Conformal positive mass theorems for asymptotically flat manifolds with inner boundary

Abstract

In this paper, we prove conformal positive mass theorems for asymptotically flat manifolds with charge. We apply conformal relations to show that if the conformal sum of scalar curvature is not less than the norm square of electric field and electric density, the sum of the mass will not less than the modulus of total electric charge. We also study the situation with inner boundary condition and manifolds with scalar charge.

Some conformal positive mass theorems

“…Moreover, equality holds if and only if g, g are the same and are flat. In [15], the second author generalized the above result to asymptotically flat manifolds with compact inner boundary.…”

“…If the scalar curvature S of g and the scalar curvature S of g = e 2f g satisfies S + αe 2f S ≥ 0 for some α > 0, then the ADM masses m(g) of g and m( g) of g satisfies m(g) + αm( g) ≥ 0 Moreover, equality holds if and only if g, g are the same and are flat. In [15], the second author generalized the above result to asymptotically flat manifolds with compact inner boundary.…”