Scalar Gravity and the Double Copy in the Framework of General Relativity

Abstract: The classical double copy relations establish correspondence between exact gravity solutions and their counterparts in biadjoint and gauge theories. In this work, we investigate a peculiar case of double copy relations arising in exact solutions of the scalar gravity equation, relating static spacetime geometry to the Komar density distribution. We use a scalar-restricted static metric ansatz to isolate the degree of freedom governed by the linear equation for the zeroth copy. The corresponding metric solutions are interpreted as describing gravity without self-interaction, based on the Komar density distribution. The single copy of these metrics reveals direct correspondence between the sources of scalar gravity and electrostatics. Furthermore, this correspondence persists even at the level of particles, their motion being governed by the same non-relativistic expressions with respect to the background space. These and other results lead us to conclude that scalar gravity is the manifestation of double copy relations encoded in the structure of general relativity.