Consistency of the mass variation formula for black holes accreting cosmological fluids

• Published in: General relativity and gravitation Vol. 44; no. 4; pp. 985 - 992
• Main Authors: Guariento, Daniel C., Horvath, J. E.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01-04-2012
• Subjects: Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Differential Geometry; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Research Article; Theoretical; Black holes; Accretion
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-011-1318-z

We address the spherical accretion of generic fluids onto black holes. We show that, if the black hole metric satisfies certain conditions, in the presence of a test fluid it is possible to derive a fully relativistic prescription for the black hole mass variation. Although the resulting equation may seem obvious due to a form of it appearing as a step in the derivation of the Schwarzschild metric, this geometrical argument is necessary to fix the added degree of freedom one gets for allowing the mass to vary with time. This result has applications on cosmological accretion models and provides a derivation from first principles to serve as a basis to the accretion equations already in use in the literature.