Classical theory of singularities

The singularities from the general relativity resulting by solving Einstein’s equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
DOI: 10.13140/RG.2.2.22006.45124

Classical theory of singularities

Hooke’s claim on the law of gravity

Hooke's claim on the law of gravity

Based on Galileo’s experiments, Newton develops the theory of gravity in his first book Philosophiæ Naturalis Principia Mathematica (“Principia“) of 1686. Immediately after, Robert Hooke accused Newton of plagiarism, claiming that he unduly assumed his “notion” of “the rule of the decrease of Gravity, being reciprocally as the squares of the distances from the Center”. But, according to Edmond Halley, Hooke agreed that “the demonstration of the curves generated by it” belongs entirely to Newton.

DOI: 10.13140/RG.2.2.16867.81441

Hooke’s claim on the law of gravity

The singularities as ontological limits of the general relativity

The singularities from the general relativity resulting by solving Einstein’s equations were and still are the subject of many scientific debates: Are there singularities in spacetime, or not? Big Bang was an initial singularity? If singularities exist, what is their ontology? Is the general theory of relativity a theory that has shown its limits in this case?
In this essay I argue that there are singularities, and the general theory of relativity, as any other scientific theory at present, is not valid for singularities. But that does not mean, as some scientists think, that it must be regarded as being obsolete.
After a brief presentation of the specific aspects of Newtonian classical theory and the special theory of relativity, and a brief presentation of the general theory of relativity, the chapter Ontology of General Relativity presents the ontological aspects of general relativity. The next chapter, Singularities, is dedicated to the presentation of the singularities resulting in general relativity, the specific aspects of the black holes and the event horizon, including the Big Bang debate as original singularity, and arguments for the existence of the singularities. In Singularity Ontology, I am talking about the possibilities of ontological framing of singularities in general and black holes in particular, about the hole argument highlighted by Einstein, and the arguments presented by scientists that there are no singularities and therefore that the general theory of relativity is in deadlock. In Conclusions I outline and summarize briefly the arguments that support my above views.

CONTENTS

Abstract
Introduction
– – – Classical Theory and Special Relativity
– – – General Relativity (GR)
1 Ontology of General Relativity
2 Singularities
– – – Black Holes
– – – – – – Event Horizon
– – – Big Bang
– – – Are there Singularities?
3 Ontology of Singularities
– – – Ontology of black holes
– – – The hole argument
– – – There are no singularities
Conclusions
Notes
Bibliography

DOI: 10.13140/RG.2.2.14521.06241/1

The singularities as ontological limits of the general relativity

Newton’s action at a distance – Different views

solar systemDifferent authors have attempted to clarify the aspects of remote action and God’s involvement on the basis of textual investigations, mainly from the Mathematical Principles of Natural Philosophy, (Newton, 1999b) Newton’s correspondence with Richard Bentley (1692/93), (Bentley 1693) and Queries that Newton introduced at the end of the Opticks book in the first three editions (between 1704 and 1721). (Newton 1952)

DOI: 10.13140/RG.2.2.12870.11844

Newton’s action at a distance – Different views

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