New Riccati equations for radiating matter

• Published in: The European physical journal. C, Particles and fields Vol. 82; no. 1; pp. 1 - 12
• Main Authors: Naidoo, Noeleen, Maharaj, Sunil D., Govinder, Keshlan S.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2022; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Astronomy; Astrophysics and Cosmology; Boundary conditions; Cosmological constant; Electromagnetic fields; Electromagnetism; Elementary Particles; Equations of state; Euclidean space; Exact solutions; Hadrons; Heavy Ions; Linear equations; Mathematical analysis; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Regular Article - Theoretical Physics; Relativity; Riccati equation; Spacetime; String Theory; Theory of relativity; Transformations (mathematics)
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-021-09984-y

The relationship between radiating stars in general relativity and Riccati equations is investigated for a general matter distribution including the electromagnetic field and the cosmological constant. A generalised transformation relating the gravitational potentials for a spherically symmetric relativistic gravitating fluid is introduced. This generates a new Riccati equation at the surface of the radiating star. Exact solutions to the boundary condition are found and the gravitational potentials are given explicitly. Some of the consistency conditions can be reduced to Bernoulli equations which admit exact solutions. We also demonstrate that the reduction of order allows us to write the boundary condition as a first order equation utilising the generalised transformation. Solutions obtained using the generalised transformation also admit a linear equation of state.