Presumably, following fundamental gravitational fields exist:

(SI units in parentheses are m-metre, s-second, k-kilogram, A-Ampere)

scalar potential g (m^2/s^2)

vector potential G (m/s)

scalar strain f (m^2/s^3)

vector strain F (m/s^2)

The gravitational constant g0 = 6.6742^-11 (m^3/s^2/k) is also used,

local energy density u (k/m/s^2), for example electromagnetic = ε0/2 • E^2 + μ0/2 • H^2

and Poynting vector S (k/s^3) = [E × H]

Time derivatives are expressed as follows:

g' = - f - c^2 • div G

G' = - F - grad g

f' = - c^2 • div grad g + fu • u

F' = c^2 • rot rot G - fs • S

The constants fu (m^3/s^2/k) and fs (m/k) are positive, signs are selected so that scalar potential g

becomes negative in presence of positive density u in vicinity of point.

The equations are similar to electromagnetic equations expressed in potentials:

a' = - c^2 • div A

A' = - E - grad a

E' = c^2 • rot rot A

In stationary state, for example, during formation of gravitational fields by stable elementary particle

or single celestial body:

S = 0, G = 0, f = 0

F = - grad g

div grad g = fu • u / c^2 = 4 • π • g0 • ρ, according to Newton's potential

Hence we get at ρ = u / c^2: fu = 4 • π • g0

The effect of gravitational fields on other fundamental ones can manifest itself as a curvature of space, and direct effect on velocity vector V, mentioned in this topic:

Hypothesis about the formation of particles from fields | Sciforums

With zero u and S, following types of "pure" gravitational waves can exist:

1. Longitudinal potential-potential: g' = - c^2 • div G, G' = - grad g

2. Longitudinal with phase shift of 90 degrees: g' = - f, f' = - c^2 • div grad g

3. Transverse: g' = - c^2 • div G, G' = - F - grad g, F' = c^2 • rot rot G

Transverse ones are probably easier to detect in experiments.