Sources of stellar energy, Einstein–Eddington timescale of gravitational contraction and eternally collapsing objects

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 highlight 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 = Mc2). Accordingly, Eddington defined an “Einstein time scale” of Evolution where the maximum age of the Sun turned out to be tE ≈ 1.4 × 1013 yr. This concept has a fundamental importance though we know now that Sun in its present form cannot survive for more than 10 billion years. We extend this concept by introducing general relativity and show that the minimum value of depletion of total mass–energy is tE = ∞ 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 eternally collapsing objects (ECO). Further since ECOs are expected to have strong intrinsic magnetic field, they are also known as “Magnetospheric ECO” or MECO.