Behavior of quasilocal mass under conformal transformations - art. no. 044019

We show that in a generic scalar-tensor theory of gravity, the "referenced" quasilocal mass of a spatially bounded region in a classical solution is i nvariant under conformal transformations of the spacetime metric. We first extend the Brown-York quasilocal formalism to such theories to obtain the ' 'unreferenced'' quasilocal mass and prove it to be conformally invariant. H owever, this quantity is typically divergent. It is, therefore, essential t o subtract from it a properly defined reference term to obtain a finite and physically meaningful quantity, namely, the referenced quasilocal mass. Th e appropriate reference term in this case is defined by generalizing the Ha wking-Horowitz prescription, which was originally proposed for general rela tivity. For such a choice of reference term, the referenced quasilocal mass for a general spacetime solution is obtained. This expression is shown to be a conformal invariant provided the conformal factor is a monotonic funct ion of the scalar field. We apply this expression to the case of static sph erically symmetric solutions with arbitrary asymptotics to obtain the refer enced quasilocal mass of such solutions. Finally, we demonstrate the confor mal invariance of our quasilocal mass formula by applying it to specific ca ses of four-dimensional charged black hole spacetimes, of both the asymptot ically flat and non-flat kinds, in conformally related theories. [S0556-282 1(99)01402-1].