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

Spanish Relativity Meeting: almost 100 years after Einstein's revolution

Reina, Borja^1 ; Vera, Raül^1

Dept. of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 644 PK, Bilbao, Basque Country

48080, Spain^1

关键词: Energy density;    General Relativity;    General theory;    Matchings;    Rotating stars;    Second order perturbation;    Second order problem;    Second orders;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/600/1/012013/pdf
DOI  :  10.1088/1742-6596/600/1/012013

来源: IOP

【 摘 要 】

Hartle'smodel 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 Hartleis 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.