Survival of the black hole's Cauchy horizon under non-compact perturbations

We study numerically the evolution of spactime, and in particular of a spacetime singularity, inside a black hole under a class of perturbations of non-compact support. We use a very simplified toy model of a spherical charged black hole which is perturbed nonlinearly by a self-gravitating, spherical scalar field. The latter grows logarithmically with advanced time along an outgoing characteristic hypersurface. We find that for that class of perturbations a portion of the Cauchy horizon survives as a non-central, null singularity.Comment: 5 pages, 4 figure

Orbital evolution for extreme mass-ratio binaries: conservative self forces

The conservative dephasing effects of gravitational self forces for extreme mass-ratio inspirals are studied. Both secular and non-secular conservative effects may have a significant effect on LISA waveforms that is independent of the mass ratio of the system. Such effects need to be included in generated waveforms to allow for accurate gravitational wave astronomy that requires integration times as long as a year.Comment: 3 figures, in Proceedings of the Sixth International LISA Symposium (AIP, 2006

A Piecewise-Conserved Constant of Motion for a Dissipative System

We discuss a piecewise-conserved constant of motion for a simple dissipative oscillatory mechanical system. The system is a harmonic oscillator with sliding (dry) friction. The piecewise-conserved constant of motion corresponds to the time average of the energy of the system during one half-period of the motion, and changes abruptly at the turning points of the motion. At late times the piecewise-conserved constant of motion degenerates to a constant of motion in the usual sense.Comment: 8 pages, 6 Encapsulated PostScript figure

Self-force approach to synchrotron radiation

We analyze radiation reaction for synchrotron radiation by computing, via a multipole expansion, the near field and derive from it the Lorentz four-force, which we evaluate on the world-line of the charge. We find that the temporal component of the self four-force agrees with the radiated power, which one calculates in the radiation zone. This is the case for each mode in the multipole decomposition. We also find agreement with the Abraham–Lorentz–Dirac equation