All transverse and TT tensors in flat spaces of any dimension

We present general formulas for transverse and transverse-traceless (TT) symmetric tensors in flat spaces. TT tensors in conformally flat spaces can be obtained by means of a conformal transformation.Comment: 9 page

Symmetries of the Robinson-Trautman equation

We study point symmetries of the Robinson--Trautman equation. The cases of one- and two-dimensional algebras of infinitesimal symmetries are discussed in detail. The corresponding symmetry reductions of the equation are given. Higher dimensional symmetries are shortly discussed. It turns out that all known exact solutions of the Robinson--Trautman equation are symmetric.Comment: 8 pages, latex2e, 4 tables, several references adde

On the energy of a null cone

We derive a formula for the Bondi mass aspect in terms of asymptotic data of the Bondi-Sachs metric in the affine gauge. We prove the positivity of the total energy of a regular null cone in agreement with a recent result of Chru\'{s}ciel and Paetz.Comment: 8 page

Asymptotic properties of the C-Metric

The aim of this article is to analyze the asymptotic properties of the C-metric, using a general method specified in work of Tafel and coworkers, [1], [2], [3]. By finding an appropriate conformal factor $\Omega$, it allows the investigation of the asymptotic properties of a given asymptotically flat spacetime. The news function and Bondi mass aspect are computed, their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.Comment: 28 pages, 11 figure