Celebratio Mathematica

C. Rourke: A new paradigm for the universe. Preprint, 2003. ArXiv abs/astro-ph/0311033 techreport

R. S. MacKay and C. P. Rourke: “Natural observer fields and redshift,” J. Cosmol. 15 (2011), pp. 6079–6099. article

R. S. MacKay and C. Rourke: “Natural flat observer fields in spherically symmetric space-times,” J. Phys. A, Math. Theor. 48 : 22 (2015), pp. 225204, 11. Id/No 225204. MR 3355220 Zbl 1318.83002 article

An observer field in a space-time is a time-like unit vector field. It is natural if the integral curves (field lines) are geodesic and the perpendicular three-plane field is integrable (giving normal space slices). We prove that a natural observer field determines a coherent notion of time: a coordinate that is constant on the perpendicular space slices and whose difference between two space-slices is the proper time along any field line.

A natural observer field is flat if the normal space slices are metrically flat. For static spherically symmetric space-times we find a necessary and sufficient condition for possession of a spherically symmetric natural flat observer field. In this case, which includes the Schwarzschild and the Kottler space-times, there is in fact a dual pair of spherically symmetric natural flat observer fields. One of these observer fields is expanding and the other contracting and it is natural to describe the expanding field as the ‘escape’ field and the dual contracting field as the ‘capture’ field.

Observer fields are useful for understanding redshift and the fields described here are used in a possible explanation of redshift explored in [McKay and Rourke 2015].

R. S. Mackay and C. Rourke: “Are gamma-ray bursts optical illusions?,” Palest. J. Math. 5 (2016), pp. 175–197. MR 3477629 Zbl 1346.83071 article

C. Rourke, R. Toalá-Enríquez, and R. S. MacKay: Black holes, redshift and quasars. Preprint, 2017. techreport

C. Rourke: The geometry of the universe. Series on Knots and Everything 71. World Scientific Publishing (Hackensack, NJ), 2021. MR 4375354 book

R. S. MacKay and C. P. Rourke: Polarisation of gamma-ray bursts, 2021. preprint. misc

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Colin P. Rourke

Colin Rourke’s new paradigm for the universe

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