Home on Anandh Krishna Murichatta

Connections, curvature & holonomy

Sat, 13 Jun 2026 00:00:00 +0530

The connection is the rule for comparing vectors at neighbouring points; its curvature is the obstruction to comparing them globally. This chapter assembles the whole apparatus — equations, a definition, a theorem, a proof, and a short Julia experiment — around one classical fact: parallel transport around a loop remembers the curvature it enclosed.

Curriculum Vitae

Mon, 26 Oct 2026 04:25:33 +0530

Now

Mon, 26 Oct 2026 04:25:33 +0530

Research

Mon, 26 Oct 2026 04:25:33 +0530

I work in mathematical general relativity, mainly on black-hole stability and on the asymptotic structure of spacetime at null infinity.

Resources

Mon, 26 Oct 2026 04:25:33 +0530

Organised loosely by topic.

Foundations of GR#

Wald — General Relativity. The standard graduate reference; rigorous and geometric.
Misner, Thorne & Wheeler — Gravitation. Encyclopaedic; best for physical intuition.
Hawking & Ellis — The Large Scale Structure of Space-Time. Global methods, causal structure, singularity theorems.
O’Neill — Semi-Riemannian Geometry. The cleanest account of the underlying geometry.

The Einstein equations as PDE#

Choquet-Bruhat — General Relativity and the Einstein Equations. The reference for the Cauchy problem.
Ringström — The Cauchy Problem in General Relativity. Modern and self-contained.
Chruściel — Elements of General Relativity. Excellent modern notes.

Causal structure & global methods#

Penrose — Techniques of Differential Topology in Relativity.
Beem, Ehrlich & Easley — Global Lorentzian Geometry.

Black holes & perturbations#

Chandrasekhar — The Mathematical Theory of Black Holes.
Dafermos & Rodnianski — Lectures on black holes and linear waves (arXiv:0811.0354).

Spinors & spin coefficients#

Penrose & Rindler — Spinors and Space-Time, vols. 1–2.
Stewart — Advanced General Relativity. A compact route to NP and GHP.

Numerical relativity#

Alcubierre — Introduction to 3+1 Numerical Relativity.
Baumgarte & Shapiro — Numerical Relativity.

Lectures online#

Frederic Schuller — GR lectures — extremely clear mathematical foundations
Sean Carroll — Lecture notes on general relativity
PIRSA — Perimeter Institute recorded seminars

Tools#

xAct (Mathematica) — tensor computer algebra; what I use most.
Cadabra — field-theory-friendly computer algebra.
SageManifolds — symbolic differential geometry in Python.
Black Hole Perturbation Toolkit — codes and data for perturbation theory.

Some doodles and Cartoons

Fri, 26 Dec 2025 04:37:00 +0530

Just posting some doodles and cartoons I made recently, while I getting bored during my work. Finding some place to dump them - Academic life, according to cats, rabbits and all of that.

Abyss

A personal Anecdote with Prof. Naresh Dadhich

Mon, 22 Dec 2025 00:26:00 +0530

This is a post in memory of Prof. Naresh Dadhich and I would like to share a personal anecdote that highlights his influence on my academic journey. This is my first blog writing here. I was confused about how to start writing a blog post. So, I decided to share a personal anecdote about my interaction with Prof. Naresh Dadhich.

A note on Birkhoff's theorem

Mon, 22 Dec 2025 00:00:00 +0530

Birkhoff’s theorem is one of the most elegant results in classical general relativity. It asserts that the geometry outside any spherically symmetric matter distribution is uniquely fixed — regardless of whether the source is static, pulsating, or collapsing.