  We point out that although conventional stars are primarily fed by burning of
nuclear fuel at their cores, in a strict sense, the process of release of
stored gravitational energy, known as, Kelvin - Helmholtz (KH) process is
either also operational albeit at an arbitrary slow rate, or lying in wait to
take over at the disruption of the nuclear channel. In fact, the latter mode of
energy release is the true feature of any self-gravity bound object including
stars. We also highligh the almost forgotten fact that Eddington was the first
physicist to introduce Special Relativity into the problem and correctly insist
that, actually, total energy stored in a star is not the mere Newtonian energy
but the total mass energy (E = M c^2). Accordingly, Eddington defined an
``Einstein Time Scale'' of Evolution where the maximum age of the Sun turned
out to be t_E = 1.4. 10^{13} yr. We extend this concept by introducing General
Relativity and show that the minimum value of depletion of total mass-energy is
t_E =infty not only for Sun but for and sufficiently massive or dense object.
We propose that this time scale be known in the name of ``Einstein -
Eddington''. We also point out that, recently, it has been shown that as
massive stars undergo continued collapse to become a Black Hole, first they
become extremely relativistic Radiation Pressure Supported Stars. And the life
time of such relativistic radiation pressure supported compact stars is indeed
dictated by this Einstein -Eddington time scale whose concept is formally
developed here. Since this observed time scale of this radiation pressure
supported quasistatic state turns out to be infinite, such objects are called
Magnetospheric Eternally Collapsing Objects (MECO).
