On the Schwarzschild Solution: a Review

Carmine Cataldo

Vacuum Field, Weak Field Approximation, Schwarzschild Metric, Alternative Derivation.

In this paper the well-known Schwarzschild Solution is discussed. In the first section, by resorting, as usual, to the Einstein Field Equations, a short summary of the conventional derivation is provided. In the second section, we carry out an alternative derivation of the Schwarzschild Metric. The above-mentioned procedureis based upon several noteworthy hypotheses, among which the existence of a further spatial dimension stands out. Initially, we postulate a Universe identifiable with a 4-ball, homogeneously filled with matter, whose radius equates the Schwarzschild Radius. Then, in order to obtain the vacuum field, all the available mass is ideally concentrated in a single point.By imposing a specific condition concerning the measured radius, we deduce a metric that, if subjected to an appropriate parametrization, allows us to finally obtain the Schwarzschild solution.

10.22161/ijaers.4.9.10