2016/05/11 by Ivan P. Costa e Silva, Silva, Ivan P. Costa e, José Luis Flores +3
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1605.03619
openalex publication_date 2016/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider restrictions placed by geodesic completeness on spacetimes possessing a null parallel vector field, the so-called Brinkmann spacetimes. This class of spacetimes includes important idealized gravitational wave models in General Relativity, namely the plane-fronted waves with parallel rays, or pp-waves, which in turn have been intensely and fruitfully studied in the mathematical and physical literatures for over half a century. More concretely, we prove a restricted version of a conjectural analogue for Brinkmann spacetimes of a rigidity result obtained by M.T. Anderson for stationary spacetimes. We also highlight its relation with a long-standing 1962 conjecture by Ehlers and Kundt. Indeed, it turns out that the subclass of Brinkmann spacetimes we consider in our main theorem is enough to settle an important special case of the Ehlers-Kundt conjecture in terms of the well known class of Cahen-Wallach spaces.