摘要
Using an alternative representation of the Ricci tensor, we argue that the theory of gravitation can be easily developed in such a way that the formal description of gravity in the transition from classical Newtonian physics to general relativity remains essentially unchanged. That is to say, we show how arguments concerning the plausible conceptual compatibility of Newtonian and general-relativistic models of gravity can be replaced by a demonstration of their actual formal identity. More specifically, we find that both the classical Newtonian and the general relativistic field equations are equivalent to a velocity-field divergence equation of the form v [div (v)] + div (v,v) = -4πρ where the term div (v,v) is defined to be the trace of the square of the Jacobian derivative matrix of v (or of its general-relativistic analogue).
Using an alternative representation of the Ricci tensor, we argue that the theory of gravitation can be easily developed in such a way that the formal description of gravity in the transition from classical Newtonian physics to general relativity remains essentially unchanged. That is to say, we show how arguments concerning the plausible conceptual compatibility of Newtonian and general-relativistic models of gravity can be replaced by a demonstration of their actual formal identity. More specifically, we find that both the classical Newtonian and the general relativistic field equations are equivalent to a velocity-field divergence equation of the form v [div (v)] + div (v,v) = -4πρ where the term div (v,v) is defined to be the trace of the square of the Jacobian derivative matrix of v (or of its general-relativistic analogue).
作者
Frank Blume
Frank Blume(John Brown University, Siloam Springs, USA)
