The gradient of Einstein field equations

Einstein field equations in their most basic form give the bending of spacetime- the ‘R’ tensor, in response to an energy momentum density tensor input ‘T’ that expresses the distribution of various energy types in space. The idea of spacetime bending in response to energy in space is not intuitive to many, leading to a question if this is the true physical interpretation of these equations. We show here that it is possible to change this and make the equations intuitive and simply understood, if we take the gradient of the two sides of the equations. That is so because; the gradient of energy density on the RHS gives an ‘acceleration’/ force that is equalled by the gradient of the LHS curvature of the path of a moving mass. This can be immediately visible by checking the units involved- in which energy density divided by a length (to get a gradient) has the units of acceleration. And the gradient of the curvature of the LHS is the second derivative along the path and gives units of acceleration too. This amounts to saying that gravity acceleration/force at a point is simply the result of the negative gradient of the energy density at that point. This is the same rule that drives fluids due to pressure and electrons in wires due to electric potential, and also heat due to the (random) kinetic energy density gradient. The explanation is clear; particles move from high to low energy densities and pocket the difference. A gravity derived from an energy gradient idea has many perks. Gravity become both local and nonlocal- since a gradient is local but the energy on which it depends obeys an integral equation that requires summation over all space. It further makes voids in space as important as matter filled regions as both affect the gradient along a specified path. It also allows the calculation of the universal gravity constant G as a gradient of the energy density of the distant masses as Mach suggested before. This work compliments an earlier work that showed a similar property of Einstein geodesic equation 2.