The existence of a fundamental length in general relativity, the Planck length, may lead to a breakdown of Lorentz invariance of the vacuum. The third quantization introduces renormalization fields of negative energy which do not interact with matter however. This revision leads to a measurable modification of the Casimir effect and can, at least in principle, lead to an eternal universe.

A manifestly covariant extension of the Low-Sturrock Lagrangian is formulated and its invariance properties are investigated. In particular we clarify the meaning of particle displacements which play the role of the configuration variables of the variational principle in general relativity. As a consequence of the variational principle we derive a conservation law for Whitham's wave-vector action in the WKB approximation.

We introduce A Weyl integrable space-time as a consequence of a dynamical process. We study the particular case of a vector field non-minimally coupled to gravity. The consequences for cosmology are considered. We find that it is possible to connect one riemannian region of space-time with another riemannian region of space-time by a series of Weyl integrable domains.

Primordial nucleosynthesis is used in order to investigate the possible cosmological dependence of the weak interaction. Specifically we consider the time dependence of the ratio of the vector and the axial vector coupling strengths. It is shown that the helium abundance depends critically in this ratio. We suggest that the parity violating process may be a consequence of the expansion of the universe.

Theoretical arguments about the progenitors of pulsars suggest that all neutron stars may have essentially the same mass1,2 m and the same magnetic moment3,4 M⃗. Direct determinations5,6 support this view and give m ≃ 1033.5g (the Chandrasekhar mass) and M⃗ ≃ 1030.5 G cm3 and theoretically inferred values for accreting binary systems7,1 show a surprisingly small scatter. Can this apparent uniformity of binary pulsars be reconciled with the timing data for (single) radio pulsars, many of which may have also been binaries for some time? In most theories it is assumed that the neutron star is slowed-down by the combined action of a plasma-current torque and a vacuum-wave torque. This has led to the conclusion that there is a deficiency in ‘old’ pulsars (as measured by their ‘Slow-down age’ P/Ṗ) and that the inferred magnetic moments vary by two orders of magnitude. A worse result is the derived pulsar birth rate2 of one per 10 yr if the half life of a pulsar is 106 yr as follows from the standard slow-down theory. From these facts we present a new model for pulsar slow-down. The present model predicts four different slow-down epochs from evolutionary changes of the magneto-sphere, which are dominated by different braking mechanisms. The model assumes that the masses, magnetic moments and initial rotation periods of all neutron stars are equal. We show that no direct relationship can exist between the ‘slow-down age’ and the true age of a pulsar and that the pulsar birth rate is one per 100 yr.

Abstract A Lorentz-covariant method is developed for the determination of the amplitudes of waves propagating through a cold, one-component plasma in arbitrary motion. The method is based on the construction of a conserved current (“adiabatic invariant”) for the waves which can be derived from Sturrock's lagrangian for the plasma or from the corresponding phenomenological description by means of the dielectric tensor.

A manifestly Lorentz covariant method is developed to describe wave propagation through a cold one-component plasma in arbitrary motion. The covariant eikonal method is applied to a model pulsar plasma and the dispersion relation is derived.

The dispersion relations for weak waves in a cold, charge-separated plasma (due to a strong rotating magnetic field) show that radio waves, and even low frequency waves can propagate through a (one-component) pulsar magnetosphere.