Schwartzschild

Convection will not drastically alter the results of our calculations. Smarr et al. (1981) found that with complete core overturn the luminosity increased at most by 30%. Mayle (1985) in a series of calculations with mixing length theory found about a 20% enhancement of the luminosity. Our models are unstable by the LeDoux and salt finger criteria but not the Schwartzschild criteria. Future calculations will include convection. 

It is interesting that our present global superposition principle unequivocally leads to the famous Laplace-Schwarzschild radius r = 2/x = RL (we assume that M is totally confined inside RLs)- There is a difference, however. Although the classical "Schwartzschild singularity" depends on the choice of the coordinate system, the present result is a generic property that exhibits the autonomic nature of the universal linear principle. Hence, decoherence to classical reality may occur for 0 < x(r) < while potential quantum-like structures arise inside RLs for < x(r) < 1. 

It is obvious that the behavior at the Schwartzschild radius is different for the cases m0 A 0 and m0 = 0, see Eqs. (95), (103), and (104). Hence, we need to find consistent relations that link the two, independent of the specific eigenvalue of the mass operator examining the conjugate operator formulation based on the representations, i.e., Eqs. (98) and (104), where the energies scale as EopVl — 2k (r). By a straightforward generalization of Eq. (72), we obtain... 

Find the radius of the black hole, and determine its mass M. Compare M it to the mass of our sun, 1.985 x 103°kg. Discuss the Schwartzschild singularity and Hawking s96 explanation. 

It is remarkable that the exceptional point Eq. 1.79 corresponds to the celebrated Laplace-Schwarzschild radius r = 2/i = Rls (given that M is confined inside a sphere with radius Rls). Note that the present result is a universal property of the present formulation in contrast to the classical Schwartzschild singularity , which depends on the choice of coordinate system. Stated in a different way decoherence to classical reality might take place for 0 < rc(r) < whilst potential quantum like structures appears inside Rls for j < K(r) < 1. 

Again we note that the present complex symmetric ansatz has generated a covariant transformation, compatible with the classical Schwartzschild gauge but, as has been stated recurrently, we have not yet proven or explained the origin of time irreversibility. 

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