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General Relativity and Relativistic Cosmology

  • Wladimir-Georges Boskoff,
  • Salvatore Capozziello

摘要

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?