INTRODUCTION TO
GENERAL RELATIVITY
ASTROPHYSICS AND COSMOLOGY

Tonatiuh Matos

GRAVITATION

MATHEMATICAL INTRODUCTION

TOPOLOGICAL SPACES

Definition and Examples

Closure, Interior and Boundary

Continues Functions

Quotient Topology

Compact Spaces

Connected Spaces

DIFFERENTIAL MANIFOLDS

Manfolds

Smooth Functions

Tangent Vectors

One Forms

TENSORS Y P-FORMS

Tensors

p-Forms

Differentiation and Integration in Manifolds

Lie and Covariant Derivatives

Curvature

General Relativity

COSMOLOGY

I THE OBSERVED UNIVERSE

1. Cosmo kinematics
2. Cosmo dynamics 1 y 2
3. The Early Universe
4. Thermal history of the Universe
5. Nucleosynthesis
5. Inflation

ASTROPHYSICS

II THE LARGE SCALE STRUCTURE OF THE UNIVERSE

1. Fluctuations
2. Clusters and Superclusters Formation
3. Galaxies Formation
4. Stellar Formation
5. The Microwave Background Radiation
6. Dark Matter

III GRAVITATIONAL COLLAPSE

1. Spherical Collapse
2. Stars and Neutron Stars Formation
3. Black Hole Formation
4. Non Spherical Collapse
5. Galaxy Formation

IV OPEN PROBLEMS

Texts

Introduction to General Relativity, B. Shultz
Introduction to General Relativity, H. Stephanie
Principles of Physical Cosmology, Peebles
The Early Universe, Kolb and Turner
Structure Formation in the Universe, Padmanabhan
Cosmology, Coles and Lucchin
Cosmological Inflation, Liddle and Lyth
Cosmology, Weinberg
The CMB, Durrer
The Primordial Density Perturbation, Lyth and Liddle
Cosmological Physics, Peacock