Negative-mass lagging cores of the big bang

Examples are given of spherically symmetric cosmological models containing space-sections with the following properties: at large values of the geometrically defined coordinate R, the mass is positive, while at small values of R, the mass is negative. The negative-mass region of spacetime has local properties similar to those of the negative-mass Schwarzschild solution. The big bang in these models is partially spacelike and partially timelike, so the spacetimes do not obey the strong form of the cosmic censorship hypothesis. The timelike, negative-mass segments of the big bang are unlimited sources of electromagnetic and gravitational radiation, and as such may be attractive as ''lagging core'' models of highly energetic astrophysical phenomena