Multiply Warped Products with Non-Smooth Metrics

TL;DR

This paper explores Lorentzian multiply warped product manifolds with non-smooth ($C^{0}$) metrics, analyzing their curvature properties and representing Schwarzschild space-time within this framework.

Contribution

It introduces the study of multiply warped products with non-smooth metrics and derives Ricci curvature expressions for specific warped product models.

Findings

Representation of Schwarzschild space-time as a multiply warped product.

Curvature analysis of multiply warped products with $C^0$-warping functions.

Explicit Ricci curvature formulas for specific warped product structures.

Abstract

In this article we study manifolds with $C^{0}$-metrics and properties of Lorentzian multiply warped products. We represent the interior Schwarzschild space-time as a multiply warped product space-time with warping functions and we also investigate the curvature of a multiply warped product with $C^0$-warping functions. We given the {\it{Ricci curvature}} in terms of $f_1$, $f_2$ for the multiply warped products of the form $M=(0,\ 2m)\times_{f_1}R^1\times_{f_2} S^2$.