arXiv subjects

O. Santillan

Publications and source records attributed to O. Santillan.

9 recordsLinked to original sources

arXiv2026

Corrections of the GR eikonal limit by a class of renormalizable gravity models

In the present work, the scattering between a light scalar particle $ϕ$ and a heavy scalar $σ$ in the eikonal limit is considered, for gravity scenarios containing higher order derivatives, such as the ones studied in \cite{stelle1}-\cite{modesto4}. It is suggested that if one of the new gravity scales introduced in the higher order action is smaller than the Planck mass, for instance of the order of $M_{GUT}\sim 10^{15}$ GeV, the functional form of the GR eikonal formulas appears changed by a factor. However, in this situation, the conditions for the eikonal approximation to hold has to be revised, this issue is analyzed in the text. The statements of the present work should be taken with a grain of salt, as the Schwarzschild radius for these polynomials theories is not yet established. The results presented here, in our opinion, are in agreement with the suppression of corrections to GR pointed out in \cite{brandhuber}, \cite{fradkin} and \cite{deser} for the Stelle gravity. The next to leading order approximation and part of the seagull diagrams are estimated. Different to the GR case, this order generically is non vanishing. An explicit regularization scheme is presented, based on Riesz and Hadamard procedures. The need of a regularization is partially expected, as the inclusion of small energy fluctuations may spoil the eikonal approximation.

gr-qc↗

arXiv2023

Peculiarities for domain walls in Taub coordinates

In the present letter the infinite domain wall geometry in GR \cite{vilenkin1}-\cite{ipser} is reconsidered in Taub coordinates \cite{taub}. The use of these coordinates makes explicit that the regions between the horizons and the wall and the outer ones are flat. By use of these coordinates, it is suggested that points inside the horizon and outside never communicate each other. The wall is seen on the left and the right side as contracting and expanding portions of spheres and a plane singularity, which is the imprint the contracting and expanding domain wall. Particles of each region will never reach this imprint. In addition, at some point during the evolution of the system, four curious holes inside the space time appear, growing at the speed of light. This region is not parameterized by the standard Taub coordinates, and the boundary of this hole adsorbs all the particles that intersect it. The boundary of these holes are composed by points which in the coordinates of \cite{vilenkin1}-\cite{ipser} are asymptotic, in the sense that they correspond to trajectories tending to infinite values of the time or space like coordinates, while the proper time elapsed for the travel is in fact finite. This is not paradoxical, as the coordinates \cite{vilenkin1}-\cite{ipser} are not to be identified with the true lengths or proper time on the space time. The correct interpretation of the boundary is particularity relevant when studying scattering of quantum fields approaching the domain wall. A partial analysis about this issue is done in the last section.

gr-qc↗

arXiv2020

Electric and magnetic axion quark nuggets, their stability and their detection

The present work studies the dynamics of axion quark nuggets introduced in \cite{zhitnitsky} and exploited in the works \cite{zhitnitsky2}-\cite{zhitnitsky13}. The new feature considered here is the possibility that these nuggets become ferromagnetic. This possibility was pointed out in \cite{tatsumi}, although ferromagnetism may also take place due some anomaly terms found in \cite{son}-\cite{son2}. The purpose of the present letter however, is not to give evidence in favor or against these statements. Instead, it is focused in some direct consequences of this ferromagnetic behavior, if it exists. The first is that the nugget magnetic field induces an electric field due to the axion wall, which may induce pair production by Schwinger effect. Depending on the value of the magnetic field, the pair production can be quite large. A critical value for such magnetic field at the surface of the nugget is obtained, and it is argued that the value of the magnetic field of \cite{tatsumi} is at the verge of stability and may induce large pair production. The consequences of this enhanced pair production may be unclear. It may indicate that the the nugget evaporates, but on the other hand it may be just an indication that the intrinsic magnetic field disappears and the nuggets evolves to a non magnetized state such as \cite{zhitnitsky}-\cite{zhitnitsky13}. The interaction of such magnetic and electric nugget with the troposphere of the earth is also analyzed. However, if the magnetic field does not decay before the actual universe, then this would lead to high energy electron flux due to its interaction with the electron gases of the Milky Way. This suggests that these magnetized quarks may be a considerably part of dark matter, but only if their hypothetical magnetic and electric fields are evaporated.

hep-ph↗

arXiv2018

The existence of smooth solutions in q-theories

The q-models are scenarios that may explain the smallness of the cosmological constant [1]-[7]. The vacuum in these theories is presented as a self-sustainable medium and include a new degree of freedom, the q-variable, which stablish the equilibrium of the quantum vacuum. In the present work, the Cauchy formulation for these models is studied. It has been already noted that there exist some limits where these theories are described by an F(R) model, which posses a well formulated Cauchy problem. This paper shows that the Cauchy problem is well posed even not reaching this limit. By use of some mathematical theorems about second order non linear systems, it is shown that these scenarios admit a smooth solution for at least a finite time when some specific type of initial conditions are imposed. Some technical conditions of [11] play an important role in this discussion.

gr-qc↗

arXiv2018

Gauss-Bonnet models with cosmological constant and non zero spatial curvature in $D=4$

In the present paper the possibility of eternal universes in Gauss-Bonnet theories of gravity in four dimensions is analysed. It is shown that, for zero spatial curvature and zero cosmological constant, if the coupling is such that $0<f'(ϕ)\leq c \exp(\frac{\sqrt{8}}{\sqrt{10}}ϕ)$, then there are solutions that are eternal. Similar conclusions are found when a cosmological constant turned on. These conclusions are not generalized for the case when the spatial curvature is present, but we are able to find some general results about the possible nature of the singularities. The presented results correct some dubious arguments in [54], although the same conclusions are reached. On the other hand, these past results are considerably generalized to a wide class of situations which were not considered in [54].

gr-qc↗

arXiv2017

The Newton constant and gravitational waves in some vector field adjusting mechanisms

As is well known, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant in the present era. An important aspect to analyze is the propagation of gravitational waves and the screening or enhancement of the Newton constant $G_N$ in these models. The problem is that the Lorentz symmetry breaking terms may induce an unacceptable value of the Newton constant $G_N$ or introduce longitudinal modes in the gravitational waves. Furthermore there may spoil the standard dispersion relation $ω=ck$. In [21] the authors have presented a model for which they suggest that the behavior of the gravitational constant is the correct one for asymptotic times. In the present work, an explicit checking is made and we finally agree with these claims. Furthermore, it is suggested that the gravitational waves are also well behaved for large times. In the process, some new models with the same behavior are obtained, thus enlarging the list of possible adjustment mechanisms.

gr-qc↗

arXiv2017

General aspects of Gauss-Bonnet models without potential in dimension four

In the present work, the isotropic and homogenous solutions with spatial curvature $k=0$ of four dimensional Gauss-Bonnet models are characterized. The main assumption is that the scalar field $ϕ$ which is coupled to the Gauss-Bonnet term has no potential [50]-[51]. Some singular and some eternal solutions are described. The evolution of the universe is given in terms of a curve $γ=(H(ϕ), ϕ)$ which is the solution of a polynomial equation $P(H^2, ϕ)=0$ with $ϕ$ dependent coefficients. In addition, it is shown that the initial conditions in these models put several restrictions on the evolution. For instance, an universe initially contracting will be contracting always for future times and an universe that is expanding was always expanding at past times. Thus, there are no cyclic cosmological solutions for this model. These results are universal, that is, independent on the form of the coupling $f(ϕ)$ between the scalar field and the Gauss-Bonnet term. In addition, a proof that at a turning point $\dotϕ\to0$ a singularity necessarily emerges is presented. This is valid unless the Hubble constant $H\to 0$ at this point. This proof is based on the Raychaudhuri equation for the model. The description presented here is in part inspired in the works [32]-[34]. However, the mathematical methods that are implemented are complementary of those in these references, and they may be helpful for study more complicated situations in a future.

gr-qc↗

arXiv2009

New Spin(7) holonomy metrics admiting G2 holonomy reductions and M-theory/IIA dualities

IAs is well known, when D6 branes wrap a special lagrangian cycle on a non compact CY 3-fold in such a way that the internal string frame metric is Kahler there exists a dual description, which is given in terms of a purely geometrical eleven dimensional background with an internal metric of $G_2$ holonomy. It is also known that when D6 branes wrap a coassociative cycle of a non compact $G_2$ manifold in presence of a self-dual two form strength the internal part of the string frame metric is conformal to the $G_2$ metric and there exists a dual description, which is expressed in terms of a purely geometrical eleven dimensional background with an internal non compact metric of Spin(7) holonomy. In the present work it is shown that any $G_2$ metric participating in the first of these dualities necessarily participates in one of the second type. Additionally, several explicit Spin(7) holonomy metrics admitting a $G_2$ holonomy reduction along one isometry are constructed. These metrics can be described as $R$-fibrations over a 6-dimensional Kahler metric, thus realizing the pattern Spin(7) $\to G_2\to$ (Kahler) mentioned above. Several of these examples are further described as fibrations over the Eguchi-Hanson gravitational instanton and, to the best of our knowledge, have not been previously considered in the literature.

hep-th↗

arXiv2002

Generalized Grassmann Algebras and its Connection to the Extended Supersymmetric Models

It is shown that the fermionic Heisenberg-Weyl algebra with 2N=D fermionic generators is equivalent to the generalized Grassmann algebra with two fractional generators. The 2,3 and 4 dimensional Heisenberg - Weyl algebra is explicitly given in terms of the fractional generators. These algebras are used for the formulation of the N=2,3,4 extended supersymmetry. As an example we reformulate the Lax approach of the supersymmetric Korteweg - de Vries equation in terms of the generators of the generalized Grassmann algebra.

hep-th↗