Born--Infeld gravitation: Spherically symmetric static solutions

In this paper attention is focused on gravitational sector of the Born--Infeld theory, suggested in quant-ph/9608014. Vacuum equations for gravitational field are derived. The asymptotic for modified Schwarzschild solution is obtained, as a decomposition in parameter $L \approx 10^{-32}$ cm. It is shown, that singularity at $r = 0$ is absent, being replaced by a `ball of matter' with finite dimensions, such that density of matter is of order of magnitude of the Planck's density. Another solution of the same symmetry is obtained, corresponding to a closed space of finite volume of order $L^3$.