Collapse and rebound of a charged dust-like star

It is shown that a charged spherically symmetric star, made out of a continuous superposition of thin shells with Poincaré stresses, undergoes gravitational collapse in free fall like an uncharged star of dust. The interior solution is a Friedmann universe matching the Reissner-Nordström geometry at the boundary of the star. When the absolute value of the chargeQ does not exceed the massM, the star rebounds elastically inside the event horizon at the radial coordinateQ ²/(2M). The further history of the charged star after the bounce is analyzed. Besides, a simple mechanism which accounts for the development of Poincaré stresses in an originally charged star of dust is suggested. It is also verified that the energy density is nonnegative all along the collapse process.