Gravitational Radiation from a Naked Singularity — Odd - Parity Perturbation —

The study involved in the attempt to detect gravitational waves represents one of the most exciting field in modern physics. The detection will provide a decisive test of general relativity and open a new window for astrophysical observation. Unfortunately, in spite a great deal of effort, no one has yet succeeded in the detection of the gravitational waves. However ground-based laser interferometers, such as LIGO, [1] VIRGO, [2] TAMA [3] and GEO600, [4] are being constructed and will soon enter a stage of data taking. Strong sources of gravitational waves should be regions where gravity is general relativistic and where the velocities of bulk motion are near the speed of light. Many researchers have theoretically investigated coalescing and colliding black holes and neutron stars as candidates for detection. In addition, gravitational waves emitted during stellar collapse to black holes have been studied by perturbative calculations of a spherically symmetric background. [5,6] Because of the existence of event horizon, the emitted gravitational waves are dominated by the quasi-normal modes of the Schwarzschild black hole in the asymptotic region. Some other realistic candidates exist, e.g., supernovae, rapidly rotating neutron stars, relic gravitational waves of the early universe, stochastic gravitational waves from cosmic strings, and so on. In this paper we attempt to investigate whether a naked singularity, if such exists, is a strong source of gravitational radiation, and, moreover, to understand the dynamics and observational meaning of naked singularity formation. Several researchers have shown that the final fate of gravitational collapse is not always a singularity covered by an event horizon. For example, in the Lemâıtre-Tolman-Bondi (LTB) spacetime, [7,8] a naked shell-focusing singularity appears from generic initial data for spherically symmetric configurations of the rest mass density and a specific energy of the dust fluid. [9–12] The initial functions in the most general expandable form have been considered. [13] The matter content in such a spacetime may satisfy even the dominant energy condition. In this case with a small disturbance of the spacetime, very short wavelength gravitational waves, which are created in the high density region around a singularity, may propagate to the observer outside the dust cloud because of the absence of an event horizon. If this is true, extremely high energy phenomena which cannot be realized by any high energy experiment on Earth can be observed. In this case information regarding the physics of so-called ‘quantum gravity’ may be obtained. Also, these waves may be so intense that they destroy the Cauchy horizon. In this paper the generation of gravitational waves during the collapse of spherical dust ball with small rotational motion is considered. Nakamura, Shibata and Nakao [14] have suggested that a naked singularity may emit considerable gravitational wave radiation. This was proposed from the estimate of gravitational radiation from a spindle-like naked singularity.