Nontrivial zeros of the Riemann zeta function (2023)
Working Paper
Austin, J. Nontrivial zeros of the Riemann zeta function

The Riemann hypothesis, stating that all nontrivial zeros of the Riemann zeta function have real parts equal to 1/2, is one of the most important conjectures in mathematics. In this paper we prove the Riemann hypothesis by solving an integral form of... Read More about Nontrivial zeros of the Riemann zeta function.

Do Causality Violations Initiating a Compactly Generated Cauchy Horizon Require Exotic Matter? (2023)
Book Chapter
Austin, J. (2023). Do Causality Violations Initiating a Compactly Generated Cauchy Horizon Require Exotic Matter?. In Hidden Aspects of Time. Cambridge Scholars Publishing

This short paper summarises the proof that a causality violation formed from a bounded region requires matter that violates the null energy condition. Therefore the answer to the question in the title is yes. This is one of the results on which Steph... Read More about Do Causality Violations Initiating a Compactly Generated Cauchy Horizon Require Exotic Matter?.

Black hole inconsistencies? (2020)
Working Paper
Austin, J. Black hole inconsistencies?

For large enough astrophysical objects, internal pressures are insufficient to prevent gravitational collapse to sizes smaller than a critical radius where the magnitude of escape velocity is equal to the speed of light. In coordinates natural for di... Read More about Black hole inconsistencies?.