Abstract: It is known that a nonlinear Schrodinger equation describes the self-modulation of a large amplitude circularly polarized wave in relativistic electron-positron plasmas in the weakly and strongly magnetized limits. Here, we show that such an equation can be written as a modified second Painleve equation, producing accelerated propagating wave solutions for those nonlinear plasmas. This solution even allows the plasma wave to reverse its direction of propagation. The acceleration parameter depends on the plasma magnetization. This accelerating solution is different to the usual soliton solution propagating at constant speed.

Abstract: The ideal magnetohydrodynamic theorem on the conservation of the magnetic connections between plasma elements is generalized to relativistic plasmas in curved spacetime. The connections between plasma elements, which are established by a covariant connection equation, display a particularly complex structure in curved spacetime. Nevertheless, it is shown that these connections can be interpreted in terms of magnetic field lines alone by adopting a 3 + 1 foliation of spacetime.

Abstract: We analytically explore the effects of the gravitational electromotive force on magnetic reconnection around Schwarzschild black holes through a generalized general-relativistic magnetohydrodynamic model that retains two-fluid effects. It is shown that the gravitational electromotive force can couple to collisionless two-fluid effects and drive magnetic reconnection. This is allowed by the departure from quasineutrality in curved spacetime, which is explicitly manifested as the emergence of an effective resistivity in Ohm's law. The departure from quasineutrality is owed to different gravitational pulls experienced by separate parts of the current layer. This produces an enhancement of the reconnecion rate due to purely gravitational effects.

Abstract: A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann-Robertson-Walker 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.

Abstract: The massless Klein-Gordon 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 Klein-Gordon equation is presented, which always exhibits null geodesic propagation of waves on arbitrary curved space-times. This new equation is derived from a Lagrangian which exhibits current-current interaction. Its non-linearity is due to a self-coupling term which is related to the quantum mechanical Bohm potential.

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.

Abstract: It is proved that accelerating nondiffracting gravitational Airy wave-packets are solutions of linearized gravity. It is also showed that Airy functions are exact solutions to Einstein equations for non-accelerating nondiffracting gravitational wave-packets.

Abstract: New localized structured solutions for the three-dimensional linear heat (diffusion) equation are presented. These new solutions are written in terms of Airy functions. They are constructed as wave packet-like structures formed by a superposition of Bessel functions through the introduction of spectral functions. These diffusive solutions accelerate along their propagation direction, while in the plane orthogonal to it, they retain their confined structure. These heat (diffusion) densities retain a complete localized form in space as they propagate, and may be considered the heat analogue of Airy light bullets.

Abstract: It is shown that any cosmological anisotropic model produces supersymmetric theories for both massless scalar and electromagnetic (abelian) fields. This supersymmetric theory is the time-domain analogue of a supersymmetric quantum mechanics algebra theory. In this case, the variations of the anisotropic scale factors of the Universe are responsible for triggering the supersymmetry. For scalar fields, the superpartner fields evolve in two different cosmological scenarios (Universes). On the other hand, for propagating electromagnetic fields, supersymmetry is manifested through its polarization degrees of freedom in one Universe. In this case, polarization degrees of freedom of electromagnetic waves, which are orthogonal to its propagation direction, become superpartners from each other. This behavior can be measured, for example, through the rotation of the plane of polarization of cosmological light.

Abstract: Using a generally covariant electrovortic (magnetofluid) formalism for relativistic plasmas, the dynamical evolution of a generalized vorticity (a combination of the magnetic and kinematic parts) is studied in a cosmological context. We derive macroscopic vorticity and magnetic field structures that can emerge in spatial equilibrium configurations of the relativistic plasma. These fields, however, evolve in time. These magnetic and velocity fields, self-consistently sustained in a plasma with arbitrary thermodynamics, constitute a diamagnetic state in the expanding universe. In particular, we explore a special class of magnetic and velocity field structures supported by a plasma in which the generalized vorticity vanishes. We derive a highly interesting characteristic of such “superconductor-like” fields in a cosmological plasmas in the radiation era in the early universe. In that case, the fields grow proportional to the scale factor, establishing a deep connection between the expanding universe and the primordial magnetic fields.