Advanced General Relativity

mathematics
physics

elective courses

Knowledge of the Einstein theory at the level of lectures General Relativity I is expected.

Classroom

This is continuation of lectures General Relativity I. The following topics will be discussed: black holes, global structure of spacetime, energy and momentum of gravitational field, gravitational radiation, initial constraints and the Hamiltonian formalism.

In this edition we will focus on asymptotic issues and the related theory of gravitational radiation. The cases of zero cosmological constant and positive cosmological constant will require separate discussion. We will introduce descriptions using Bondi-Sachs and Fefferman-Graham coordinate systems. We will give a detailed connection to the Newman-Penrose formalism using the Weyl tensor and the geometry of the conformal boundary of space-time (scri). In all these formalisms, we will calculate the charges associated with the symmetries, the corresponding fluxes, and the balance laws derived from Einstein's equations. Then we will apply it to the description of gravitational radiation, and illustrate on examples of merging black holes. We will pay attention to the dependence of the results on the presence (or not) of a cosmological constant. In the asymptotically flat case, the geometric and physical structures introduced will be applicable to the celestial holography. As time permits, we will discuss the radiation of black hole space-time perturbations in more detail.

R.M.Wald, General Relativity

G. Comp`ere, A. Fiorucci, and R. Ruzziconi, The Λ-BMS4 group of dS4 and new boundary conditions for AdS4, Class. Quant. Grav. 36, 195017 (2019), [Erratum: Class.Quant.Grav. 38, 229501 (2021)], arXiv:1905.00971 [gr-qc].

Adam Bac, licencjat, Relation between the Bondi-Sachs theory of gravitational radiation and that of Newman-Penrose-Ashtekar

Marc Geiller, Céline Zwikel, arXiv:2401.09540,

The partial Bondi gauge: Gauge fixings and asymptotic charges

Upon completion of the course, the student will have the tools of covariant geometry on the one hand and using commonly used coordinate systems on the other to describe the conformal edge of space-time. In the case of the zero cosmological constant, this will be well established yet quite advanced knowledge. It will allow the student to better understand new directions of research, such as celestial holography or description of the radiation produced by merging black hioles. In the case of a positive cosmological constant, it is a hot research topic, so the student will learn about the latest ideas and will even have the opportunity to become actively involved in research on his own.

A passion for exploring the secrets and misteries of general relativity makes evaluation of learning results just a formality.

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