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Abstract |
We investigate Ricci almost solitons (RASs) associated with four-dimensional spherically symmetric static spacetimes. Starting from the general static spherically symmetric metric, the Ricci almost soliton equation is reduced to an overdetermined system of differential equations for the metric functions, the RAS vector field, and the almost soliton factor. By imposing suitable conditions on the resulting differential constraints, several explicit families of non-Einstein metrics admitting RAS structures are obtained. The corresponding RAS vector fields have dimensions ranging from four to fifteen, with a six-dimensional structure in Case (I), fifteen-dimensional structures in Cases (II-A), (II-B), (III-A), (III-B), (IV-A), and (IV-B), and four- and five-dimensional structures for the two particular solutions of Case (V). The sign of the almost soliton factor is analyzed on the admissible radial domains, showing that the obtained geometries may exhibit shrinking, expanding, and steady regions depending on the model parameters and angular variables. The effective energy density, radial pressure, and tangential pressure are reconstructed from the Einstein equations, and the null, weak, strong, and dominant energy conditions are examined. The resulting matter profiles include anisotropic and isotropic fluids, vacuum, cosmological-constant-type configurations, and effective sources with negative energy density. One solution admits a formal finite-radius Schwarzschild junction at its zero radial-pressure surface, although the density is negative there and the solution is therefore not a conventional stellar interior. Another solution has positive constant density but negative pressure throughout its admissible finite radial domain and does not possess a finite pressure-free surface for the considered positive-parameter branch. Other cases exhibit anti-de Sitter asymptotic structures. These results demonstrate that the Ricci almost soliton structure provides a systematic geometric framework for constructing exact static spherically symmetric spacetimes, while the energy conditions and admissible radial domains determine their possible physical interpretation. |
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