The theoretical analysis of the existence of a limit mass for compact astronomic objects requires the solution of the Einstein’s equations of general relativity together with an appropriate equation of state. Analytical solutions exist in some special cases like the spherically symmetric static object without energy sources that is here considered. Solutions, i.e. the spacetime metrics, can have a singular mathematical form (the so called Schwarzschild metric due to Hilbert) or a nonsingular form (original work of Schwarzschild). The former predicts a limit mass and, consequently, the existence of black holes above this limit. Here it is shown that, the original Schwarzschild metric permits compact objects, without mass limit, having reasonable values for central density and pressure. The lack of a limit mass is also demonstrated analytically just imposing reasonable conditions on the energy-matter density, of positivity and decreasing with radius. Finally the ratio between proper mass and total mass tends to 2 for high values of mass so that the binding energy reaches the limit m (total mass seen by a distant observer). As it is known the negative binding energy reduces the gravitational mass of the object; the limit of m for the binding energy provides a mechanism for stable equilibrium of any amount of mass to contrast the gravitational collapse.
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|Titolo:||Binding energy and equilibrium of compact objects|
|Data di pubblicazione:||2014|
|Appare nella tipologia:||01a Articolo in rivista|