Hartle's model within the general theory of perturbatiye matchings: the change in mass

Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit assumptions, there are some implicit, like the "continuity" of the functions in the perturbed metric across the surface of the body. In this work we sketch the basics for the analysis of the second order problem using the modern theory of perturbed matchings. In particular, the result we present is that when the energy density of the fluid in the static configuration does not vanish at the boundary, one of the functions of the second order perturbation in the setting of the original work by Hartle is not continuous. This discrepancy affects the calculation of the change in mass of the rotating star with respect to the static configuration needed to keep the central energy density unchanged.

Using theory of change to achieve impact in AAS

The CGIAR Strategy and Results Framework sets out four system level outcomes (SLOs), namely: reducing rural poverty, improving food security, improving nutrition and health and sustainable management of natural resources. In pursuit of these objectives the CGIAR has developed a set of sixteen CGIAR Research Programs (CRPs), each of which is expected to make specific contributions to a range of intermediate development outcomes (IDOs) linked to the SLOs. As part of this work the CRPs are developing impact pathways and theories of change designed to explain how the programs will achieve IDOs. The purpose of the present paper is to explain the approach that the CRP on Aquatic Agricultural Systems (AAS) is taking to using these programmatic tools to help achieve impact.