2026/07/16 by Bobby EkaGunara
#gr-qc #math-ph #math.DG #math.MP
We establish a local obstruction to continuous Lorentzian extensions at a class of warped spacelike singularities. The criterion is expressed through two integrability conditions, a monotonicity condition on the relative warp factors, and divergence of the longitudinal factor; it does not require any symmetry of the closed fiber. The main geometric step is a radial compression of terminal causal traces, which replaces the rotational deformation available in spherical symmetry. The compression yields a compact chronological separator in an adapted boundary chart. Longitudinal translations then produce radial-slice distances that diverge intrinsically while remaining uniformly controlled in the extension chart. Next, we construct the canonical one-horizon Birmingham-Kottler spacetime in global Kruskal coordinates and classify all finite proper-time ends of its timelike geodesics. Every boundary-approaching finite maximizer supplied by a putative extension is thereby forced to the singular end. The local obstruction and the geodesic classification imply C0-inextendibility for the one-horizon Birmingham-Kottler family with nonpositive cosmological constant and every closed connected fiber satisfying RicγΣ=(n-2)kγΣ, without assumptions of homogeneity, orientability, or simple connectivity.