Armaza, C., Hojman, S. A., Koch, B., & Zalaquett, N. (2016). On the possibility of nongeodesic motion of massless spinning tops. Class. Quantum Gravity, 33(14), 18 pp.
Abstract: The motion of spinning massless particles in gravitationally curved backgrounds is revisited by considering new types of constraints. Those constraints guarantee zero mass (P μP μ= 0) and they allow for the possibility of trajectories which are not simply null geodesics. To exemplify this previously unknown possibility, the equations of motion are solved for radial motion in Schwarzschild background. It is found that the particle experiences a spininduced energy shift, which is proportional to the Hawking temperature of the black hole background.

Asenjo, F. A., & Hojman, S. A. (2017). Birefringent light propagation on anisotropic cosmological backgrounds. Phys. Rev. D, 96(4), 12 pp.
Abstract: Exact electromagnetic wave solutions to Maxwell equations on anisotropic Bianchi I cosmological spacetime backgrounds are studied. The waves evolving on Bianchi I spacetimes exhibit birefringence (associated with linear polarization) and dispersion. The particular case of a vacuumdominated anisotropic Universe, which reproduces a FriedmannRobertsonWalker Universe (for late times)while, for earlier times, it matches a Kasner Universeis studied. The electromagnetic waves do not, in general, follow null geodesics. This produces a modification of the cosmological redshift, which is then dependent on light polarization, its dispersion, and its nonnull geodesic behavior. New results presented here may help to tackle some issues related to the “horizon” problem.

Asenjo, F. A., & Hojman, S. A. (2017). Class of Exact Solutions for a Cosmological Model of Unified Gravitational and Quintessence Fields. Found. Phys., 47(7), 887–896.
Abstract: A new approach to tackle Einstein equations for an isotropic and homogeneous FriedmannRobertsonWalker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these equations. This solution determines the quintessence potential uniquely and it differs from solutions which have been used to study inflation previously. It relays on a unification of geometry and dark matter implemented through the definition of a functional relation between the scale factor of the Universe and the quintessence field. For a positive curvature Universe, this solution produces perpetual accelerated expansion rate of the Universe, while the Hubble parameter increases abruptly, attains a maximum value and decreases thereafter. The behavior of this cosmological solution is discussed and its main features are displayed. The formalism is extended to include matter and radiation.

Asenjo, F. A., & Hojman, S. A. (2017). Do electromagnetic waves always propagate along null geodesics? Class. Quantum Gravity, 34(20), 12 pp.
Abstract: We find exact solutions to Maxwell equations written in terms of fourvector potentials in nonrotating, as well as in Gdel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled secondorder differential equations for combinations of the components of the fourvector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in nonrotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on Gdel and Kerr spacetimes do not exhibit that behavior.

Asenjo, F. A., & Hojman, S. A. (2017). New nonlinear modified massless KleinGordon equation. Eur. Phys. J. C, 77(11), 5 pp.
Abstract: The massless KleinGordon equation on arbitrary curved backgrounds allows for solutions which develop “tails” inside the light cone and, therefore, do not strictly follow null geodesics as discovered by DeWitt and Brehme almost 60 years ago. A modification of the massless KleinGordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved spacetimes. This new equation is derived from a Lagrangian which exhibits currentcurrent interaction. Its nonlinearity is due to a selfcoupling term which is related to the quantum mechanical Bohm potential.

Asenjo, F. A., & Hojman, S. A. (2019). Correspondence between dark energy quantum cosmology and Maxwell equations. Eur. Phys. J. C, 79(9), 5 pp.
Abstract: A FriedmannRobertsonWalker cosmology with dark energy can be modelled using a quintessence field. That system is equivalent to a relativistic particle moving on a twodimensional conformal spacetime. When the quintessence behaves as a free massless scalar field in a Universe with cosmological constant, the quantized version of that theory can lead to a supersymmetric Majorana quantum cosmology. The purpose of this work is to show that such quantum cosmological model corresponds to the Maxwell equations for electromagnetic waves propagating in a medium with specific values for its relative permittivity and relative permeability. The form of those media parameters are calculated, implying that a Majorana quantum cosmology can be studied in an analogue electromagnetic system.

Asenjo, F. A., & Hojman, S. A. (2020). Casimir force induced by electromagnetic wave polarization in Kerr, Godel and BianchiI spacetimes. Eur. Phys. J. C, 80(11), 7 pp.
Abstract: Electromagnetic waves propagation on either rotating or anisotropic spacetime backgrounds (such as Kerr and Gödel metrics, or Bianchi�I metric) produce a reduction of the magnitude of Casimir forces between plates. These
curved spacetimes behave as chiral or birefringent materials producing dispersion of electromagnetic waves, in such a way that right� and left�circularly polarized light waves propagate with different phase velocities. Results are explicitly calculated for discussed cases. The difference on the wavevectors of the two polarized electromagnetic waves produces an abatement of a Casimir force which depends on the interaction between the polarization of electromagnetic
waves and the properties of the spacetime.

Asenjo, F. A., & Hojman, S. A. (2021). Accelerating solutions to diffusion equation. Eur. Phys. J. Plus., 136(6), 677.
Abstract: We report accelerating diffusive solutions to the diffusion equation with a constant diffusion tensor. The maximum values of the diffusion density evolve in an accelerating fashion described by Airy functions. We show the diffusive accelerating behavior for onedimensional systems, as well as for a general threedimensional case. We also construct a modulated modified form of the diffusion solution that retains the accelerating features.

Asenjo, F. A., & Hojman, S. A. (2021). Nondiffracting gravitational waves. Eur. Phys. J. C, 81(1), 98.
Abstract: It is proved that accelerating nondiffracting gravitational Airy wavepackets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for nonaccelerating nondiffracting gravitational wavepackets.

Asenjo, F. A., & Hojman, S. A. (2021). Reply to Comment on 'Do electromagnetic waves always propagate along null geodesics?' Reply. Class. Quantum Gravity, 38(23), 238002.
Abstract: A reply to the previous article commenting on nongeodesical propagation of electromagnetic fields on gravitational backgrounds and the eikonal limit are presented.

Asenjo, F. A., & Hojman, S. A. (2022). Lightlike propagation of selfinteracting KleinGordon fields in cosmology. Eur. Phys. J. Plus., 137(1), 20.
Abstract: It is showed that complex scalar fields with a selfinteraction potential may propagate along null geodesics on isotropic flat FriedmannLemaitreRobertsonWalker universes with different timedependent scale factors. This effect appears for certain kinds of selfinteractions only, for different forms of potentials, and even for the massive case.

Asenjo, F. A., Erices, C., Gomberoff, A., Hojman, S. A., & Montecinos, A. (2017). Differential geometry approach to asymmetric transmission of light. Opt. Express, 25(22), 26405–26416.
Abstract: In the last ten years, the technology of differential geometry, ubiquitous in gravitational physics, has found its place in the field of optics. It has been successfully used in the design of optical metamaterials through a technique now known as “transformation optics.” This method, however, only applies for the particular class of metamaterials known as impedance matched, that is, materials whose electric permittivity is equal to their magnetic permeability. In that case, the material may be described by a spacetime metric. In the present work we will introduce a generalization of the geometric methods of transformation optics to situations in which the material is not impedance matched. In such situations, the material or more precisely, its constitutive tensorwill not be described by a metric only. We bring in a second tensor, with the local symmetries of the Weyl tensor, the “Wtensor.” In the geometric optics approximation we show how the properties of the Wtensor are related to the asymmetric transmission of the material. We apply this feature to the design of a particularly interesting set of asymmetric materials. These materials are birefringent when light rays approach the material in a given direction, but behave just like vacuum when the rays have the opposite direction with the appropriate polarization (or, in some cases, independently of the polarization). (C) 2017 Optical Society of America

Asenjo, F. A., Hojman, S. A., MoyaCessa, H. M., & SotoEguibar, F. (2021). Propagation of light in linear and quadratic GRIN media: The Bohm potential. Opt. Commun., 490, 126947.
Abstract: It is shown that field propagation in linear and quadratic gradientindex (GRIN) media obeys the same rules of free propagation in the sense that a field propagating in free space has a (mathematical) form that may be exported to those particular GRIN media. The Bohm potential is introduced in order to explain the reason of such behavior: it changes the dynamics by modifying the original potential . The concrete cases of two different initials conditions for each potential are analyzed.

Asenjo, F. A., Hojman, S. A., MoyaCessa, H. M., & SotoEguibar, F. (2022). Supersymmetric relativistic quantum mechanics in timedomain. Phys. Lett. A, 450, 128371.
Abstract: A supersymmetric relativistic quantum theory in the temporal domain is developed for bispinor fields satisfying the Dirac equation. The simplest timedomain supersymmetric theory can be postulated for fields with timedependent mass, showing an equivalence with the bosonic supersymmetric theory in timedomain. Solutions are presented and they are used to produce probability oscillations between mass states. As an application of this idea, we study the twoneutrino oscillation problem, showing that flavour state oscillations may emerge from the supersymmetry originated by the timedependence of the unique mass of the neutrino.(c) 2022 Elsevier B.V. All rights reserved.

Contreras, M., & Hojman, S. A. (2014). Option pricing, stochastic volatility, singular dynamics and constrained path integrals. Physica A, 393, 391–403.
Abstract: Stochastic volatility models have been widely studied and used in the financial world. The Heston model (Heston, 1993) [7] is one of the best known models to deal with this issue. These stochastic volatility models are characterized by the fact that they explicitly depend on a correlation parameter p which relates the two Brownian motions that drive the stochastic dynamics associated to the volatility and the underlying asset. Solutions to the Heston model in the context of option pricing, using a path integral approach, are found in Lemmens et al. (2008) [21] while in Baaquie (2007,1997) [12,13] propagators for different stochastic volatility models are constructed. In all previous cases, the propagator is not defined for extreme cases rho = +/ 1. It is therefore necessary to obtain a solution for these extreme cases and also to understand the origin of the divergence of the propagator. In this paper we study in detail a general class of stochastic volatility models for extreme values rho = +/ 1 and show that in these two cases, the associated classical dynamics corresponds to a system with second class constraints, which must be dealt with using Dirac's method for constrained systems (Dirac, 1958,1967) [22,23] in order to properly obtain the propagator in the form of a Euclidean Hamiltonian path integral (Henneaux and Teitelboim, 1992) [25]. After integrating over momenta, one gets an Euclidean Lagrangian path integral without constraints, which in the case of the Heston model corresponds to a path integral of a repulsive radial harmonic oscillator. In all the cases studied, the price of the underlying asset is completely determined by one of the second class constraints in terms of volatility and plays no active role in the path integral. (C) 2013 Elsevier B.V. All rights reserved.

Hojman, S. A. (2014). Origin of conical dispersion relations. Rev. Mex. Fis., 60(5), 336–339.
Abstract: A mechanism that produces conical dispersion relations is presented. A Kronig Penney one dimensional array with two different strengths delta function potentials gives rise to both the gap closure and the dispersion relation observed in graphene and other materials. The Schrodinger eigenvalue problem is locally invariant under, the infinite dimensional Virasoro algebra near conical dispersion points in reciprocal space, thus suggesting a possible relation to string theory.

Hojman, S. A. (2015). Construction of Lagrangian and Hamiltonian structures starting from one constant of motion. Acta Mech., 226(3), 735–744.
Abstract: The problem of the construction of Lagrangian and Hamiltonian structures starting from two firstorder equations of motion is presented. This approach requires the knowledge of one (time independent) constant of motion for the dynamical system only. The Hamiltonian and Lagrangian structures are constructed, the HamiltonJacobi equation is then written and solved, and the second (time dependent) constant of the motion for the problem is explicitly exhibited.

Hojman, S. A., & Asenjo, F. A. (2013). Can gravitation accelerate neutrinos? Class. Quantum Gravity, 30(2), 10 pp.
Abstract: The Lagrangian equations of motion for massive spinning test particles (tops) moving on a gravitational background using general relativity are presented. The paths followed by tops are nongeodesic. An exact solution for the motion of tops on a Schwarzschild background which allows for superluminal propagation of tops is studied. It is shown that the solution becomes relevant for particles with small masses, such as neutrinos. This general result is used to calculate the necessary condition to produce superluminal motion in part of the trajectory of a small mass particle in a weak gravitational field. The condition for superluminal motion establishes a relation between the mass, energy and total angular momentum of the particle.

Hojman, S. A., & Asenjo, F. A. (2015). Supersymmetric Majorana quantum cosmologies. Phys. Rev. D, 92(8), 7 pp.
Abstract: The Einstein equations for an isotropic and homogeneous FriedmannRobertsonWalker universe in the presence of a quintessence scalar field are shown to be described in a compact way, formally identical to the dynamics of a relativistic particle moving on a twodimensional spacetime. The correct Lagrangian for the system is presented and used to construct a spinor quantum cosmology theory using Breit's prescription. The theory is supersymmetric when written in the Majorana representation. The spinor field components interact through a potential that correlates the spacetime metric and the quintessence. An exact supersymmetric solution for k = 0 case is exhibited. This quantum cosmology model may be interpreted as a theory of interacting universes.

Hojman, S. A., & Asenjo, F. A. (2016). Comment on “Highly relativistic spingravity coupling for fermions”. Phys. Rev. D, 93(2), 4 pp.
Abstract: We exhibit difficulties of different sorts which appear when using the MathissonPapapetrou equations, in particular in the description of highly relativistic particles presented in R. Plyatsko and M. Fenyk [Phys. Rev. D 91, 064033 (2015)]. We compare some results of this theory and of the aforementioned work with the ones obtained using a Lagrangian formulation for massive spinning particles and show that the issues mentioned in the preceding sentence do not appear in the Lagrangian treatment.
