What is the name of the equations which are a set of partial differential equations produced by Einstein relating to the description of gravity as a geometric property of space and time which went on to replace Isaac Newton's rotating spheres argument which attempts to define that true rotational motion can be defined by observing the tension in the string joining two identical spheres?
Rotating spheres Isaac Newton's rotating spheres argument attempts to demonstrate that true rotational motion can be defined by observing the tension in the string joining two identical spheres. The basis of the argument is that all observers make two observations: the tension in the string joining the bodies (which is the same for all observers) and the rate of rotation of the spheres (which is different for observers with differing rates of rotation). Only for the truly non-rotating observer will the tension in the string be explained using only the observed rate of rotation. For all other observers a "correction" is required (a centrifugal force) that accounts for the tension calculated being different from the one expected using the observed rate of rotation. It is one of five arguments from the "properties, causes, and effects" of true motion and rest that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to "what"?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.
Non-exact solutions in general relativity Non-exact solutions in general relativity are solutions of Albert Einstein's field equations of general relativity which hold only approximately. These solutions are typically found by treating the gravitational field, formula_1, as a background space-time, formula_2, (which is usually an exact solution) plus some small perturbation, formula_3. Then one is able to solve the Einstein field equations as a series in formula_3, dropping higher order terms for simplicity.