Schwarzschild coordinates

Table 1. Here are summarized the used models. The letter (A-E) indicates the mass and number part indicates the 1-hadronic and 2-hybrid Equations of State (EsoS). Mao denotes the gravitational mass of one NS in isolation, C is the compactness, P the orbital period, few,o the corresponding GW frequency, do the initial orbital separation and Roo the radius of one single isolated NS measured in Schwarzschild coordinates.

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. 

The separation of time-like and space-like events creates the impression of two types of response to increased curvature of space-time. If only space coordinates are curved it results in the inversion of the time coordinate and the conversion of matter into antimatter. This situation will be encountered in the Schwarzschild solution of the gravitational field equations, which serves as a model of a black hole, and assumed here to account for an inversion at Z/A = 1.04. It resembles the limitless time-like accumulation of matter, resulting in a space-time singularity. 

These catastrophic effects are the subject of relativistic theories of black holes. In Newtonian theory a black hole appears as the mass of a star increases to the point where its escape velocity exceeds the speed of light. In relativistic theory the singularity at the Schwarzschild radius complicates this description. The problem is avoided by demonstrating that the singularity at r = 2m disappears with a suitable choice of coordinates, as in Figure 6.1. 

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. 

With this simple analogy we will draw some conclusions regarding our black-hole-like entity obtained above. Comparing the Kerr- [29] and the Schwarzschild metric one distinguishes two physical surfaces in the former where the metric either changes sign or becomes singular (spherical coordinate system), i.e. 

---