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

In this paper 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 gravitational 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 tachyonic fluid (this latter concept arises inevitably in the r-form description of fluids for any D). It is shown that in 2 + 1 there exists a vast family of static solutions for non-coherent dust, in a sharp contrast to the (3 + 1)-dimensional case. Several new null fluid solutions (including rotating ones) are found in 2 + 1 as well. 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 only