Gravitational Collapse of Bose-Einstein condensate dark matter in Generalized Vaidya spacetime

TL;DR

This paper investigates gravitational collapse of Bose-Einstein condensate dark matter within generalized Vaidya spacetime, exploring conditions leading to black hole or naked singularity formation and analyzing causal structures.

Contribution

It introduces a model combining Bose-Einstein condensate dark matter with generalized Vaidya spacetime to study collapse outcomes and singularity nature, including junction conditions and Penrose diagrams.

Findings

Collapse can result in black holes or naked singularities depending on initial conditions.

Derived junction conditions for Vaidya exterior and Friedmann interior.

Generated and analyzed Penrose diagrams illustrating causal relations.

Abstract

In this work, we study the gravitational collapse procedure in generalized Vaidya spacetime with Bose-Einstein condensate dark matter density profile. We use the generalized Vaidya metric to simulate the spacetime of a big star and subsequently obtain the field equations. Then we proceed to determine the star system's mass parameter by solving the field equations. Then the gravitational collapse mechanism is investigated using the derived solutions. Investigating the nature of the singularity (if formed) as the end state of the collapse is the main goal. Dark matter in the form of Bose-Einstein condensate is expected to play a crucial role in the fate of the collapse. We see that there is a possibility of the formation of both black holes and naked singularities as the end state of the collapse depending upon the initial conditions. The junction conditions are derived with a Vaidya exterior and a Friedmann interior and some important insights are obtained. A Penrose diagram showing the causal relations between the spacetimes is generated and studied in detail.