https://anandhkrishnam.github.io/subjects/mathematics/Recent content in Mathematics on Anandh Krishna MurichattaHugoen-GB© {year} Anandh Krishna Murichatta · text licensed CC BY 4.0Mon, 26 Oct 2026 04:25:33 +0530https://anandhkrishnam.github.io/lectures/mathematical-gr/Mon, 26 Oct 2026 04:25:33 +0530https://anandhkrishnam.github.io/lectures/mathematical-gr/<p>These notes follow Wald, Hawking and Ellis, and O&rsquo;Neill. Notation and sign conventions are listed on the <a href="https://anandhkrishnam.github.io/notes/">notes page</a>.</p>https://anandhkrishnam.github.io/notes/mathematics/Mon, 26 Oct 2026 04:25:33 +0530https://anandhkrishnam.github.io/notes/mathematics/https://anandhkrishnam.github.io/lectures/np-ghp/Mon, 26 Oct 2026 04:25:33 +0530https://anandhkrishnam.github.io/lectures/np-ghp/<p>Notes on the spin-coefficient formalisms, following Penrose and Rindler for two-component spinors and <a class="cite" href="#ref-ghp1973" title="R. Geroch, A. Held, R. Penrose — A space-time calculus based on pairs of null directions (1973)">[GHP73]</a> for the GHP calculus.</p>https://anandhkrishnam.github.io/lectures/mathematical-gr/curvature-and-holonomy/Sat, 13 Jun 2026 00:00:00 +0530https://anandhkrishnam.github.io/lectures/mathematical-gr/curvature-and-holonomy/<p>The connection is the rule for comparing vectors at neighbouring points; its curvature is the obstruction to comparing them <em>globally</em>. This chapter assembles the whole apparatus — equations, a definition, a theorem, a proof, and a short Julia experiment — around one classical fact: <strong>parallel transport around a loop remembers the curvature it enclosed.</strong></p>