The covariant Tolman-Oppenheimer-Volkoff equations I: The isotropic case
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We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar objects. Using a reconstruction algorithm we find two physically interesting generalisations of previously known stellar interior solutions. The variables that we use also allow an easier formulation of known generating theorems for solutions associated to relativistic stellar objects.
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Cited by 3 Pith papers
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In Energy-Momentum Squared Gravity, stellar equilibrium equations for perfect fluids retain the standard TOV form in effective variables and reduce to an autonomous planar dynamical system for linear equations of state.
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Covariant Dynamical Systems Formulation of the Tolman-Oppenheimer-Volkoff Equations
Reformulates TOV stellar equations as covariant autonomous dynamical system in 1+1+2 formalism, reducing to planar flow for linear EoS with geometrically interpreted equilibria.
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