Open AccessA generic relation between baryonic and radiative energy densities of stars
Author(s) -
Mitra A.
Publication year - 2006
Publication title -
monthly notices of the royal astronomical society: letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.067
H-Index - 122
eISSN - 1745-3933
pISSN - 1745-3925
DOI - 10.1111/j.1745-3933.2006.00141.x
Subject(s) - physics , astrophysics , gravitational redshift , redshift , gravitational energy , gravitation , general relativity , gravitational collapse , metric expansion of space , gravitational binding energy , luminosity , dark energy , gravitational wave , astronomy , classical mechanics , cosmology , galaxy
By using elementary astrophysical concepts, we show that for any self‐luminous astrophysical object the ratio of radiation energy density inside the body (ρ r ) and the baryonic energy density (ρ 0 ) may be crudely approximated, in the Newtonian limit, as ρ r /ρ 0 ∝ GM / Rc 2 , where G is constant of gravitation, c is the speed of light, M is gravitational mass and R is the radius of the body. The key idea is that radiation quanta must move out in a diffusive manner rather than stream freely inside the body of the star. When one would move to the extreme general relativistic case, i.e. if the surface gravitational redshift z ≫ 1 , it is found that ρ r /ρ 0 ∝ (1 + z ) . Earlier treatments of gravitational collapse, in contrast, generally assumed ρ r /ρ 0 ≪ 1 . Thus, actually, during continued general relativistic gravitational collapse to the black hole state ( z →∞) , the collapsing matter may essentially become an extremely hot fireball with ρ r /ρ 0 ≫ 1 , a la the very early Universe, even though the observed luminosity of the body as seen by a faraway observer L ∞ ∝ (1 + z ) −1 → 0 as z →∞ , and the collapse might appear as ‘adiabatic’.