Probing the stability of gravastars by dropping dust shells onto them

As a preparation for the dynamical investigations, this paper begins with a short review of the three-layer gravastar model with distinguished attention to the structure of the pertinent parameter space of gravastars in equilibrium. Then the radial stability of these types of gravastars is studied by determining their response for the totally inelastic collision of their surface layer with a dust shell. It is assumed that the dominant energy condition holds and the speed of sound does not exceed that of the light in the matter of the surface layer. While in the analytic setup the equation of state is kept to be generic, in the numerical investigations three functionally distinct classes of equations of states are applied. In the corresponding particular cases the maximal mass of the dust shell that may fall onto a gravastar without converting it into a black hole is determined. For those configurations which remain stable the excursion of their radius is assigned. It is found that even the most compact gravastars cannot get beyond the lower limit of the size of conventional stars, provided that the dominant energy condition holds in both cases. It is also shown---independent of any assumption concerning the matter interbridging the internal de Sitter and the external Schwarzschild regions---that the better is a gravastar in mimicking a black hole the easier is to get the system formed by a dust shell and the gravastar beyond the event horizon of the composite system. In addition, a generic description of the totally inelastic collision of spherical shells in spherically symmetric spacetimes is also provided in the appendix.Comment: 29 pages, 10 figure

Detection Rate Estimates of Gravity-waves Emitted During Parabolic Encounters of Stellar Black Holes in Globular Clusters

The rapid advance of gravitational-wave (GW) detector facilities makes it very important to estimate the event rates of possible detection candidates. We consider an additional possibility of GW bursts produced during parabolic encounters (PEs) of stellar mass compact objects. We estimate the rate of successful detections for specific detectors: the initial Laser Interferometric Gravitational-Wave Observatory (InLIGO), the French-Italian gravitational-wave antenna VIRGO, the near-future Advanced-LIGO (AdLIGO), the space-based Laser Interferometric Space Antenna (LISA), and the Next Generation LISA (NGLISA). Simple GC models are constructed to account for the compact object mass function, mass segregation, number density distribution, and velocity distribution. We calculate encounters both classically and account for general relativistic corrections by extrapolating the results for infinite mass ratios. We also include the cosmological redshift of waveforms and event rates. We find that typical PEs with masses m_1=m_2=40 Msun are detectable with matched filtering over a signal to noise ratio of 5 within a distance d_L~200Mpc for InLIGO and VIRGO, z=1 for AdLIGO, 0.4Mpc for LISA, and 1Gpc for NGLISA. We estimate single datastream total detection rates of 5.5 x 10^{-5} for InLIGO, 7.2 x 10^{-5} for VIRGO, 0.063 for AdLIGO, 2.9 x 10^{-6} for LISA, and 1.0 for NGLISA per year, for reasonably conservative assumptions. These estimates are subject to uncertainties in the GC parameters, most importantly the total number and mass-distribution of black holes (BHs) in the cluster core. In reasonably optimistic cases, we get >~1 detections for AdLIGO per year. The regular detection of GWs during PEs would provide a unique observational probe for constraining the stellar BH mass function of dense clusters. (abridged)Comment: 19 pages, 8 figures, version accepted for publication in ApJ; added quantitative estimate of the unresolved parabolic encounter background (Sec 7.4.3