Abstract
We study the general properties of fluid spheres satisfying the heuristic assumption that theirs areal and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all models are necessarily geodesic and a subclass of the Lemaître–Tolman–Bondi solution is obtained. In the dissipative case solutions are non-geodesic and are characterized by the fact that all non-gravitational forces acting on any fluid element produces a radial three-acceleration independent on its inertial mass.
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Herrera, L., Santos, N.O. Collapsing spheres satisfying an “Euclidean condition”. Gen Relativ Gravit 42, 2383–2391 (2010). https://doi.org/10.1007/s10714-010-0986-4
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DOI: https://doi.org/10.1007/s10714-010-0986-4