Electromagnetism and perfect fluids interplay in multidimensional spacetimes

TL;DR

This paper explores how electromagnetic and perfect fluid fields interact in higher-dimensional spacetimes, revealing that electromagnetic fields behave uniquely in four dimensions and can mimic perfect fluids in three dimensions.

Contribution

It demonstrates that vector fields in higher dimensions only describe electromagnetism in four dimensions and shows how these fields can emulate perfect fluids depending on the Lagrangian.

Findings

Electromagnetic fields are unique to four-dimensional spacetime.

In three dimensions, vector fields can behave as perfect fluids.

The energy-momentum tensor of certain fields matches that of perfect fluids.

Abstract

We consider fields in (D>2)-dimensional spacetime, whose potential is r-form (skew-symmetric tensor of rank r), the field tensor F being its exterior derivative and the Lagrangian, a function of the quadratic invariant I of this tensor. It is shown that vector field (r=1) describes electromagnetic field only for D=4. In particular, for D=3 and the Lagrangean L as any function of the above-mentioned invariant, the (r=1)-field has energy-momentum tensor identical with that of a perfect fluid whose equation of state depends on the choice of L(I).