Static and stationary dark fluid universes: a gravitoelectromagnetic perspective

Abstract

The usual characterization of exact solutions of Einstein field equations, including cosmological solutions, is based on the symmetry properties of their corresponding metrics which is obviously mathematically involved. Here we present a physical characterization of the static and stationary perfect fluid solutions of the Einstein field equations by employing the $$1+3$$ 1 + 3 formulation of spacetime decomposition which introduces the so-called quasi-Maxwell form of the Einstein field equations in the broader context of gravitoelectromagnetism. These solutions have a single or 2-component perfect fluid sources, and are characterized according to their gravitoelectric and gravitomagnetic fields which are the gravitational analogs of the electromagnetic fields. It is shown that the absence or presence of either or both of these fields could restrict the equations of state of the contributing perfect fluid sources. As the representative of each family of solutions, we consider those spaces that include the cosmological term as a dark fluid source with the equation of state $$p=-\rho = constant$$ p = - ρ = c o n s t a n t .

Free Fractional Gauge Fields: An Elementary Model Based on the Standard Model (SM)

“…(2.5) Thus, T i , T j , and T k are the group generators of SU (3). A more detailed description of non-abelian gauge theory will be discussed in Subsection (2.5).…”

“…Here, we have made use of the Caputo fractional derivative 3 , and we now have two fractional analogs of Maxwell's equations instead of four-Eqs. (3.61 and 3.63); similar to d F = 0, and d F = j , the Hodge dual.…”

“…Thereafter, we explore the relationship between the electromagnetic and gravitational fields. These two concepts depend on the so-called harmonic gauge and form an area studied in physics known as Gravitoelectromagnetism (GEM) [3]. Note that these concepts share commonality not only because of the harmonic gauge condition, but because general relativity must be adhered to in the weak field limit.…”

Invariant stationary vacuum solutions by symmetry analysis and Jacobi elliptic rational expansion method

“…Solutions of static and stationary spacetimes are introduced in some papers, for example, [18,37,[39][40][41].…”

Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal

“…The remaining 95 percent of space-time is filled with an unknown substance called dark matter [19][20][21][22][23][24][25] and dark energy [26][27][28]. For the sake of generality, we will call this substance a dark fluid [29,30]. This fluid appears to be a Bose-Einstein superfluid condensate [21,22,25,28,31,32].…”