Advanced gravitation and cosmology

A growing fraction of the research that is published today is related to the gravitational interaction in some of its manifestations. Significant advances have been made not only in the theoretical field but also, and especially, in the experimental one. Among them it is possible to emphasize the consecration of the Cosmoloxía like a science of precision, and the appearance of the Astronomy of Waves Gravitate you. Both disciplines generated very high expectations of being the prelude to new discoveries. As a consequence, an intense research and teaching activity was unleashed worldwide both theoretically and experimentally.

Learning outcomes:

-Introduce students to advanced topics in General Relativity and Cosmology with an emphasis on gravitational waves.
-Study formal and analytical methods based on symbolic and numerical programming
-Study the most accepted cosmological models and theories and open questions
-Knowledge of the experimental data and its treatment

1. Methods: Geometric methods. Analytical Solutions. Hamiltonian approach. Energy and Angular Moment. Initial conditions problem. Numerical relatividade.
2. Black Holes: Types of horizon. Local and global aspects. Loaded and rotating holes. Unicidade. You read the mechanics of Black Holes. Thermodynamics. Hawking radiation. Stellar collapse and astrophysical holes.
3. Gravitational Waves: Propagation and generation of linearized waves. Multipolar expansion, post-Newtonian approach. Compact binary systems. Quasinorm modes. Indirect and direct observation. Data treatment.
4. Advanced Cosmoloxy: Singularity Theorems. Cosmoloxic models. FRW, dS, inflation. Observational aspects: CMB, dark matter, Lambda-CMB model. Primordial gravitational waves. Cosmic microwave background radiation polarization.

1. Robert Wald, General Relativity and Gravitation, Univ. Chicago Press.
2. Eric Poisson, A Relativist's Toolkit, Cambridge University Press.
3. Michele Maggiore, Gravitational Waves, Oxford University Press.
4. V. Mukhanov, Physical Foundations of Cosmology, Cambridge University Press.
5. Valery P. Frolov and Igor D. Novikov, Black Hole Physics, Springer.
6. Steven Weinberg, Cosmology, Oxford University Press.
7. David Tong, Cosmology [http://www.damtp.cam.ac.uk/user/tong/cosmo.html]

Apart from the basic and general competences, common to any master subject, this course aims to generate specific competences of the following type:

- master the general tensor calculation and advanced notions of differential geometry that are explained in the course.
- be able to read articles of General Relativity and Gravitation as those published daily.
- have a global vision of the most important problems that are being addressed today in the field.
- know and be able to use basic tools of symbolic and numerical calculation to address tasks that require it.
- be able to access public databases of experiments such as Planck, or Ligo, and download and analyze simple data packages.

The course will be developed in lectures in which the teacher will explain the theoretical concepts on the board and propose exercises, and interactive classes where they will proceed to correct those exercises. Work will be proposed to deepen aspects in which the student shows greater interest. There will be practical sessions by computer, both for performing symbolic calculation exercises and analyzing experimental data. The student will have the corresponding tutoring hours.

The evaluation of the subject will be a combination of the different activities carried out in class so attendance is essential and will be controlled.

Within the evaluable activities are problem bulletins and small jobs.
At the end of the course a more complete work will be done that must be exposed and put in common with the rest of the class.

The evaluation of the subject will contain a combination of:
- Bulletins of problems and small class work: 60%
- Final work of the subject and exhibition: 40%

This type of evaluation implies that the student must attend most classes and maintain a participative attitude. In case of an absence of more than 20% of the total class hours, the student must be evaluated through an examination of the subject.

In cases of fraudulent completion of exercises or tests, the following will apply to the provisions of the "Regulations for evaluating students' academic performance and reviewing grades":

"Article 16. Fraudulent performance of exercises or tests.

The fraudulent performance of any exercise or test required in the evaluation of a subject will imply the qualification of failed in the corresponding call, regardless of the disciplinary process that may be followed against the offending student. It is considered fraudulent, among other things, the realization of plagiarized works or obtained from sources accessible to the public without re-elaboration or reinterpretation and without citations to the authors and the sources ”.

The subject consists of 3 ECTS, so the total hours of work of the student, including evaluation activities is 75 hours, structured in:

- 20 hours of expository class
- 10 hours of interactive class
- 1 hour of tutoring
- 44 hours of student's personal work

It is a subject with a high level of abstraction. Therefore, an internalization of the concepts requires a constant and measured study with teaching.

Some familiarity with the Python programming language is recommended.

It is recommended to use the personalized tutorials.