Abstract
The relation between gravitational memory effects and Bondi-Metzner-Sachs symmetries of the asymptotically flat spacetimes is studied in the scalar-tensor theory. For this purpose, the solutions to the equations of motion near the future null infinity are obtained in the generalized Bondi-Sachs coordinates with a suitable determinant condition. It turns out that the Bondi-Metzner-Sachs group is also a semi-direct product of an infinite dimensional supertranslation group and the Lorentz group as in general relativity. There are also degenerate vacua in both the tensor and the scalar sectors in the scalar-tensor theory. The supertranslation relates the vacua in the tensor sector, while in the scalar sector, it is the Lorentz transformation that transforms the vacua to each other. So there are the tensor memory effects similar to the ones in general relativity, and the scalar memory effect, which is new. The evolution equations for the Bondi mass and angular momentum aspects suggest that the null energy fluxes and the angular momentum fluxes across the null infinity induce the transition among the vacua in the tensor and the scalar sectors, respectively.
Highlights
Such as Horndeski gravity [41], Degenerate Higher-Order Scalar-Tensor theories [42,43,44] and spatially covariant gravity [45,46,47], contain more general interactions for the metric field and the scalar field φ
The evolution equations for the Bondi mass and angular momentum aspects suggest that the null energy fluxes and the angular momentum fluxes across the null infinity induce the transition among the vacua in the tensor and the scalar sectors, respectively
The terms in the round brackets in the second line are the angular momentum fluxes of the matter, the tensor GW and the scalar GW, respectively [71]. This means that the scalar memory effect is related to the transition among the scalar vacua induced by the angular momentum fluxes through I +
Summary
The asymptotically flat spacetime, i.e., an isolated system, in Brans-Dicke theory is studied. Where ω is a constant, G0 is the bare gravitational constant, and Sm is the matter action This theory has been studied and well tested for a long time [48]. After solving the equations of motion, these metric functions and the scalar field φ can be expanded in powers of 1/r. One needs know the boundary conditions, i.e., the asymptotic behaviors of gab and φ. Equation (2.9a) φ = φ0 + O r−1 takes the similar form as in , again with a constant φ0, GR one with a canonical expects that gab scalar would have the same behavior as the one in GR. The remaining metric functions have exactly the same asymptotic behaviors as those in GR, except that the determinant conditions (2.7) and (2.11) are different
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