Topics in General Relativity and Cosmology - Topicos de Relatividade Geral e Cosmologia


I fought really hard and for a long time for this course to be offered to students. Finally, it became available as an optional course to the 4th and final year students in the Teaching of Physics-Chemestry (eventually becoming High or Secondary School teachers).

As in the course of Astrophysics, I aim on (a) providing students with a fair description of different physical and mathematical aspects, together with (b) exploring with simple but rigourous calculations how one can actually explain how the universe is or can be. I do not agree with some amateurish attitudes that some General Relativity concepts are only to be merely "described" to students by means of diagrams and a lot of "that's it!". I tried to also "put physics" (and some mathematics) in it. Otherwise, students will neither understand the "why" and "how" of A. Einstein's overwhelming achievement.

The course covers a basic introduction on why Special Relativity is not (good) enough when gravity is present, then invoking all the features and sidelines of the Equivalence Principle. A lot of geometry follows (always with a properly justified insight of physical interpretation and its need). It culminates in the Einstein's equations, the geodesic deviation effect and the Newtonian limit (students felt particularly relieved when getting to this - maybe their "natural everyday ground"). But the excitment is too strong and the lecturer continues his unfailling path. He then focuses on the Schwarzschild solution and its physical consequences,with a brief spell on Gravitational Waves (if time allows). The course ends with Relativistic Cosmology. Students here seemed to enjoy getting aware on how General Relativity features and cosmological big-bang features can actually be retrieved, calculated and scientifically explained, instead of just displaying nice pictures of the night sky or a diagram of the Hubble law.

But if you are in doubt whether Relativity and Cosmology aspects may arise when the least you expect, perhaps you should consider otherwise.

(If you got curious have a look at my research career and research projects list - for different ranges of students/collaborators).

Program, Evaluation Methods and Bibliography

In the following links you may find

Lecture Notes

Lecture notes are being made available!! Thanks to the unfailing assistance of a few students, the handwritten (in the lecturer usual cryptic style) lines are transformed in a monograph. You may obtain it here. I do hope it will be both useful and enjoyful for you as for me.

Tutorials Schedulle

Students can consult me [Horario de Atendimento - 2002/03] on Thursday - 5a Feira between 11.00 - 12.00 am, either in my office or LAG.

Exams, Tests,Problem Sets and Marks (classifications)

Students may peruse previous example/exercice sheets and tests/exams (some may be missing - I will try to update this section):

Students may also find the several problem sets and project assignments posted here.

This is the current academic year (2002/2003) Marks/Classifications (Excel format)

Other Resources Available

My report submitted for my Agregacao can be found here. It constitutes a (Detailed) Description of the Course, but please note there are some slight changes and diferences concerning the programme, bibliography and assessement.

Finally, the following links may provide additional material for your study. These are on-line resources about General Relativity and Cosmology:

Here you will find more lecture notes on General Relativity and Cosmology

A varied list or varied resources on various aspects of phsycs...

A suggestive list of some relevant (and not just!) review articles can be found here:

If you are interested in advancing your knowledge in cosmology this is a good starting point to begin your "wild" explorations about the universe:

In the links below you will find a "must have read" series of papers. Some cannot be missed (if you want to learn more):

So, you still feel brave enough? Here is a good sample on CMB and Cosmological Perturbations

... And another list of interesting references is as follows. They concern what may become a XXIth century paradigm on our understanding of the universe. It seems the universe has been expanding and "recently" it started ... to accelerate! So here are a few references focusing on the really recently "weird" (maybe not, in fact) features of the universe - Dark Energy and the Cosmological Constant:

And not to be missed for the curious one (may the force be with you, oh brave wanderer...) is the following list of papers on Dark Matter

Oh, I see. Good heavens, you made it up to here! So you are really interested in the subject and many of its related features. You can therefore find here a list of possible topics and further useful links as well as as description of my research work in (Quantum) Cosmological Implications of Superstring Theory. On the whole, you will find either reviews or research papers on the borderline where Field Theory, Particle Physics, Supersymmetry, String-Branes-M-theory may merge within a cosmological scenario. Have fun, but be aware: Ich warne Neugierige, quoting the wise words of W. Pauli.

Students Feedback on the Course

Finally, I have asked the students to fill in THIS questionaire (Inquerito1) Query1 at the start of the semester and THIS questionaire (Inquerito2) Query2 at the end. I stress that these are THE questionaires that interest me the most. I am further grateful in advance for any constructive criticism that may have assisted me and the teaching of Topics in General Relativity and Cosmology to be both more effective in the (very!) near future.

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