Gravitational potential from maximum entropy principle
It is shown here in the framework of standard general relativity that the gravitational potential in static spacetime, equivalently the redshift factor, inside any kind of matter, can be derived from maximum entropy principle. It is used only the Hamiltonian constraint, without further invoking Einstein's equations or any new principle. The Newtonian potential arises from the same procedure.
Roupas, Zacharias, "Gravitational potential from maximum entropy principle" (2020). Centre for Theoretical Physics. 208.