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Advanced Topics
in Theoretical Physics

Perugia, Department of Physics and Geology, 14-15-16 April 2025

Program

The course will address the following topics:

  1. I. The spinorial description of General Relativity, and its applications to black hole physics, course held by David Pereñiguez:

    I will review Penrose’s observation that gravity in four dimensions admits a strikingly simple description in terms of 2-spinors. The main topics of discussion will be the description of the curvature tensor in terms of its irreducible spinor representations, the algebraic classification of the Weyl tensor in Petrov types, and the GHP formalism to translate spinor equations into tensorial ones. As an application, I will derive the master wave equation governing the generation and propagation of gravitational waves in the vicinity of Kerr black holes, and I will use it to compute their quasinormal frequency spectrum. I will conclude by discussing how this can yield promising tests of GR and new physics beyond, as well as mentioning current challenges in the field.

    While the various formalisms will be treated in some detail, the discussion will not be excessively formal and always oriented towards practical applications. Together with the course I will provide lecture notes as well as some mathematica notebooks, which make use of several xAct mathematica packages.
  2. II. General-relativistic cosmology, course held by Asta Heinesen:

    I will present the 1+3 covariant formulation of general relativity, which is based on decomposing the space-time into a three dimensional congruence of worldlines. This formulation allows to decompose Einstein’s equations into relations between variables of physical/geometrical significance, and is useful for describing dynamics, geometry and observables in general relativistic cosmological models defined in the widest sense. I will go through the set of constraint and evolution equations for the geometry obtained from the Ricci and Bianchi identities in the 1+3 covariant approach, and I will formulate observables that may be used to test a wide range of cosmologies within the formalism presented. I will furthermore describe some of the most important exact cosmological models and how these can be obtained by imposing restrictions within the general equations, in particular, I will show how the spatially maximally-symmetric Friedmann–Lemaitre–Robertson–Walker cosmologies are recovered.

Lectures Schedule

14 April
  • 10:30-12:30 - Aula E - A. Heinesen
  • 14:30-16:30 - Aula C - D. Pereñiguez
15 April
  • 10:30-12:30 - Aula C - A. Heinesen
  • 14:30-16:30 - Aula B - D. Pereñiguez
16 April
  • 13:30-15:30 - Aula C - A. Heinesen
  • 15:30-17:30 - Aula C - D. Pereñiguez

Lecturers

Dr. David Pereñiguez
David Pereñiguez

Postdoctoral Fellow at Center of Gravity, Niels Bohr Institute, Copenhagen (Denmark)

David Pereñiguez obtained his PhD from the Institute of Theoretical Physics, in the Autonomous University of Madrid. He joined NBI in October 2022. His research focuses on black hole physics. At NBI, he works on theoretical aspects of gravitational wave propagation in black hole spacetimes, and studies how these encode information about the black hole structure, with special emphasis on signatures of new physics. For more information about his research, visit this page.

Dr. Asta Heinesen
Asta Heinesen

Postdoctoral Fellow at Center of Gravity, Niels Bohr Institute, Copenhagen (Denmark)

Asta Heinesen is a postdoctoral researcher working on questions within cosmology and general relativity. Her research is in the interface between theoretical and observational cosmology, and focuses on developing model - independent methods for analysing, for instance, standard candles, standard sirens, and the ages and distribution of galaxies in the Universe. For more information about her research, look at this page.

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