to compare both classes of solutions within the linear regime. We discover that the linearized Halilsoy and Chandrasekhar standing waves are gravitational analogues of two different types of electromagnetic polarization standing waves.

gr-qc↗