arXiv subjects

Alberto Saa

Publications and source records attributed to Alberto Saa.

At least 73 records · Page 4Linked to original sources

arXiv2007

Quasinormal mode characterization of evaporating mini black holes

According to recent theoretical developments, it might be possible to produce mini black holes in the high energy experiments in the LHC at CERN. We propose here a model based on the $n$-dimensional Vaidya metric in double null coordinates for these decaying black holes. The associated quasinormal modes are considered. It is shown that only in the very last instants of the evaporation process the stationary regime for the quasinormal modes is broken, implying specific power spectra for the perturbations around these mini black-holes. From scattered fields one could recover, in principle, the black hole parameters as well as the number of extra dimensions. The still mysterious final fate of such objects should not alter significantly our main conclusions.

gr-qc↗

arXiv2007

N-dimensional Vaidya metric with cosmological constant in double-null coordinates

A recently proposed approach to the construction of the Vaidya metric in double-null coordinates for generic mass functions is extended to the $n$-dimensional $(n>2)$ case and to allow the inclusion of a cosmological constant. The approach is based on a qualitative study of the null-geodesics, allowing the description of light-cones and revealing many features of the underlying causal structure. Possible applications are illustrated by explicit examples. Some new exact solutions are also presented and discussed. The results presented here can simplify considerably the study of spherically symmetric gravitational collapse and mass accretion in arbitrary dimensions.

gr-qc↗

arXiv2007

A note on a third order curvature invariant in static spacetimes

We consider here the third order curvature invariant $I=R_{μνρσ;δ}R^{μνρσ;δ}$ in static spacetimes ${\cal M}=R\timesΣ$ for which $Σ$ is conformally flat. We evaluate explicitly the invariant for the $N$-dimensional Majumdar-Papapetrou multi black-holes solution, confirming that $I$ does indeed vanish on the event horizons of such black-holes. Our calculations show, however, that solely the vanishing of $I$ is not sufficient to locate an event horizon in non-spherically symmetric spacetimes. We discuss also some tidal effects associated to the invariant $I$.

gr-qc↗

arXiv2007

Homogeneous cosmologies and the Maupertuis-Jacobi principle

A recent work showing that homogeneous and isotropic cosmologies involving scalar fields are equivalent to the geodesics of certain effective manifolds is generalized to the non-minimally coupled and anisotropic cases. As the Maupertuis-Jacobi principle in classical mechanics, such result permits us to infer some dynamical properties of cosmological models from the geometry of the associated effective manifolds, allowing us to go a step further in the study of cosmological dynamics. By means of some explicit examples, we show how the geometrical analysis can simplify considerably the dynamical analysis of cosmological models.

gr-qc↗

arXiv2007

Non-Minimally Coupled Cosmology as Geodesic Motion

Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.

gr-qc↗

arXiv2006

Quasinormal modes for the Vaidya metric

We consider here scalar and electromagnetic perturbations for the Vaidya metric in double-null coordinates. Such an approach allows one to go a step further in the analysis of quasinormal modes for time-dependent spacetimes. Some recent results are refined, and a new non-stationary behavior corresponding to some sort of inertia for quasinormal modes is identified. Our conclusions can enlighten some aspects of the wave scattering by black holes undergoing some mass accretion processes.

gr-qc↗

arXiv2006

Extracellular polymeric bacterial coverages as minimal area surfaces

Surfaces formed by extracellular polymeric substances enclosing individual and some small communities of {\it Acidithiobacillus ferrooxidans} on plates of hydrophobic silicon and hydrophilic mica are analyzed by means of atomic force microscopy imaging. Accurate nanoscale descriptions of such coverage surfaces are obtained. The good agreement with the predictions of a rather simple but realistic theoretical model allows us to conclude that they correspond, indeed, to minimal area surfaces enclosing a given volume associated with the encased bacteria. This is, to the best of our knowledge, the first shape characterization of the coverage formed by these biomolecules, with potential applications to the study of biofilms.

physics.bio-ph↗

arXiv2005

The radiation of a uniformly accelerated charge is beyond the horizon: a simple derivation

We show, by exploring some elementary consequences of the covariance of Maxwell's equations under general coordinate transformations, that, despite inertial observers can indeed detect electromagnetic radiation emitted from a uniformly accelerated charge, comoving observers will see only a static electric field. This simple analysis can help understanding one of the most celebrated paradoxes of last century.

physics.class-ph↗

arXiv2005

Volume elements and torsion

We reexamine here the issue of consistency of minimal action formulation with the minimal coupling procedure (MCP) in spaces with torsion. In Riemann-Cartan spaces, it is known that a proper use of the MCP requires that the trace of the torsion tensor be a gradient, $T_μ=\partial_μθ$, and that the modified volume element $τ_θ= e^θ\sqrt{g} dx^1\wedge...\wedge dx^n $ be used in the action formulation of a physical model. We rederive this result here under considerably weaker assumptions, reinforcing some recent results about the inadequacy of propagating torsion theories of gravity to explain the available observational data. The results presented here also open the door to possible applications of the modified volume element in the geometric theory of crystalline defects.

gr-qc↗

arXiv2004

Non-minimal coupling, exponential potentials and the $w<-1$ regime of dark energy

Recent observations and theoretical considerations have motivated the study of models for dark energy with equation of state characterized by a parameter $w=p/ρ<-1$. Such models, however, are usually believed to be inviable due to their instabilities against classical perturbations or potentially catastrophic vacuum decays. In this paper, we show that a simple quintessential model with potential $V(ϕ)=Ae^{-σϕ}$ and a gravitational coupling of the form $(1+|ξ|ϕ^2)R$ can exhibit, for large sets of initial conditions, asymptotic de Sitter behavior with $w<-1$ regimes. Nevertheless, the model is indeed stable at classical and quantum level.

astro-ph↗

arXiv2004

Semi-analytical approach for the Vaidya metric in double-null coordinates

We reexamine here a problem considered in detail before by Waugh and Lake: the solutions of spherically symmetric Einstein's equations with a radial flow of unpolarized radiation (the Vaidya metric) in double-null coordinates. This problem is known to be not analytically solvable, the only known explicit solutions correspond to the constant mass case (Schwarzschild solution in Kruskal-Szekeres form) and the linear and exponential mass functions originally discovered by Waugh and Lake. We present here a semi-analytical approach that can be used to discuss some qualitative and quantitative aspects of the Vaidya metric in double-null coordinates for generic mass functions. We present also a new analytical solution corresponding to $(1/v)$-mass function.

gr-qc↗

arXiv2004

On the viability of local criteria for chaos

We consider here a recently proposed geometrical criterion for local instability based on the geodesic deviation equation. Although such a criterion can be useful in some cases, we show here that, in general, it is neither necessary nor sufficient for the occurrence of chaos. To this purpose, we introduce a class of chaotic two-dimensional systems with Gaussian curvature everywhere positive and, hence, locally stable. We show explicitly that chaotic behavior arises from some trajectories that reach certain non convex parts of the boundary of the effective Riemannian manifold. Our result questions, once more, the viability of local, curvature-based criteria to predict chaotic behavior.

gr-qc↗

arXiv2004

Conformal quantum effects and the anisotropic singularities of scalar-tensor theories of gravity

We show that the inclusion of a term $C_{abcd}C^{abcd}$ in the action can remove the recently described anisotropic singularity occurring on the hypersurface $F(ϕ)=0$ of scalar-tensor theories of gravity of the type $$ S=\int d^4x \sqrt{-g} {F(ϕ)R - \partial_aϕ\partial^aϕ-2V(ϕ)}, $$ preserving, by construction, all of their isotropic solutions. We show that, in principle, a higher order term of this type can arise from considerations about the renormalizability of the semiclassical approach to the theory. Such result brings again into consideration the quintessential models recently proposed based in a conformally coupled scalar field ($F(ϕ)=1-{1/6}ϕ^2$) with potential $V(ϕ)=\frac{m}{2}ϕ^2 -\fracΩ{4}ϕ^4$, that have been discharged as unrealistic precisely by their anisotropic instabilities on the hypersurface $F(ϕ)=0$.

gr-qc↗

arXiv2004

Quantum effects and superquintessence in the new age of precision cosmology

Recent observations of Type Ia supernova at high redshifts establish that the dark energy component of the universe has (a probably constant) ratio between pressure and energy density $w=p/ρ=-1.02(^{+0.13}_{-0.19})$. The conventional quintessence models for dark energy are restricted to the range $-1\le w < 0$, with the cosmological constant corresponding to $w=-1$. Conformally coupled quintessence models are the simplest ones compatible with the marginally allowed superaccelerated regime ($w<-1$). However, they are known to be plagued with anisotropic singularities. We argue here that the extension of the classical approach to the semiclassical one, with the inclusion of quantum counterterms necessary to ensure the renormalization, can eliminate the anisotropic singularities preserving the isotropic behavior of conformally coupled superquintessence models. Hence, besides of having other interesting properties, they are consistent candidates to describe the superaccelerated phases of the universe compatible with the present experimental data.

gr-qc↗

arXiv2003

Dynamical study of the singularities of gravity in the presence of non-minimally coupled scalar fields

We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action $$ S=\int d^4x \sqrt{-g}{F(ϕ)R - \partial_aϕ\partial^aϕ-2V(ϕ)}, $$ with general $F(ϕ)$ and $V(ϕ)$. The dynamical nature of each singularity is elucidated, and we show that both are, in general, dynamically unavoidable, reinforcing the unstable character of previous isotropic and homogeneous cosmological results obtained for the conformal coupling case.

gr-qc↗

arXiv2003

Stability properties and asymptotics for N non-minimally coupled scalar fields cosmology

We consider here the dynamics of some homogeneous and isotropic cosmological models with $N$ interacting classical scalar fields non-minimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for one and two scalar fields. We show that a Lyapunov function can be constructed under certain conditions for a large class of models, suggesting that chaotic behavior is ruled out for them. Typical solutions tend generically to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic results obtained for the one field model remain valid. In particular, we confirm that, for large times and a vanishing cosmological constant, even in the presence of the extra scalar fields, the universe tends to an infinite diluted matter dominated era.

gr-qc↗

arXiv2002

On the singularities of gravity in the presence of non-minimally coupled scalar fields

We investigate the robustness of some recent results obtained for homogeneous and isotropic cosmological models with conformally coupled scalar fields. For this purpose, we investigate anisotropic homogeneous solutions of the models described by the action $$ S=\int d^4x \sqrt{-g}\left\{F(ϕ)R - \partial_aϕ\partial^aϕ-2V(ϕ) \right\}, $$ with general $F(ϕ)$ and $V(ϕ)$. We show that such a class of models leads generically to geometrical singularities if for some value of $ϕ$, $F(ϕ)=0$, rendering previous cosmological results obtained for the conformal coupling case highly unstable. We show that stable models can be obtained for suitable choices of $F(ϕ)$ and $V(ϕ)$. Implications for other recent results are also discussed.

gr-qc↗

arXiv2000

A geometrical action for dilaton gravity

We study the gravitational interaction involving the dilaton and the anti-symmetrical $B_{μν}$ fields that arises in the low-energy limit of string theory. It is shown that such interaction can be derived from a geometrical action principle, with the scalar of curvature of a non-Riemannian, but {\em metric-compatible}, connection as the lagrangian, and with a non-parallel volume-element. This action is contrasted with the recently proposed geometrical action for the 4-dimensional axi-dilaton gravity.

hep-th↗