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

Hossein Ghaffarnejad

doi:10.1088/1742-6596/738/1/012031

Abstract

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.

Highlights

Around a collapsing star, gravity takes an ultra-strong intensity
Internal dynamics of the collapse can be determine type of singularities. They will be naked and visible from view of external observer if collapse process delays the formation of the event horizon [3,4,5]
Space-time singularities created from gravitational collapse should be usually covered by the event horizon hyper-surface

Summary

Introduction

Corresponding matter density and space-time curvature diverge to infinity It is predicted from singularity theorems in general relativity [2] that end of stellar collapse leads to a visible naked or invisible covered singularity. Penrose represented ‘cosmic censorship hypotheses‘ [6], which explains properties of the final singularity of a gravitational collapse In this conjecture, space-time singularities created from gravitational collapse should be usually covered by the event horizon hyper-surface. Space-time singularities created from gravitational collapse should be usually covered by the event horizon hyper-surface It will be invisible from view of outside observers of collapsed object namely black hole [7].

Dilatonic Brans-Dicke collapsing sphere

Concluding remarks