A very strong mathematical foundation for Astrology can be related to Einstein’s Field Equations of General Theory of Relativity.
According to the General Theory of Relativity, all motions are relative. With respect to Sun (with respect to its Rest frame), all objects are in motion. With respect to Earth (with respect to its Rest frame), all objects in the Universe are in motion. With respect to Moon (with respect to its Rest frame), all objects in the Universe are in motion. With respect to any arbitrary Observer (with respect to his Rest frame) everything is moving around the Observer.
This idea is complemented by the most beautiful equations in human history
describing the nature of existence of the material distribution in this Universe.
is called Einstein's Tensor. Representing gravitational field manifested in the form of space-time curvature. It's a highly complicated mathematical object (very difficult to analyze) : that is why Einstein called it Pillar of Iron.
is called Energy-momentum Tensor of material distribution. Einstein called it as Pillar of Straw (very easy to analyze).
is Einstein’s gravitational constant.
Solving these equations with respect to an Astronomical object, one gets gij(the metric tensor of space-time) with respect to rest frame of the Astronomical object. The distance between two events is “ds” is expressed by the equation
being the coordinate differentials representing the 4-vector separation between events. Every observer is influenced by the totality of material distribution in the universe.
is the Metric tensor of spacetime. Every object must have its own influence on an observer through the metric tensor.
The most difficult aspect of this concept is that the influence is always non-linear (other mathematical difficulties exist). So it is not practically easy to find the “effective gij” on the observer. Once we find the “effective gij” on the observer, equations for geodesics
can be used to determine the world line of observer in space-time. In general theory of relativity, every event is a predetermined absolute reality because, general theory of relativity is a pure geometrical theory.
So birth, death and every event on the world line of the observer are all predetermined absolute realties. The world-lines are frozen curves in space-time. There’s no concept of free-will in general theory of relativity. If it is possible for us to calculate the world-line of the observer, making use of these equations of geodesic, one shall be able to predict the past , present and future of the observer or of any object in this universe.
Ages of observations on Astronomical object by Astrologers compelled them to setup a set of empirical mathematical relations for their prediction. Rahu, Ketu, Gulikan... etc can be interpreted as pure mathematical objects, that astrologers introduced for feasibility of their mathematical calculations. These objects may not be physically observed in space-time.
Einstein's Field Equations are true in any arbitrary space-time coordinate system.
“effective gij”on an observer A is equal to gij(A).
“effective gij” on an observer B is equal to gij(B).
In general gij(A) can never be identical to gij(B). So horoscope (world line) of one observer can never be identical to horoscope of another observer even though all other physical conditions may appear to be identical. This concept is purely based on fundamentals of General Theory of Relativity