The singularities as ontological limits of the general relativity by Nicolae Sfetcu - HTML preview

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Notes

1) For each event A, there is a set of independent events of observers which can, in principle, influence or be influenced by A through signals or interactions that do not have to travel faster than light and a set of events for which such influence is impossible.

2) Einstein field equations:

Gμν ≡ Rμν - (1/2)Rgμν = (8πG/c)T > μν

where Gμν is the Einstein tensor, a specific combination without distinction of the Ricci tensor Rμν and the metrics, and Tμν is the energy-momentum tensor. The proportionality constant can be fixed as k = 8πG/c4, where G is the gravitational constant and c the speed of light. In vacuum, Rμν = 0.

3) Restrictions of singularities in the future exclude original singularities, such as Big Bang, which are, in principle, visible to observers at a later cosmic moment. The cosmic censorship conjecture was first presented by Penrose in a work in 1969. (Penrose 1969) incomplete paths or to the idea of space-time "missing points" or an idea combining the two above concepts, respectively a single structure with "pathological" behavior (spacetime deformation which manifests himself as a gravitational field). (Curiel and Bokulich 2018)

4) In a common field equation, knowing the source of the field and the boundary conditions determines the field everywhere. However, they do not determine the vector potential. Einstein found that if the gravitational equations are generally covariant, then the metric can not be determined uniquely by its sources as a function of spacetime coordinates. Some philosophers of physics call for argument to raise a problem of manifold substantiality, according to which the manifestation of events in space is a "substance" that exists independently of the metric field defined on it or its matter. Others consider the argument to be a confusion in terms of gauge.