arXiv subjects

Roberto Giambò

Publications and source records attributed to Roberto Giambò.

At least 19 recordsLinked to original sources

arXiv2026

Photon surfaces extensions for dynamical gravitational collapse

The equations for the photon surface in spherical symmetry are worked out, starting from arXiv:gr-qc/0005050, in the most general dynamical setting. We show that the condition for a timelike hypersurface to be a photon surface can be reformulated as a non-autonomous dynamical system, whose analysis reveals that the same condition also holds when the surface is generated by a null radial geodesic. As an application, we consider a well-known model of a spherical dust cloud undergoing gravitational collapse. In the marginally bound case the photon surface condition reduces to an exact planar dynamical system, whose analysis shows that the extension of the exterior photon surface $r=3M$ into the cloud is unique, and null, if and only if the central singularity is covered, an open set of timelike extensions being available otherwise. Comparing our findings with those in arXiv:1910.13758, we then investigate analytically whether the null extension covers the singularity developing in the Lemaitre-Tolman-Bondi (LTB) model.

gr-qc↗

arXiv2026

Photon surfaces extension in general spherical dust collapse

We extend the analysis of photon surfaces in spherical dust collapse to the general, non-marginally bound case, i.e.\ allowing the \textit{energy function} $k(x)$ of the Lema\^ıtre--Tolman--Bondi (LTB) model to be non-zero. Starting from the dynamical-systems formulation developed in our previous work for the marginally bound case (arXiv:2509.01368), we derive the photon surface equations for the LTB metric with $k(x)\neq 0$, and we recast the geometric condition for a timelike hypersurface to be a photon surface as a non-autonomous first-order dynamical system. Even though the LTB evolution equation does not integrate in closed form when $k(x)\neq 0$, the implicit solutions available in the literature, together with comparison theorems for ordinary differential equations, are sufficient to show that the only physically acceptable extension of the exterior photon sphere $r=3M$ into the collapsing dust cloud is a null hypersurface, generated by outgoing radial null geodesics. Combining this fact with the known results on the causal structure of the general LTB model, we then establish that the photon surface reaches the central singularity if and only if the singularity is naked, thereby extending to the general case the picture already known in the marginally bound regime. The structural dichotomy between the naked and covered end states is also discussed in connection with possible observational signatures in the early-time evolution of black-hole shadows.

gr-qc↗

arXiv2025

Bondi accretion disk luminosity around neutral and charged Simpson-Visser spacetimes

We investigate relativistic Bondi accretion in the Simpson-Visser spacetime, which, via a single parameter $\ell$, interpolates between the Schwarzschild, regular black hole, extremal and wormhole regimes. First, we analyze the neutral Simpson-Visser geometry, recovering Schwarzschild at $\ell=0$, and then its charged extension of the Reissner-Nordström metric. In both these cases, we derive the conservation equations and analyze two representative fluid models: a barotropic perfect fluid and a constituent with an exponential density profile. By varying the parameters across regimes, we locate critical (sonic) points and integrate velocity, density and pressure profiles. While near-horizon inflow velocities are similar across the different solutions, we find that the critical radius and the resulting accretion rates and luminosities severely change, depending on the value of the parameter and type of fluid. Remarkably, the barotropic and exponential cases exhibit different trends in the outer regions. Moreover, by extending the analysis to the charged SV spacetime, we find that the presence of a central charge $Q$ produces additional, albeit modest, shifts in the sonic radius which, in combination with those induced by the regularization parameter $\ell$, could provide a double observational marker. In particular, while $\ell$ acts predominantly on the position of the critical point, in the barotropic fluid case, the electromagnetic contribution of $Q$ slightly dampens the inflow velocity near the horizon.

gr-qc↗

arXiv2025

Generalizing the relativistic precession model of quasi-periodic oscillations through anharmonic corrections

We critically reanalyze the relativistic precession model of quasi-periodic oscillations, exploring its natural extension beyond the standard harmonic approximation. To do so, we show that the perturbed geodesic equations must include anharmonic contributions arising from the higher-order expansion of the effective potential that cannot be neglected \emph{a priori}, as commonly done in all the approaches pursued so far. More specifically, independently of the underlying spacetime geometry, we find that in the radial sector the non-negligible anharmonic correction is quadratic in the radial displacement, i.e. $\propto δr^2$, and significantly affects the radial epicyclic frequency close to the innermost stable circular orbit. Conversely, polar oscillations $δθ$ remain approximately decoupled from radial ones, preserving their independent dynamical behavior. To show the need of anharmonic corrections, we thus carry out Monte Carlo-Markov chain analyses on eight neutron star sources of quasi-periodic oscillations. Afterwards, we first work out the outcomes of the harmonic approximation in Schwarzschild, Schwarzschild--de Sitter, and Kerr spacetimes. Subsequently, we apply the anharmonic corrections to them and use it to fit the aforementioned neutron star sources. Our findings indicate that the standard paradigm requires a systematic generalization to include the leading anharmonic corrections that appear physically necessary, although still insufficient to fully account for the observed phenomenology of quasi-periodic oscillations. Accordingly, we speculate on possible refinements of the relativistic precession model, showing the need to revise it at a fundamental level.

gr-qc↗

arXiv2024

A note on the regularity and the existence of Riemannian splines

In this paper, we present a comprehensive proof concerning the regularity of critical points for the spline energy functional on Riemannian manifolds, even for the general higher-order case. Although this result is widely acknowledged in the literature, a detailed proof was previously absent. Our proof relies on a generalization of the DuBois-Reymond Lemma. Furthermore, we establish the existence of minimizers for the spline energy functional in cases where multiple interpolation points are prescribed alongside just one velocity.

math.AP↗

arXiv2024

Alleviating the cosmological constant problem from particle production

We explore a toy model mechanism of geometric cancellation, alleviating the (classical) cosmological constant problem. To do so, we assume at primordial times that vacuum energy fuels an inflationary quadratic hilltop potential nonminimally coupled to gravity through a standard Yukawa-like interacting term, whose background lies on a perturbed Friedmann-Robertson-Walker metric. We demonstrate how vacuum energy release transforms into geometric particles, adopting a quasi-de Sitter phase where we compute the expected particle density and mass ranges. Perturbations are introduced by means of the usual external-field appproximation, so that the back-reaction of the created particles on the geometry is not considered here. We discuss the limitations of this approach and we also suggest possible refinements. We then propose the most suitable dark matter candidates, showing under which circumstances we can interpret dark matter as constituted by geometric quasiparticles. We confront our predictions with quantum particle production and constraints made using a Higgs portal. In addition, the role of the bare cosmological constant is reinterpreted to speed up the universe today. Thus, consequences on the standard $Λ$CDM paradigm are critically highlighted, showing how both coincidence and fine-tuning issues can be healed requiring the Israel-Darmois matching conditions between our involved inhomogeneous and homogeneous phases.

gr-qc↗

arXiv2024

Global models of collapsing scalar field: endstate

The study of dynamic singularity formation in spacetime, focusing on scalar field collapse models, is analysed. We revisit key findings regarding open spatial topologies, concentrating on minimal conditions necessary for singularity and apparent horizon formation. Moreover, we examine the stability of initial data in the dynamical system governed by Einstein's equations, considering variations in parameters that influence naked singularity formation. We illustrate how these results apply to a family of scalar field models, concluding with a discussion on the concept of genericity in singularity studies.

gr-qc↗

arXiv2024

De Sitter-like configurations with asymptotic quintessence environment

We examine a spherically-symmetric class of spacetimes carrying vacuum energy, while considering the influence of an external dark energy environment represented by a non-dynamical quintessence field. Our investigation focuses on a specific set of solutions affected by this field, leading to distinct kinds of spacetime deformations, resulting in regular, singular, and wormhole solutions. We thoroughly discuss the underlying physics associated with each case and demonstrate that more complex deformations are prone to instability. Ultimately, we find that our results lead to an \emph{isotropic de Sitter-like solution} that behaves as a quintessence fluid. To achieve this, we investigate the nature of the corresponding fluid, showing that it cannot provide the sound speed equal to a constant equation of state {parameter} near the center. Consequently, we reinterpret the fluid as a slow-roll quintessence by investigating its behavior in asymptotic regimes. Further, we explore the potential implications of violating the isotropy condition on the pressures and we finally compare our findings with the de Sitter and Hayward solutions, highlighting both the advantages and disadvantages of our scenarios.

gr-qc↗

arXiv2024

Motion of test particles in quasi anti-de Sitter regular black holes

We explore the characteristics of two novel regular spacetimes that exhibit a non-zero vacuum energy term, under the form of a (quasi) anti-de Sitter phase. Specifically, the first metric is spherical, while the second, derived by applying the generalized Newman-Janis algorithm to the first, is axisymmetric. We show that the equations of state of the effective fluids associated with the two metrics asymptotically tend to negative values, resembling quintessence. In addition, we study test particle motions, illustrating the main discrepancies among our models and more conventional metrics exhibiting non-vanishing anti-de Sitter phase.

gr-qc↗

arXiv2024

Fixed energy solutions to the Euler-Lagrange equations of an indefinite Lagrangian with affine Noether charge

We consider an autonomous, indefinite Lagrangian admitting an infinitesimal symmetry whose associated Noether charge is linear in each tangent space. Our focus lies in investigating solutions to the Euler-Lagrange equations having fixed energy and that connect a given point to a flow line of the infinitesimal generator $K$. By utilizing the invariance of the Lagrangian under the flow of $K$, we simplify the problem into a two-point boundary problem. Consequently, we derive an equation that involves the differential of the ``arrival time'', seen as a functional on the infinite dimensional manifold of connecting paths satisfying the semi-holonomic constraint defined by the Noether charge. When the Lagrangian is positively homogeneous of degree two in the velocities, the resulting equation establishes a variational principle that extends the Fermat's principle in a stationary spacetime. Furthermore, we also analyze the scenario where the Noether charge is affine.

math.DS↗

arXiv2023

Gravitational collapse of a spherical scalar field

Examining the relativistic collapse of a spherical spacetime where gravity is coupled with a scalar field, this review provides a thorough analysis of some of the most relevant studies from both analytical and numerical perspectives. The discussion includes achievements made in this field, with a focus on those related to cosmic censorship, as well as recent perspectives on the topic.

gr-qc↗

arXiv2023

Constraining primordial black holes as a fraction of dark matter through accretion disk luminosity

In this paper, we consider the hypothesis that fractions of dark matter could be constituted by primordial black holes (PBHs). To test this possibility, we work out the observational properties of a static black hole embedded in the dark matter envelope made of a PBH source. The corresponding modifications of geometry due to such a physical system are investigated, with a particular focus on the accretion disk luminosity in spiral galaxies. The impact of the PBH presence is analyzed through modification of the disk luminosity and kinematic quantities. Thus, we discuss possible constraints on the PBH abundance in view of the most recent theoretical bounds. The results of our study indicate that suitable PBH masses are $M_\text{PBH}\in[10^6,10^{12}]M_\odot$ for PBH fractions $f_\text{PBH}\in[10^{-3},1]$. In particular, a comparison with the predictions of the exponential sphere density profile for dark matter suggests that the best-matching configuration is achieved for $f_\text{PBH}=1$ and $M_\text{PBH}=10^6 M_\odot$. Consequences with respect to the current knowledge on primordial black hole physics are discussed.

gr-qc↗

arXiv2022

Red and blue shift in spherical and axisymmetric spacetimes and astrophysical constraints

We compute the red and blue shifts for astrophysical and cosmological sources. In particular, we consider low, intermediate and high gravitational energy domains. Thereby, we handle the binary system Earth - Mars as low energy landscape whereas white dwarfs and neutron stars as higher energy sources. To this end, we take into account a spherical Schwarzschild - de Sitter spacetime and an axially symmetric Zipoy - Voorhees metric to model all the aforementioned systems. Feasible outcomes come from modelling neutron stars and white dwarfs with the Zipoy - Voorhees metric, where quadrupole effects are relevant, and framing solar system objects using a Schwarzschild - de Sitter spacetime. In the first case, large $δ$ parameters seem to be favorite, leading to acceptable bounds mainly for neutron stars. In the second case, we demonstrate incompatible red and blue shifts with respect to lunar and satellite laser ranging expectations, once the cosmological constant is taken to Planck satellite's best fit. To heal this issue, we suggest coarse-grained experimental setups and propose Phobos for working out satellite laser ranging in order to get more suitable red and blue shift intervals, possibly more compatible than current experimental bounds. Implications to cosmological tensions are also debated.

gr-qc↗

arXiv2021

Accretion disk luminosity for black holes surrounded by dark matter with anisotropic pressure

We investigate the luminosity of the accretion disk for a static black hole surrounded by dark matter with anisotropic pressure. We calculate all basic orbital parameters of test particles in the accretion disk, such as angular velocity, angular momentum, energy and radius of the innermost circular stable orbit as functions of the dark matter density, radial pressure and anisotropic parameter, which establishes the relationship between the radial and tangential pressures. We show that the presence of dark matter with anisotropic pressure makes a noticeable difference in the geometry around a Schwarzschild black hole, affecting the radiative flux, differential luminosity and spectral luminosity of the accretion disk.

astro-ph.HE↗

arXiv2020

Repulsive regions in Lemaître-Tolman-Bondi gravitational collapse

We show that in the inhomogeneous Lema{î}tre-Tolman-Bondi space-time there are specific regions in which repulsive gravity exists. To find these regions, we use an invariant definition of repulsive gravity based upon the behavior of the curvature eigenvalues. In addition, we analyze the effects of repulsive gravity on the dynamics of the gravitational collapse. In particular, we investigate the collapse in the case of the parabolic solution for the effective scale factor of the Lema{î}tre-Tolman-Bondi metric, corresponding to the marginally bound case. Exploring the corresponding cut-offs at which gravity becomes repulsive, we notice that black holes with dominant repulsive effects are not excluded \emph{a priori}. Indeed, we demonstrate that the collapse leads, in general, to the formation of a central naked singularity; however, for particular values of the free parameters entering the model, black holes with dominant repulsive gravity can exist. We show that the expected physical process is not modified as the marginally bound condition is dropped out. Moreover, we show that this is true independently of the hypothesis that the energy-momentum tensor is built up in terms of pressureless matter. Further, we demonstrate that geodesic deviations can depend on the sign of the curvature eigenvalues. Finally, we give an astrophysical interpretation of black holes with dominant repulsive gravity. Indeed, we argue that compact objects with dominant repulsive gravity could be interpreted as progenitors of Gamma Ray Bursts.

gr-qc↗

arXiv2020

Late time evolution of negatively curved FLRW models

We study the late time evolution of negatively curved Friedmann--Le\-ma\^ıtre--Robert\-son--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter. Since, under mild assumptions on the potential $V$, it is already known that equilibria corresponding to non-negative local minima for $V$ are asymptotically stable, we classify all cases where one of the energy components eventually dominates. In particular for nondegenerate minima with zero critical value, we rigorously prove that if $γ$, the parameter of the equation of state is larger than $2/3$, then there is a transfer of energy from the fluid and the scalar field to the energy density of the scalar curvature. Thus, the scalar curvature, if present, has a dominant effect on the late evolution of the universe and eventually dominates over both the perfect fluid and the scalar field. The analysis in complemented with the case where $V$ is exponential and therefore the scalar field diverges to infinity.

gr-qc↗

arXiv2019

Effective field description of the Anton-Schmidt cosmic fluid

The effective theory of the Anton-Schmidt cosmic fluid within the Debye approximation is investigated. In this picture, the universe is modeled out by means of a medium without cosmological constant. In particular, the Anton-Schmidt representation of matter describes the pressure of crystalline solids under deformations imposed by isotropic stresses. The approach scheme is related to the fact that the universe deforms under the action of the cosmic expansion itself. Thus, we frame the dark energy term as a function of scalar fields and obtain the corresponding dark energy potential $V(φ)$. Different epochs of the universe evolution are investigated in terms of the evolution of $φ$. We show how the Anton-Schmidt equation of state is capable of describing both late and early epochs of cosmic evolution. Finally, numerical bounds on the Anton-Schmidt model with $n=-1$ are derived through a Markov Chain Monte Carlo analysis on the combination of data coming from type Ia Supernovae, observations of Hubble parameter and baryon acoustic oscillations. Statistical comparison with the $Λ$CDM model is performed by the AIC and BIC selection criteria. Results are in excellent agreement with the low-redshift data. A further generalization of the model is presented to satisfy the theoretical predictions at early-stage cosmology.

gr-qc↗

arXiv2018

Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles

We use nonsmooth critical point theory and the theory of geodesics with obstacle to show a multiplicity result about orthogonal geodesic chords in a Riemannian manifold (with boundary) which is homeomorphic to an $N$-disk. This applies to brake orbits in a potential well of a natural Hamiltonian system, providing a further step towards the proof of a celebrated conjecture by Seifert.

math.DS↗