Topics in General Relativity

May 12th – May 30th, 2025


Gran Sasso Science Institute, L'Aquila (IT)

The course will introduce Penrose’s incompleteness theorem to a broad mathematical audience. The course will be delivered in the format of a reading seminar and will include introductory modules on the basics of differential geometry and general relativity, to which no prior exposure will be assumed.

Calendar

Angia Lauri & Eugenio Turchet

Manifolds, tensors and flows

Sec 2.1--2.3, 2.5, 2.14

Francesco Tornabene

Connection and curvature

Sec 2.6--2.12, 2.15--2.16

Martino Caliaro

Lorentzian geometry and Einstein equations

Sec 2.4, 2.13, 2.17

Martina Giachello

Minkowski space and Schwarzschild geometry

Sec 3.1 (excl. 3.1.4), 3.2 (excl. 3.2.1)

Ginevra Braga

Global hyperbolicity and well-posedness for geometric wave equations

Sec 4.5--4.7

Vishnu Sanjay

Well-posedness for Einstein equations

Sec 4.8--4.11 (perhaps excl. Sec 4.9)

Flavio Rossetti

Penrose's Incompleteness Theorem I

Sec 6.1--6.2 + extra

Pierfrancesco Martini

Penrose's Incompleteness Theorem II

Sec 6.3

Gabriele Benomio

Penrose's Incompleteness Theorem III

Sec 6.4--6.7

Gabriele Benomio

Q&A and outlook


Reading material: G. Holzegel, General Relativity and the Analysis of Black Hole Spacetimes

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