A scale invariant, Weyl geometric, Lagrangian approach to cosmology is explored, with a a scalar field φ of (scale) weight −1 as a crucial ingredient besides classical matter (Tann 1998, Drechsler 1999). For a particularly simple class of Weyl geometric models (called Einstein-Weyl universes) the Klein-Gordon equation for φ is explicitly solvable. In this case the energy-stress tensor of the sc...

This equation has been of interest in general relativity in various contexts, as well as some other fields of theoretical physics, for over twenty years. One derivation was given by one of us and Charles Boyer[1] in 1982, showing that it determines all self-dual, vacuum solutions of the Einstein field equations which admit a rotational Killing vector. (The description of that metric is given in...

We obtain the equation of state of interacting alpha matter and the critical temperature of Bose-Einstein condensation of alpha particles within an effective scalar field theory. We start from a non-relativistic model of uniform alpha matter interacting with attractive two-body and repulsive three-body potentials and reformulate this model as a O(2) symmetric scalar φ6 field theory with negativ...

We generalize the well-known lower estimates for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold proved by Th. Friedrich (1980) and O. Hijazi (1986, 1992). The special solutions of the Einstein-Dirac equation constructed recently by Friedrich/Kim are examples for the limiting case of these inequalities. The discussion of the limiting case of these estimates yiel...

The Helmholtz equation for symmetric, traceless, second-rank tensor fields in three-dimensional flat space is solved in spherical and cylindrical coordinates by separation of variables making use of the corresponding spin-weighted harmonics. It is shown that any symmetric, traceless, divergenceless second-rank tensor field that satisfies the Helmholtz equation can be expressed in terms of two s...

The condition for pressure isotropy, for spherically symmetric gravitational fields with charged and uncharged matter, is reduced to a recurrence equation with variable, rational coefficients. This difference equation is solved in general using mathematical induction leading to an exact solution to the Einstein field equations which extends the isotropic model of John and Maharaj. The metric fu...

Using the mean-field Gross-Pitaevskii (GP) equation we study the evolution of Josephson current in a repulsive Bose-Einstein condensate in an optical-lattice potential initiated by a sudden displacement of the trapping potential. Similarly, we also study the evolution of quantum tunneling in a double-well potential in one and three dimensions initiated by a trap displacement leading to a period...

It has previously been shown that the Einstein equation can be derived from the requirement that the Clausius relation dS=deltaQ/T hold for all local acceleration horizons through each spacetime point, where is one-quarter the horizon area change in Planck units and deltaQ and T are the energy flux across the horizon and the Unruh temperature seen by an accelerating observer just inside the hor...

An example is given of a plane topological defect solution of linearized Einstein-Cartan (EC) field equation representing a cosmic wall boundary of spinning matter. The source of Cartan torsion is composed of two orthogonal lines of static polarized spins bounded by the cosmic plane wall. The KopczyńskiObukhov Tresguerres (KOT) spin fluid stress-energy current coincides with thin planar matter ...

We present a general numerical method for investigating prescribed Ricci curvature problems on toric Kähler manifolds. This method is applied to two generalisations of Einstein metrics, namely Ricci solitons and quasi-Einstein metrics. We begin by recovering the Koiso–Cao soliton and the Lü–Page–Pope quasi-Einstein metrics on CP2]CP (in both cases the metrics are known explicitly). We also find...