Sergio Dain

We show that there exist asymptotically flat almost-smooth initial data for the Einstein–perfect-fluid equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary.

The Goldberg-Sachs theorem has been very useful in constructing algebraically special exact solutions of Einstein vacuum equation. Most of the physical meaningful vacuum exact solutions are algebraically special. We show that the Goldberg-Sachs theorem is not true in linearized gravity. This is a remarkable result, which gives light on the understanding of the physical meaning of the linearized solutions.

The Newman–Penrose constants of the spacetime corresponding to the development of the Brill–Lindquist initial data are calculated by making use of a particular representation of spatial infinity due to H Friedrich. The Brill–Lindquist initial data set represents the head-on collision of two non-rotating black holes. In this case one non-zero constant is obtained. Its value is given in terms of the product of the individual masses of the black holes and the square of a distance parameter separating the two black holes. This constant retains its value all along null infinity, and therefore it provides information about the late time evolution of the collision process. In particular, it is argued that the magnitude of the constants provides information about the amount of residual radiation contained in the spacetime after the collision of the black holes.

We show that there exist asymptotically flat almost-smooth initial data for Einstein-perfect fluid's equation that represent an isolated liquid-type body. By liquid-type body we mean that the fluid energy density has compact support and takes a strictly positive constant value at its boundary. By almost-smooth we mean that all initial data fields are smooth everywhere on the initial hypersurface except at the body boundary, where tangential derivatives of any order are continuous at that boundary. PACS: 04.20.Ex, 04.40.Nr, 02.30.Jr

We report a new result on the nice section construction used in the definition of rest frame systems in general relativity. This construction is needed in the study of non-trivial gravitational radiating systems. We prove the existence, regularity and non-self-crossing property of solutions of the nice section equation for general asymptotically flat spacetimes. This proves a conjecture given in a previous work.

We report on calculations of the total gravitational energy radiated in head-on black hole collisions, where we use the geometry of the Robinson-Trautman metrics. © 1996 The American Physical Society.