Expanding perfect fluid generalizations of theCmetric

Abstract

Petrov type D gravitational fields, generated by a perfect fluid with spatially homogeneous energy density and with flow lines which form a non-shearing and non-rotating timelike congruence, are re-examined. It turns out that the anisotropic such spacetimes, which comprise the vacuum Cmetric as a limit case, can have non-zero expansion, contrary to the conclusion in the original investigation by Barnes [1]. Apart from the static members, this class consists of cosmological models with precisely one symmetry. The general line element is constructed and some important properties are discussed. It is also shown that purely electric Petrov type D vacuum spacetimes admit shearfree normal timelike congruences everywhere, even in the non-static regions. This result incited to deduce intrinsic, easily testable criteria regarding shearfree normality and staticity of Petrov type D spacetimes in general, which are added in an appendix.

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

“…(The denomination "static observers" has, however, a different meaning in some literature, e.g. [25], where it designates rigid, vorticity-free congruences tangent to a timelike Killing vector field, existing only in static spacetimes). In the case of the electromagnetic systems in flat spacetime, by static observers we mean the globally inertial rest frame of the sources.…”

“…The first term in (25) embodies the Thomas precession. The second term is a covariant form for the familiar torque τ = µ × B causing the Larmor precession of a magnetic dipole under a magnetic field.…”

Gravito-electromagnetic analogies

“…Note this remarkable aspect: all the terms in the Maxwell equations (86), (88) and (89) have a gravitational counterpart in (99), (102) and (103), respectively, substituting { E, B} → { G, H} (up to some numerical factors). As for (87), there are clear gravitational analogues in (100) to the terms G × B and the current 4π j, but not to the remaining terms. It should nevertheless be noted that, as shown in Sec.…”

“…We note however that the denomination "static observers" is employed in some literature (e.g. [87,88]) with a different meaning, where it designates hypersurface orthogonal time-like Killing vector fields (which are rigid, vorticity-free congruences, existing only in static spacetimes).…”

“…It should nevertheless be noted that, as shown in Sec. 5 below, in the post-Newtonian regime (or in the "GEM limit" of linearized theory), the term 2∇θ of (100) embodies a contribution analogous to the displacement current terṁ E of (87). The gravitational equations in turn contain, as one might expect, terms with no parallel in electromagnetism, most of them involving the shear/expansion tensor K (αβ) .…”