Gravitational field within a homogeneous rotating sphere in the weak field approximation in general relativity

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Astrophysics, Gravitational Fields, Relativity, Rotating Spheres, Einstein Equations, Polynomials, Supermassive Stars, Tensor Analysis

Scientific paper

Analytical expressions are obtained for the components of the metric tensor describing the gravitational field inside a constant-density sphere rotating with constant angular velocity within the weak field approximation. The values of these components are uniquely determined from the condition of continuous matching of the given solution with the known outer solution at the surface of the sphere. The derived expressions can be used to model the gravitational field of supermassive rotating astrophysical objects and to determine their characteristics such as mass density, velocity field, and anisotropic pressure.

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