TY - JOUR

T1 - ISCOs and OSCOs in the presence of a positive cosmological constant in massive gravity

AU - Rincón, Ángel

AU - Panotopoulos, Grigoris

AU - Lopes, Ilídio

AU - Cruz, Norman

N1 - Funding Information:
We are grateful to the anonymous reviewers for their constructive criticism as well as numerous useful comments and suggestions. The authors ?.R. and N.C. acknowledge Universidad de Santiago de Chile for financial support through the Proyecto POSTDOC-DICYT, C?digo 043131 CM-POSTDOC. The authors G.P. and I.L. thank the Funda??o para a Ci?ncia e Tecnologia (FCT), Portugal, for the financial support to the Center for Astrophysics and Gravitation-CENTRA, Instituto Superior T?cnico, Universidade de Lisboa, through the Project No. UIDB/00099/2020 and grant No. PTDC/FIS-AST/28920/2017.
Funding Information:
Acknowledgments: We are grateful to the anonymous reviewers for their constructive criticism as well as numerous useful comments and suggestions. The authors Á.R. and N.C. acknowledge Uni-versidad de Santiago de Chile for financial support through the Proyecto POSTDOC-DICYT, Código 043131 CM-POSTDOC. The authors G.P. and I.L. thank the Fundação para a Ciência e Tecnologia (FCT), Portugal, for the financial support to the Center for Astrophysics and Gravitation-CENTRA, Instituto Superior Técnico, Universidade de Lisboa, through the Project No. UIDB/00099/2020 and grant No. PTDC/FIS-AST/28920/2017.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/8

Y1 - 2021/8

N2 - We study the impact of a non-vanishing (positive) cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within massive gravity in four dimensions. The gravitational field generated by a point-like object within this theory is known, generalizing the usual Schwarzschild–de Sitter geometry of General Relativity. In the non-relativistic limit, the gravitational potential differs by the one corresponding to the Schwarzschild–de Sitter geometry by a term that is linear in the radial coordinate with some prefactor γ, which is the only free parameter. Starting from the geodesic equations for massive test particles and the corresponding effective potential, we obtain a polynomial of fifth order that allows us to compute the innermost and outermost stable circular orbits. Next, we numerically compute the real and positive roots of the polynomial for several different structures (from the hydrogen atom to stars and globular clusters to galaxies and galaxy clusters) considering three distinct values of the parameter γ, determined using physical considerations, such as galaxy rotation curves and orbital precession. Similarly to the Kottler spacetime, both ISCOs and OSCOs appear. Their astrophysical relevance as well as the comparison with the Kottler spacetime are briefly discussed.

AB - We study the impact of a non-vanishing (positive) cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within massive gravity in four dimensions. The gravitational field generated by a point-like object within this theory is known, generalizing the usual Schwarzschild–de Sitter geometry of General Relativity. In the non-relativistic limit, the gravitational potential differs by the one corresponding to the Schwarzschild–de Sitter geometry by a term that is linear in the radial coordinate with some prefactor γ, which is the only free parameter. Starting from the geodesic equations for massive test particles and the corresponding effective potential, we obtain a polynomial of fifth order that allows us to compute the innermost and outermost stable circular orbits. Next, we numerically compute the real and positive roots of the polynomial for several different structures (from the hydrogen atom to stars and globular clusters to galaxies and galaxy clusters) considering three distinct values of the parameter γ, determined using physical considerations, such as galaxy rotation curves and orbital precession. Similarly to the Kottler spacetime, both ISCOs and OSCOs appear. Their astrophysical relevance as well as the comparison with the Kottler spacetime are briefly discussed.

KW - ISCOs and OSCOs of astro-physical objects

KW - Massive gravity

KW - Orbital precession

KW - Perturbative potential

UR - http://www.scopus.com/inward/record.url?scp=85112298874&partnerID=8YFLogxK

U2 - 10.3390/universe7080278

DO - 10.3390/universe7080278

M3 - Article

AN - SCOPUS:85112298874

VL - 7

JO - Universe

JF - Universe

SN - 2218-1997

IS - 8

M1 - 278

ER -