2020/04/04 by B. V. Ivanov, Б. В. Иванов
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Classical mechanics #Conformal map #Cosmology #Cosmology and Gravitation Theories #Differential equation #Differential geometry #Einstein field equations #Flatness (cosmology) #General relativity #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Riccati equation #gr-qc
paper · pdf · doi:10.1140/epjc/s10052-021-09025-8
16 pages, no figures. arXiv admin note: substantial text overlap with arXiv:2004.00907
arxiv created 2020/04/04 · openalex publication_date 2021/03/01 · arxiv updated 2021/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein–Maxwell equations may serve as generating functions for charged stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics, which do not depend on charge. In all these cases the equations are linear first order differential equations for one of the metric components and Riccati equations for the other. The latter may be always transformed into second order homogenous linear differential equations. These conclusions are illustrated by numerous particular examples from the study of charged stellar models.