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Roberto Giambò

Publications and source records attributed to Roberto Giambò.

25 records · Page 2Linked to original sources
arXiv2015

Negative potentials and collapsing universes II

Completing a previous analysis started in [1], we study flat Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter, self--interacting with a potential that may attain negative values. We prove that the evolution generically forces the Hubble function to diverge to $-\infty$ in a finite time, except in case the potential exhibits a flat plateau at infinity (tending to zero from below); in that case we find conditions which may give rise to ever expanding or recollapsing cosmologies.

gr-qc↗
arXiv2014

Negative potentials and collapsing universes

We study Friedmann--Robertson--Walker models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. We prove that a general class of bounded from above potentials which fall to minus infinity as the field goes to minus infinity, forces the Hubble function to diverge to $-\infty$ in a finite time. This finite-time singularity theorem is true for arbitrary coupling coefficient, provided that it is a bounded function of the scalar field.

gr-qc↗
arXiv2013

Qualitative analysis of collapsing isotropic fluid spacetimes

The structure of the Einstein field equations describing the gravitational collapse of spherically symmetric isotropic fluids is analyzed here for general equations of state. A suitable system of coordinates is constructed which allows us, under a hypothesis of Taylor-expandability with respect to one of the coordinates, to approach the problem of the nature of the final state without knowing explicitely the metric. The method is applied to investigate the singularities of linear barotropic perfect fluids solutions and to a family of accelerating fluids.

gr-qc↗
arXiv2010

Expanding universes in the conformal frame of $f(R) $ gravity

The late time evolution of Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source is studied in the conformal frame of $f(R) $ gravity. We assume that the corresponding scalar field, nonminimally coupled to matter, has an arbitrary non-negative potential function $V(ϕ) $. We prove that equilibria corresponding to non-negative local minima for $V$ are asymptotically stable. We investigate all cases where one of the matter components eventually dominates. The results are valid for a large class of non-negative potentials without any particular assumptions about the behavior of the potential at infinity. In particular for a nondegenerate minimum of the potential with zero critical value we show that if $γ$, the parameter of the equation of state is larger than one, then there is a transfer of energy from the fluid to the scalar field and the later eventually dominates.

gr-qc↗
arXiv2009

Genericity of nondegenerate geodesics with general boundary conditions

Let M be a possibly noncompact manifold. We prove, generically in the C^k-topology (k=2,...,\infty), that semi-Riemannian metrics of a given index on M do not possess any degenerate geodesics satisfying suitable boundary conditions. This extends a result of Biliotti, Javaloyes and Piccione for geodesics with fixed endpoints to the case where endpoints lie on a compact submanifold P of the product MxM that satisfies an admissibility condition. Such condition holds, for example, when P is transversal to the diagonal of MxM. Further aspects of these boundary conditions are discussed and general conditions under which metrics without degenerate geodesics are C^k-generic are given.

math.DG↗
arXiv2008

Gravitational collapse of homogeneous perfect fluid in HOG theories

This paper investigates the evolution of collapsing FRW models with a scalar field having the potential which arises in the conformal frame of high order gravity theories, coupled to matter described by a perfect fluid with energy density $ρ$ and pressure $p$, obeying a barotropic equation of state. The solutions are shown to evolve generically to a singular state in a finite time and they are used as sources for radiating objects undergoing complete gravitational collapse. Although these singularities may be naked in some special case, it is shown that generically a black hole forms.

gr-qc↗