Re-derivation of the constant-density star in isotropic coordinates produces a transparent metric and highlights under-appreciated special cases including pressure gravitating alone and naked singularities.
Generating Static Fluid Spheres by Conformal Transformations
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abstract
We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic coordinates). Special cases include the Schwarzschild interior solution and the Einstein static universe. The process we consider involves solving two equations of the Riccati type coupled by a single generating function rather than a specification of one of the two metric functions.
fields
gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Revisiting Schwarzschild's constant density star in isotropic coordinates
Re-derivation of the constant-density star in isotropic coordinates produces a transparent metric and highlights under-appreciated special cases including pressure gravitating alone and naked singularities.