Mass and weak-field limit of boson stars in Brans-Dicke gravity

Abstract

We study boson stars in Brans-Dicke (BD) gravity and use them to illustrate some of the properties of three different mass definitions: the Schwarzschild mass, the Keplerian mass and the tensor mass. We analyse the weak-field limit of the solutions and show that only the tensor mass leads to a physically reasonable definition of the binding energy. We examine numerically strong-field = -1 solutions and show how, in this extreme case, the three mass values and the conserved particle number behave as a function of the central boson field amplitude. The numerical studies imply that for = -1, solutions with extremal tensor mass also have extremal particle number. This is a property that a physically reasonable definition of the mass of a boson star must have, and we prove analytically that this is true for all values of . The analysis supports the conjecture that the tensor mass uniquely describes the total energy of an asymptotically flat solution in BD gravity.