Comment on “New Brans-Dicke wormholes”

Abstract

It is shown that the recently claimed two new Brans-Dicke wormhole solutions [F. He and S-W. Kim, Phys. Rev. D65, 084022 (2002) There has been a revival of interest in the Brans-Dicke theory (BDT) in recent times, particularly in the context of traversable Lorentzian wormholes. Now a days, BDT is no longer regarded merely as a Machian competitor to Einstein's General Relativity Theory (GRT) but a little more. There are several reasons. The principal reason is of course that BDT describes weak field tests of gravity reasonably well. Apart from this, it is known that the BD scalar field φ plays the role of classical exotic matter required for the construction of traversable Lorentzian wormholes [1].In a recent paper, He and Kim [2] have found two new classes of solutions of BDT and showed that the solutions represent massive Lorentzian traversable wormholes. The purpose of this short Comment is to demonstrate that these solutions can be alternatively derived by exploiting the conformal invariance of the vacuum BDT action. That is, we show that the claimed solutions are merely the Class I and II solutions of BDT in a different gauge and thus are not essentially new.We start from the BD action given by (we take units G = c = 1):

On static spherically symmetric solutions of the vacuum Brans-Dicke theory

“…Recently He and Kim [30] have claimed for two new static vacuum solutions of the BD theory. But as already shown in [31,32], these two classes of solutions are essentially limiting cases of the Brans class I solution.…”

Revisiting the Brans solutions of scalar-tensor gravity

“…(1.3) can violate all of the energy conditions. More recent solutions proposed in the literature [32] have been identified as special limits of Brans I solutions [15,33].…”

Wormholes in Vacuum Brans–dicke Theory

“…But as already shown in [21,20], these two classes of solutions are essentially limiting cases of the Brans class I solution. And moreover He-Kim classes of solutions do not satisfy all the standard weak-field observational results of gravitation.…”