On spacetimes dual to spherically symmetric solutions

By defining a duality transformation which implies interchange of active an d passive electric parts of gravitational field, it is possible to construc t spacetimes dual to solutions of the Einstein equation. Under the duality transformation a fluid spacetime maps into a fluid spacetime with density a nd pressure transforming as rho --> (rho + 3p)/2 and p --> (rho - p)/2. On the other hand a vacuum solution will acquire a global monopole charge. The remarkable feature of spherically symmetric solutions is that it is possib le to give a general prescription for writing dual solutions. We demonstrat e its application by writing dual solutions to the McVittie solution for a Schwarzschild particle in an expanding universe and to Vaidya's radiating s tar solution.