The new formula for gravitational-radiation energy loss and the axially symmetric two-body problem

Abstract

We present the new formula for gravitational-radiation energy loss that replaces the familiar quadrupole formula. The new formula helps to clarify why the quadrupole formula works when it does. The origin of the correction tensor is discussed and then applied to the axially symmetric two-body problem. With the conventional equation of state, ε = ε(P), the correction tensor vanishes and the radiation is that of the bulk-motion quadrupole formula. This is to be compared with our earlier result with an unconventional equation of state giving more radiation and with that of critics claiming dominant radiation via internal motions with the quadrupole formula. An order-of-magnitude calculation is performed for a binary system, where it is found that there is the potential for contributions from nonlinear terms to be as significant as those from the linear terms after(Gm/α)−5/6 orbits. This occurs after ~102 years for the binary pulsar PSR1913 + 16.