Infinite Resolution

Abstract

It was reported that General Relativity predicts its own breakdown, because of singularities. We will see that the mathematics of General Relativity can be naturally extended to work fine when the metric becomes degenerate. Then is proposed an extended version of Einstein's equation which remains valid at singularities. The time evolution is expressed by equations which allow passing beyond the singularities. Consequently, the problems of singularities, including Hawking's information paradox, vanish. The core principle used to extend the mathematics and physics of General Relativity beyond the singularities provides a surprising answer to the question: Is there a deep, foundational reason why reality must be purely analog, or why it must be digital?"