Gravitational waves from the Hénon-Heiles system

Gravitational waves have been known to exist since the early days of general relativity. Einstein himself showed that in the weak field limit we get solutions that obey the wave equation. Despite its importance, at the present time there is only indirect evidence of the reality of gravitational waves ~such as the analyzed binary pulsar which shows a decrease in the orbital period due to the emission of gravitational waves @1#!. It is expected that with the new generation of gravitational wave detectors under construction, more systems will be observed. In this way, several analyses of the possible sources of gravitational waves have been worked out in recent years in the belief that new detectors may be testing models and theories of gravity, stellar models, galactic dynamics, and so on @2#. In the linear regime of general theory of relativity an important feature of a gravitational wave’s emitted power is its dependence on the third-order derivative of the quadrupolar moment. In this case, any system which changes its configuration with time is expected to be a good candidate for a gravitational wave source. Systems suffering catastrophic events are among the best candidates to be observed with gravitational wave detectors and a flurry of work searching for the best candidates to be observed is being done by several groups in the world ~see @3# and references therein!. However, between these systems, which suffer changes in their configurations, there is one that has not been analyzed yet: a chaotic system. An important characteristic of this system is its high sensitivity to initial conditions and a complicated nonperiodic behavior. In gravitational systems, chaotic behavior was studied with care since the pioneering works of Poincaré which analyzed the stability of the Solar System. The three-body problem @4#, the tumbling of Saturn’s satellite hyperon @5#, Hénon-Heiles model of galactic dynamics @6#, geodesic motion around black holes @7#, Bianchi type-IX cosmological models @8#, and others @9# are examples of the chaotic behavior in some gravitational systems. In this work, we consider the emission of gravitational waves from a simple system which shows chaotic behavior: the HénonHeiles system @6#. This system was used for the first time to