A mathematical theory of gravitational collapse (Q1819392)

This paper supplements three previous papers of the author [ibid. 105, 337-362 (1986; Zbl 0608.35039), ibid. 106, 587-622 (1986), and ibid. 109, 591-611 (1987); see the preceding reviews)]. In this paper the author investigates the asymptotic behavior of the generalized solutions as the retarded time u tends to infinity. It is shown, when the final Bondi mass \(M_ 1\neq 0\) as \(u\to \infty\), a black hole forms of mass \(M_ 1\) surrounded by vacuum. Further it is shown that in the region exterior to the Schwarzschild sphere, \(r=ZM_ 1\), the solution tends to stationary as \(u\to \infty\) and the mass remaining outside this sphere tends to zero as \(u\to \infty\). Finally, it asserts the formation of an event horizon as \(u\to \infty\), which is the part of the limiting hypersurface \(u=\infty\) interior to this sphere. The rate of decay of the metric function and the asymptotic behaviour of the incoming light rays are obtained.