arXiv:2412.08026gr-qc
A Lean and Mean Introduction to Modern General Relativity
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Abstract
Notes prepared for the introductory general relativity course PHYSICS 748 at The University of Auckland. They are designed to introduce general relativity to upper-year undergraduate students directly using the modern language of differential geometry but in a physically motivated way, and throughout keeping a logical flow from section to section and chapter to chapter. In doing so, they necessarily cover a number of topics either not normally treated in an introductory course, or from a novel perspective. These include for example: affine spaces, comparing and contrasting rank-2 tensors with matrices, integration on manifolds, the Rindler metric, including a proper near-source boundary condition for the Schwarzschild metric, approaching Kruskal-Szekeres coordinates from a Rindler perspective, and more.
Simulations require supercomputers for doing large scale, detailed calculations, but simple situations can be solved completely analytically. For example, gravitational time dilation can be calculated somewhat simply for a central gravitational potential…
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