Hyperboloidal initial data for the vacuum Einstein equations with cosmological constant

The existence of smooth hyperboloidal initial data sets for the vacuum Einstein equations with non-zero cosmological constant is studied. Supposing that the trace of the (physical) second fundamental form of the initial hypersurface is constant, there is a correspondence between the solutions of the vacuum constraints with and without cosmological constant, respectively. This enables us to extend the results proved by Andersson and Chrusciel about the smoothness of the initial data with zero cosmological constant to the case

Bondi-type systems near space-like infinity and the calculation of the NP-constants

We relate Bondi systems near space-like infinity to another type of gauge conditions. While the former are based on null infinity, the latter are defined in terms of Einstein propagation, the conformal structure, and data on some Cauchy hypersurface. For a certain class of time symmetric space-times we study an expansion which allows us to determine the behavior of various fields arising in Bondi systems in the region of space-time where null infinity touches space-like infinity. The coefficients of these expansions can be read off from the initial data. We obtain in particular expressions for the constants discovered by Newman and Penrose (NP-constants) in terms of the initial data. For this purpose we calculate a certain expansion up to 3rd order.Comment: 35 page

Uniqueness of the mass in the radiating regime

The usual approaches to the definition of energy give an ambiguous result for the energy of fields in the radiating regime. We show that for a massless scalar field in Minkowski space-time the definition may be rendered unambiguous by adding the requirement that the energy cannot increase in retarded time. We present a similar theorem for the gravitational field, proved elsewhere, which establishes that the Trautman-Bondi energy is the unique (up to a multiplicative factor) functional, within a natural class, which is monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri.Comment: 8 pages, revte

On the uniqueness and global dynamics of AdS spacetimes

We study global aspects of complete, non-singular asymptotically locally AdS spacetimes solving the vacuum Einstein equations whose conformal infinity is an arbitrary globally stationary spacetime. It is proved that any such solution which is asymptotically stationary to the past and future is itself globally stationary. This gives certain rigidity or uniqueness results for exact AdS and related spacetimes.Comment: 18pp, significant revision of v

Uniqueness of the Trautman--Bondi mass

It is shown that the only functionals, within a natural class, which are monotonic in time for all solutions of the vacuum Einstein equations admitting a smooth ``piece'' of conformal null infinity Scri, are those depending on the metric only through a specific combination of the Bondi `mass aspect' and other next--to--leading order terms in the metric. Under the extra condition of passive BMS invariance, the unique such functional (up to a multiplicative factor) is the Trautman--Bondi energy. It is also shown that this energy remains well-defined for a wide class of `polyhomogeneous' metrics.Comment: latex, 33 page

Conformal Einstein evolution

We discuss various properties of the conformal field equations and their consequences for the asymptotic structure of space-times

On the existence of C infinity solutions to the asymptotic characteristic initial value problem in general relativity

The asymptotic characteristic initial value problem for Einstein's vacuum field equations is treated. It is shown that C-infinity solutions exist and are unique for C-infinity initial values. The proof is based on Friedrich's regular conformal vacuum field equations and Rendall's method of reducing the characteristic to an ordinary initial value problem

On the existence of C infinity solutions to the asymptotic characteristic initial value problem in general relativity

The asymptotic characteristic initial value problem for Einstein's vacuum field equations is treated. It is shown that C-infinity solutions exist and are unique for C-infinity initial values. The proof is based on Friedrich's regular conformal vacuum field equations and Rendall's method of reducing the characteristic to an ordinary initial value problem