Spacetimes, electromagnetism and fluids (a revision of traditional concepts)

Abstract

In this talk r-form fields in spacetimes of any dimension D are considered (r<D). The weak-field Newtonian-type limit of Einstein's equations, in general, with relativistic sources is studied in the static case yielding a revision of the equivalence principle (intrinsically relativistic sources generate twice stronger gravitational fields and hyperrelativistic sources, e.g., the stiff matter, generate four times stronger fields than non-relativistic sources). It is shown that analogues of electromagnetic field, strictly speaking, exist only in even-dimensional spacetimes. In (2+1)-dimensional spacetime, the field traditionally interpreted as "magnetic" turns out to be in fact a perfect fluid, and "electric", a perverse fluid (this latter concept arises inevitably in the r-form description of fluids for any D, and we consider here perverse fluids in (3+1)-dimensional spacetime too). New exact solutions of (2+1)-dimensional Einstein's equations with perfect and perverse fluids are obtained, and it is shown that in this case there exists a vast family of static solutions for non-coherent dust, in a sharp contrast to the (3+1)-dimensional case. New general interpretation of the cosmological term in D-dimensional Einstein's equations is given via the (D-1)-form field, and it is shown that this field is as well responsible (as this is the case in 3+1 dimensions) for rotation of perfect fluids [(D-2)-form fields], thus the "source" term in the corresponding field equations has to be interpreted as the rotation term.