Emission of spacetime waves from the partial collapse of a compact object

In this work, we describe the partial collapse of a compact object and the emission of spacetime waves as a result of back-reaction effects. As a source mass term, we propose a non-smooth continuous function that describes a mass-loss, and we then obtain the solution of such setting. We present three distinct examples of the evolution of the norm |Rnl(t, r*)| in terms of t, and four different results are shown for the parameter l = 1, 2, 5, 10; here, r* is the fixed radius of an observer outside the compact object. In all cases, the decay behavior is actually present at t ≫ 1 and becomes more evident for larger l. In addition, for the results that have smaller l’s, their amplitudes are larger when the asymptotic character of |Rnl(t, r*)| clearly appears. Finally, the farther away an observer is set, the fewer oscillations are perceived; however, from our particular fixed set of parameters, the best spot to observe the wiggles of the emitted spacetime waves is close to r* ≃ α.