All the most known theories of gravity are built on the principle of long-range action. When approximately "point" body or mass density (also electromagnetic energy) distributed in space creates gravitational potential. This article attempts to substantiate gravitational phenomena on the principle of proximity (locality). The cause of interactions is some spatial state of fundamental fields, the consequence is change of these fields over time (first derivative in time at point of continuum).

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:

https://able2know.org/topic/572511-1
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.