Field equations for gravity: An alternative route

Sumanta Chakraborty

Published 2017-04-22Version 1

We present an alternative derivation of the gravitational field equations starting from the Newton's law, which intrinsically brings in observer dependence in the theory. Projecting the Riemann curvature tensor appropriately as fit for an observer, taking a cue from Poisson's equation, the Einstein's equations immediately follow. Our derivation naturally adapts to Lovelock gravity theories where an appropriate Riemann tensor has to be used. Interestingly, in the above derivation the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerge quiet naturally.