abstract: We prove existence, uniqueness and regularity of solutions to the Einstein vacuum equations taking form $$ {}^{(4)}g = -dt^2 + \sum_{i,j=1}^3 a_{ij}t^{2 p_{\max\{i,j\}}}\,{\rm d} x^i\,{\rm x^j on $(0,T]_t\times\Bbb{T}^3_x$, where $a_{ij}(t,x)$ $p_i(x)$ are regular functions without symmetry or analyticity assumptions. These metrics singular asymptotically Kasner-like as $t\to 0^+$. ex...