An algorithm is developed for computing the nth gravitational multipole moment of an asymptotically flat, empty, stationary axisymmetric space-time. The moments are expressed in terms of the expansion coefficients of the Ernst potential on the axis of symmetry. The values of the first ten multipole moments are given.

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Quasi-breathers (QB) are time-periodic solutions with weak spatial localization introduced in G. Fodor et al. in Phys. Rev. D. 74, 124003 (2006). QB's provide a simple description of oscillons (very long-living spatially localized time dependent solutions). The small amplitude limit of QB's is worked out in a large class of scalar theories with a general self-interaction potential, in D spatial dimensions. It is shown that the problem of small amplitude QB's is reduced to a universal elliptic partial differential equation. It is also found that there is the critical dimension, Dcrit = 4, above which no small amplitude QB's exist. The QB's obtained this way are shown to provide very good initial data for oscillons. Thus these QB's provide the solution of the complicated, nonlinear time dependent problem of small amplitude oscillons in scalar theories.

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic series expansions and Borel summation. The amplitude of the radiation is beyond all orders in perturbation theory and the method used has been developed by Segur and Kruskal in Phys. Rev. Lett. 58, 747 (1987). Our results are in good agreement with those of long time numerical simulations of oscillons.Comment: 22 pages, 9 figure

The time evolution of strongly excited SU(2) Bogomol'nyi-Prasad-Sommerfield magnetic monopoles in Minkowski spacetime is investigated by using numerical simulations based on the technique of conformal compactification and on the use of the hyperboloidal initial value problem. It is found that an initially static monopole does not radiate the entire energy of the exciting pulse toward future null infinity. Rather, a long-lasting quasistable "breathing state" develops in the central region and certain expanding shell structures-built up by very high frequency oscillations-are formed in the far away region.