This is a very short introductory course on general relativity. General relativity is a beautiful but subtle theory that is best understood with help of formal mathematical tools. In this series of six lectures I try to balance physical concepts with some mathematical ideas in the hope to stimulate interested for further readings.
Differential geometry   (in portuguese / pdf format)
Special relativity   (in portuguese / pdf format)
Dynamics equations   (in portuguese / pdf format)
Black Holes   (in portuguese / pdf format)
Gravitaional waves   (in portuguese / pdf format)

Include a general description of the course (ongoing development)
Summary   (pdf format)
Bibliography   (pdf format)

Include a general description of the course (ongoing development)
Summary   (pdf format)
Bibliography   (pdf format)

Short note on Poincaré Group   (in portuguese / pdf format)
This is a short note on Poincaré Group including definition of Lie groups and irreducible representations of the Poincaré group.

Short note on Schutz's formalism.   (in portuguese / pdf format)
This is originally a section of my master dissertation on quantum cosmology. This extraction briefly introduces Schutz's velocity potential formalism, which connects thermodynamic potential with fluid’s velocity field. Amount other things, it allow us to define a variational principle to thermodynamic fluid in general relativity.

Short note on Hamiltonian formalism of GR.   (in portuguese / pdf format)
This is originally a section of my Ph.D. Thesis on quantum cosmology. This extraction briefly introduces the hamiltonian formalism of the Theory of General Relativity. It also includes an introduction to constrained hamiltonian systems and linear cosmological pertubation theory.

Short note on Inflation.   (in portuguese / pdf format)
This is originally a section of my Ph.D. Thesis on quantum cosmology. This extraction briefly introduces the inflationary paradigm for the primordial universe and lacks contrast of models to current observational data.