Dilatonic Brans-Dicke Anisotropic Collapsing Fluid Sphere And de Broglie Quantum Wave Motion

Two dimensional (2D) analogue of vacuum sector of the Brans Dicke (BD) gravity [1] is studied to obtain dynamics of anisotropic spherically symmetric perfect fluid. Our obtained static solutions behave as dark matter with state equation but in non-static regimes behave as regular perfect fluid with barotropic index ϒ > 0. Positivity property of total mass of the fluid causes that the BD parameter to be ω >2/3 and/or ω < —1. Locations of the event and apparent horizons of the collapsing fluid are obtained in its static regime. In case ω > 0 the apparent horizon is covered by event horizon where the cosmic censorship hypothesis is still valid. According to the model [1], we obtain de Broglie pilot wave of our metric solution which describes particles ensemble which become distinguishable via different values of ω. Incident current density of particles ensemble on the horizons is evaluated which describe the 'Hawking radiation'. The de Brogle-Bohm quantum potential effect is calculated also on the event (apparent) horizon which is independent (dependent) to values of ω.