(Received February 9, 1984)
A new equation for a gravitational field is proposed by following the line of arguments in the current theory of gauge fields. A linear approximation of this field equation which is the fourth order differential equation of the metric field gµν shows that it describes two kinds of particles with finite masses in addition to the familiar massless gravitons.
An application to a static case shows that the static potential consists of three parts, 1) Newtonian potential, 2) a repulsive potential with a finite range and 3) an attractive potential with another finite force-range. A very interesting result is obtained from the above-mentioned potential. Namely, it seems quite probable that a point-source can be free from the Schwarzschild singularity, provided that the mass of the source is less than some critical value.
The energy-“tensor” of the gravitational field is also investigated. It is shown that the total energy can always be transformed into an integral over a large closed surface owing to the invariant property of the Lagrangian. This feature makes it easy to compute the energy of an isolated system, the magnitude of which coincides with the value derived from the conventional theory of relativity.
URL : http://ptp.ipap.jp/link?PTP/72/83/
DOI : 10.1143/PTP.72.83