Gravitational Equilibrium in the Presence of a Positive Cosmological Constant

Abstract

We reconsider the virial theorem in the presence of a positive cosmological constant Lambda. Assuming steady state, we derive an inequality of the form rho >= A (Lambda / 4 pi GN) for the mean density rho of the astrophysical object. With a minimum at Asphere = 2, its value can increase by several orders of magnitude as the shape of the object deviates from a spherically symmetric one. This, among others, indicates that flattened matter distributions like e.g. clusters or superclusters, with low density, cannot be in gravitational equilibrium.

arXiv comment7 pages, no figures

References in corpus (5)

• Constraining dark energy with SNe Ia and large-scale structure
• The End of the Age Problem, And The Case For A Cosmological Constant Revisited
• Geometry and Destiny
• The Consistent Newtonian Limit of Einstein's Gravity with a Cosmological Constant
• Some Dynamical Effects of the Cosmological Constant

Cited by in corpus (28)

• The virial theorem and the dark matter problem in hybrid metric-Palatini gravity
• Generalized virial theorem in f(R) gravity
• Scales Set by the Cosmological Constant
• The virial theorem and the dynamics of clusters of galaxies in the brane world models
• Eleven spherically symmetric constant density solutions with cosmological constant
• The effect of an expanding universe on massive objects
• Two-body problem with the cosmological constant and observational constraints
• Astrophysical Configurations with Background Cosmology: Probing Dark Energy at Astrophysical Scales
• Comparing two approaches to Hawking radiation of Schwarzschild-de Sitter black holes
• On astrophysical bounds of the cosmological constant
• Generalized virial theorem in Palatini $f(R)$ gravity
• Brane-$f(R)$ gravity and dark matter
• Newtonian analogue of Schwarzschild de-Sitter spacetime: Influence on the local kinematics in galaxies
• Equilibrium of large astrophysical structures in the Newton-Hooke spacetime
• Gravothermal Catastrophe with a Cosmological Constant
• On the newtonian limit and cut--off scales of isothermal dark matter halos with cosmological constant
• From Global to Local Dynamics: Effects of the Expansion on Astrophysical Structures
• Ellipsoidal configurations in the de Sitter spacetime
• Viscous Cosmologies
• Gravitational instabilities of isothermal spheres in the presence of a cosmological constant
• Confrontation of Top-Hat Spherical Collapse against Dark Halos from Cosmological N-Body Simulations
• Velocity and velocity bounds in static spherically symmetric metrics
• Static perfect fluid balls with given equation of state and cosmological constant
• Virial estimator for dark energy
• Galaxy groups in the presence of Cosmological Constant: Increasing the Masses of Groups
• Dark Energy in an Astrophysical Context
• The Dirac equation in the Kerr-de Sitter metric
• Casimir Effect and Gravitational Balance: a Search for Stable Configurations