https://neckpinch.com/authors/rohit-dhormare/New arXiv papers by Rohit Dhormare, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2610.07879/arxiv:2610.07879Tue, 06 Oct 2026 00:00:00 GMTRohit Dhormare — We establish a scale-invariant spatial non-collapse estimate for hypersurface-orthogonal timelike geodesic congruences. The result extends a previous Raychaudhuri-based construction in which a comparison estimate for the expansion was used to control the volume of domains transported along the congruence. The additional ingredient here is a quantitative estimate of the spatial distance distortion induced by the expansion and shear. Assuming that the initial spatial geometry is non-collapsed up to a scale r₀, and that the expansion, shear, and timelike Ricci curvature satisfy suitable uniform bounds, we obtain, before the first blow-up time of the Raychaudhuri comparison solution, \beginequation* \operatornameVol_h_τ\bigl(B_h_τ(p_τ,r)\bigr) \geq κ_L(τ)\, r^3, \endequation* where \beginequation* κ_L(τ) = κ_0 e^-3Kτ \exp\!\left(\int_0^τΘ(s)\,ds\right), \qquad K = \fracΘ_03 + Σ_0 . \endequation* Here Θ denotes the solution of the scalar Raychaudhuri comparison equation and K controls the spatial metric distortion. For every finite time strictly before the comparison barrier, κ_L(τ) is positive. When the comparison solution has a finite blow-up time, the explicit comparison coefficient approaches zero as that time is approached from below. The comparison barrier is a boundary of the estimate and is not, by itself, a statement that the physical congruence develops a focal point or spacetime singularity. The result is structurally analogous to scale-invariant non-collapse estimates in geometric flow, but is mathematically distinct from Perelman's κ-noncollapsing theorem for Ricci flow.Ricci flowSingularities(Non)collapsing https://neckpinch.com/papers/2607.09940/arxiv:2607.09940Fri, 10 Jul 2026 00:00:00 GMTRohit Dhormare — In this paper, we establish a geometric correspondence between the Lorentzian Raychaudhuri equation and Perelman's non-collapsing theorem for the Ricci flow. By interpreting the Raychaudhuri equation as a Lorentzian analogue of Ricci flow, we connect geodesic focusing in general relativity to the monotonicity and entropy functionals of geometric analysis. Using this correspondence, we derive a Lorentzian non-collapsing theorem and introduce a covariant entropy functional governing causal volume evolution. Finally, we propose the concept of geodesic entropy capacity, a curvature-bounded limit on the information that can be stored in spacetime regions, providing a unified geometric framework linking gravitation, thermodynamics, and information.Ricci flow(Non)collapsingPhysics