Born–Infeld theory of gravitation: Static, spherically symmetric solutions

In this work a Born–Infeld type theory of gravitational field is postulated, and vacuum spherically symmetric, static solutions of respective equations are discussed. The asymptotic of modified Schwarzschild solution is studied in the two limiting cases, for r→∞ and for r→0. In the first case the solution is given as a decomposition in L/r, (up to O(L4)), where characteristic length L≈10−32 cm; this solution in the limit L→0 is reduced to the Schwarzschild solution. In the second case, it is shown that the solution doesnʹt continue up to r=0; instead, it breaks off on a boundary (a sphere r=rmin≈0.333×(rgL2)13, where rg is Schwarzschild radius). Inside the sphere the solution isnʹt valid, since metric determinant is positive there. Though metric coefficients have singularity at r=rmin, the curvature invariants are finite on the boundary. For consistency, one should assume that region r