The purpose of this series of talks is to introduce Schwarzschild universe and a non-commutative generalization. This first talk focuses on the Schwarzschild universe, by which we mean a maximal conformal analytic extension of the static, spherically symmetric space-time vacuum. We shall discuss the structure of its null geodesics (they are elliptic curves), null geodesic deviation, and the theorem proven jointly by the speaker and George Sparling that every null geodesic in Schwarzschild "feels" the temperature of the singularity (a la Gibbons and Hawking). Subsequent talks shall introduce a non-commutative generalization of Schwarzschild that includes a magnetic monopole as part of the gravitational structure, and perform the corresponding analysis in that case.

This talk assumes some familiarity with general relativity, complex variables, and Hamiltonian mechanics. Some prior exposure to elliptic functions is also desirable, although we shall state without proof basic facts as they are needed.

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