Buracos Negros e Ondas Gravitacionais

Objectives

Some of the most exciting developments in theoretical and observational physics relate to black holes, gravitational waves and curved spacetimes. The course aims to familiarize students with some of the main properties of black holes, some of the issues in contemporary research and the main tools in gravitational-wave physics.

Syllabus

Gravitational Collapse (White Dwarfs and Neutron Stars; Oppenheimer-Snyder Collapse; geodesics and affine parameterization; Symmetries and Killing Vectors; Black and White Holes) Schwarzschild Black Holes (Definition; Null Hypersurfaces; Killing Horizons; Surface Gravity and Hawking Temperature; Carter-Penrose Diagrams and Conformal Compactification; The Event Horizon; Black Holes vs. Naked Singularities; Electrically charged and rotating black holes; Cauchy horizons; Frame dragging and ergoregions; Uniqueness: the Israel and Carter Robinson results; Cosmic Censorship) Gravitational waves (Linearization of field equations; gauge symmetry; Wave equation; TT gauge; Interaction of GWs with point particles; Description in TT gauge and free- falling frame; Effective stress-energy tensor of GWs; Generation of GWs; Radiated energy, angular and linear momentum; Application to binary systems; templates for data analysis)

Prerequisites

The attendance of Differential and Integral Calculus I, II, III is highly recommended, as well as of General Relativity.

Cross Competence Component

The course will stimulate creative thinking, through non-standard problem- solving involving a broad set of classical physics. The course will develop verbal and written communication skills, by assigning a set of homework, group problems, which will be presented and discussed by students. An estimated 10% of the course time is dedicated to soft-skill acquisition.

Laboratorial Component

There is no laboratory component

Programming And Computing Component

The course has a computation and programming aspect, to be developed through examples in the class and in homeworks. These have special significance and focus on abstraction, function-definition and usage, recursive functions, algorithms and iterative processes. The course will stimulate the numerical resolution of ordinary and partial differential equations, focusing both on the physical aspects and on the algorithmic procedure. An estimated 15% of the student time will be spent on programming anf computing.

Ethical Principles

All members of a group are responsible for the group’s work In any assessment, every student shall honestly disclose any help received and sources used. In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.