Weighing the curvature invariants
arXiv:2502.12242 · doi:10.1140/epjc/s10052-025-14552-9
Abstract
We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lemaître--Robertson--Walker, and Bianchi type I metrics, independently of whether they are solutions of some particular field equations. In contrast, others hold for solutions of Einstein's gravitational field equation and a family of energy-momentum tensors (featuring ideal fluids, scalar fields and nonlinear electromagnetic fields), independently of the specific form of the spacetime metric. We illustrate different behaviour of the basic curvature invariants with numerous examples and discuss the consequences and limitations of the proven results.
25 pages; ver. 3: published version (minor typos corrected)
References in corpus (27)
- f(R) Theories Of Gravity
- f(R) theories
- Regular Magnetic Black Holes and Monopoles from Nonlinear Electrodynamics
- Construction of Regular Black Holes in General Relativity
- Regular black holes: A short topic review
- Introductory Notes on Non-linear Electrodynamics and its Applications
- When is g_{tt} g_{rr} = -1?
- Spacetimes characterized by their scalar curvature invariants
- Black hole thermodynamics in the presence of nonlinear electromagnetic fields
- Comment on "Construction of regular black holes in general relativity"
- Quest for realistic non-singular black-hole geometries: Regular-center type
- Oscillatory null singularity inside realistic spinning black holes
- Constraints on singularity resolution by nonlinear electrodynamics
- Dyonic configurations in nonlinear electrodynamics coupled to general relativity
- Identification of black hole horizons using scalar curvature invariants
- Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes
- Nonlinear electromagnetic fields in strictly stationary spacetimes
- Spacetimes dressed with stealth electromagnetic fields
- Suppression of spacetime singularities in quantum gravity
- Lagrangian reverse engineering for regular black holes
- Past extendibility and initial singularity in Friedmann-Lemaître-Robertson-Walker and Bianchi I spacetimes
- Symmetries and gravitational Chern-Simons Lagrangian terms
- Bianchi-I cosmologies, magnetic fields and singularities
- Generalizations and challenges for the spacetime block-diagonalization
- Spacetime singularities and curvature blow-ups
- The square of the Weyl tensor can be negative
- A note on a third order curvature invariant in static spacetimes