General Relativity and Relativistic Cosmology

Abstract

An imaginary discussion between Newton and Einstein could be the following. Isaac Newton:  Dear Prof. Einstein, my Universe is very simple. I can describe it using vectors and calculus. Between any two objects, a gravitational force is acting and, according to the masses of objects and the distance between them, the gravitational force law is $F=G\dfrac{mM}{r^2}$. The gravitational field, in this case, is $A=\dfrac{GM}{r^2}$. However, there exists an artifact, the gravitational potential $\varPhi =\dfrac{GM}{r}$. After me, the brilliant experimental physicist, Henry Cavendish, measured the gravitational constant $G = 6,67\times 10^{-11} \textrm{N m}^2/\textrm{kg}^2$, considered “universal”. The potential is related to the gravitational field through the formula $\triangledown \varPhi =-{\mathop {A}\limits ^{\rightarrow }}$, the vacuum field equation is $\triangledown ^2\varPhi =0$, as established by Pierre Simon Laplace, and the general gravitational field equation is $\triangledown ^2\varPhi =4\pi G \rho$ as pointed out by Siméon Denis Poisson, once the density of matter is known. The objects are moving in this gravitational field according to ${\mathop {F}\limits ^{\rightarrow }}=m{\mathop {A}\limits ^{\rightarrow }}$ and the trajectories are conics because my gravitational universal law gives a mathematical proof for the Kepler laws. What do you think?