The covariant Tolman-Oppenheimer-Volkoff equations I: The isotropic case

Abstract

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.

12 pages, 2 figures

References in corpus (4)

• A covariant approach for perturbations of rotationally symmetric spacetimes
• The role of pressure anisotropy on the maximum mass of cold compact stars
• Solution generating theorems for the TOV equation
• The covariant Tolman-Oppenheimer-Volkoff equations II: The anisotropic case

Cited by in corpus (14)

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• A simple method to generate exact physically acceptable anisotropic solutions in general relativity
• The covariant Tolman-Oppenheimer-Volkoff equations II: The anisotropic case
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• Two-fluid stellar objects in General Relativity: the covariant formulation
• Local description of S-matrix in quantum field theory in curved spacetime using Riemann-normal coordinate
• On anisotropic two-fluid stellar objects in General Relativity
• Tolman-Oppenheimer-Volkoff equation and static spheres in Conformal Killing gravity
• Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
• Some exact relativistic star solutions in $f(R)$ gravity
• Gravitational Field of a Spherical Perfect Fluid
• Locally Rotationally Symmetric Spacetimes in Einstein-Cartan Theory and Their Classification
• Generating anisotropic models for relativistic stellar objects
• Series solutions to the TOV equations