Abstract
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.
Highlights
Current observational data in astrophysics and cosmology indicate that the present Universe is dominated by dark matter and dark energy [1], the origin and nature of which still remain a mystery
Where Λ acts like a cosmological constant, while the set {γ, η} are two new parameters coming from massive gravity, which are computed in terms of the graviton mass, mg, and the other parameters of the theory as follows [17]
We studied the impact of a non-vanishing cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within four-dimensional massive gravity
Summary
Current observational data in astrophysics and cosmology indicate that the present Universe is dominated by dark matter and dark energy [1], the origin and nature of which still remain a mystery. Visser and collaborators [19], new features emerge, such as outermost stable circular orbits (OSCOs), when a positive cosmological constant (no matter how small) is taken into account In this respect, OSCOs has been investigated in alternative contexts, for instance: (i) accretion disks [20,21], (ii) galaxies [22,23], and in (iii) modified theories of gravity [24,25]. Our goal is twofold: First, we shall use the recent data reported by the GRAVITY Collaboration to place limits on the parameters of massive gravity Assuming those values, we shall investigate the existence and nature of the stable circular orbits of several different structures in the Universe from the atomic level to clusters of galaxies.
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