Naked Singularity Formation In f(R) Gravity

Details Naked Singularity Formation In f(R) Gravity Naked Singularity Formation In f(R) Gravity

2011-06-28

arxiv.org/abs/1106.5638v1

Gen Relativ Gravit 43 (2011) 2943

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, 4 figures, to appear in GRG

Scientific paper

We study the gravitational collapse of a star with barotropic equation of state $p=w\rho$ in the context of $f({\mathcal R})$ theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as $f({\mathcal R})=\alpha{\mathcal R}^{m}$, we show that for an appropriate initial value of the energy density, if $\alpha$ and $m$ satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter $\alpha$ obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.

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