An approximate global solution of Einstein's equations for a differentially rotating compact body

作者：Molina A^*; Ruiz E

来源：General Relativity and Gravitation, 2017, 49(10): 135.

DOI：10.1007/s10714-017-2297-5

• Global axisymmetric and stationary solutions
• Differential rotation
• Analytic post-Minkowskian solutions

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought of as a simple star model: a selfgravitating perfect fluid ball with a differential rotation motion pattern. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic coordinates. Interior and exterior solutions are matched, in the sense described by Lichnerowicz, on the surface of zero pressure, to obtain a global solution. The resulting metric depends on four arbitrary constants: mass density; rotational velocity at r = 0; a parameter that accounts for the change in rotational velocity through the star; and the star radius in the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined in terms of these four parameters.

• 出版日期2017-10