Quantum gravity is expected to remove the classical singularity that arises as the end state of gravitational collapse. To investigate this, we work with a toy model of a collapsing homogeneous scalar field. We show that nonperturbative semiclassical effects of loop quantum gravity cause a bounce and remove the black hole singularity. Furthermore, we find a critical threshold scale below which no horizon forms: quantum gravity may exclude very small astrophysical black holes.

We investigate here quantum effects in gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that nonperturbative semiclassical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before the singularity can form. Quantum gravitational effects thus censor naked singularities by avoiding their formation. Further, quantum gravity induced mass flux has a distinct feature which may lead to a novel observable signature in astrophysical bursts.

We perform a careful investigation of the problem of physically realistic gravitational collapse of massive stars in f (R)-gravity. We show that the extra matching conditions that arise in the modified gravity impose strong constraints on the stellar structure and thermodynamic properties. In our opinion these constraints are unphysical. We prove that no homogeneous stars with nonconstant Ricci scalar can be matched smoothly with a static exterior for any nonlinear function f (R). Therefore, these extra constraints make classes of physically realistic collapse scenarios in general relativity, non-admissible in these theories. We also find an exact solution for an inhomogeneous collapsing star in the Starobinski model that obeys all the energy and matching conditions. However, we argue that such solutions are fine-tuned and unstable to matter perturbations. Possible consequences on black hole physics and the cosmic censorship conjecture are also discussed.

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We study the structure of neutron stars in the fðRÞ ¼ R þ αR 2 theory of gravity (the Starobinsky model) in an exact and nonperturbative approach. In this model, apart from the standard general relativistic junction conditions, two extra conditions-namely, the continuity of the curvature scalar and its first derivative-need to be satisfied. For an exterior Schwarzschild solution, the curvature scalar and its derivative must be zero at the stellar surface. We show that for some equation of state (EoS) of matter, matching all conditions at the surface of the star is impossible. Hence the model brings two major finetuning problems: (i) only some particular classes of EoS are consistent with Schwarzschild at the surface, and (ii) given the EoS, only a very particular set of boundary conditions at the center of the star will satisfy the given boundary conditions at the surface. Hence we show that this model [and subsequently many other fðRÞ models where the uniqueness theorem is valid] is highly unnatural for the existence of compact astrophysical objects. This is because the EoS of a compact star should be completely determined by the physics of nuclear matter at high density and not the theory of gravity.