Multiply warped products with nonsmooth metrics (Q2731827)

A multiply warped products space-time with base \( (B, -dt^2)\), fibres \((F_i, g_i)\), \(i=1,\ldots n\), and warping functions \(f_i>0\) is the product manifold \((B\times F_1\times\ldots \times F_n, g)\) endowed with the Lorentzian metric NEWLINE\[NEWLINEg= -\pi ^*_B dt^2 + \sum _{i=1}^n (f_i\circ \pi _B)^2 \pi ^* _ig_i\equiv -dt_2 + \sum _{i=1}^n f_i^2g_i,NEWLINE\]NEWLINE where \(\pi _B\), \(\pi _i\), \( i= 1, \ldots , n\) are the natural projections of \(B\times F_1\times\ldots \times F_n\) onto \(B\) and \(F_1,\ldots , F_n\), respectively. In the paper under review the author represents the interior Schwarzschild space-time as a multiply warped product space time with warping functions and also investigates the curvature of a multiply warped product with \(C^0\)-warping functions. The Ricci curvature in terms of \(f_1\), \(f_2\) for the multiply warped products of the form \(M = (0,2m)\times _{f_1} R^1\times _{f_2}S^2\) is given.