20410086 - ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA

The course aims to provide students with the basic concepts of general relativity and its applications to physical systems, with particular reference to compact objects (black holes), gravitational waves and the universe

BRANCHINI ENZO FRANCO

teacher profile | teaching materials

Programme

- SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGY-MOMENTUM TENSOR.
- GENERAL RELATIVITY. UNDERLYING CONCEPTS. AFFINE CONNECTION. PARALLEL TRANSPORT. GEODESICS EQUATION.
- SYMMETRY AND KILLING VECTORS. RIEMANN TENSOR. SINGULARITY.
- EINSTEIN EQUATIONS.
- SCHWARZSCHILD METRIC.
- ORBITS IN THE SCHWARZSCHILD METRIC. MERCURY’S ORBIT.
- NON ROTATING BLACK HOLES. EVENT HORIZON AND THE CHOICE OF COORDINATES.
- KERR METRIC. ROTATING BLACK HOLES AND FRAME DRAGGING.
- INTRODUCTION TO GRAVITATIONAL WAVES.
- THE COSMOLOGICAL PRINCIPLE AND ROBERTSON-WALKER METRIC.
- FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.
- COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. CO-MOVING COORDINATES AND PROPER DISTANCE.
- LUMINOSITY DISTANCE. ANGULAR DIAMETER DISTANCE.
- OBSERVATIONAL TESTS: HUBBLE TEST, ANGULAR DIAMETER TEST, NUMBER COUNTS.
- FLUIDS RELEVANT IN COSMOLOGY: EQUATION OF STATE AND DENSITY EVOLUTION. Cosmological constant.
- THE EQUIVALENCE EPOCH.
- THERMAL HISTORY OF THE UNIVERSE: DECOUPLING. RECOMBINATION.
- MATTER/ANTIMATTER AND THE BARYON ASYMMETRY.
- PLANCK EPOCH AND QUANTUM GRAVITY.
- HORIZON PARADOX. FLATNESS PARADOX. INFLATIONARY SOLUTION. COSMIC INFLATION.
- DARK MATTER.
- A BRIEF HISTORY OF THE UNIVERSE. HADRONIC EPOCH. LEPTONIC EPOCH. RADIATIVE EPOCH.
- NEUTRINO DECOUPLING.
- COSMOLOGICAL NUCLEOSYNTHESIS. MATTER EPOCH. FIRST OBJECTS. RE-IONIZATION.
- INHOMOGENEITY AND ANISOTROPY. JEANS GRAVITATIONAL INSTABILITY AND THE GROWTH OF COSMIC STRUCTURES

Core Documentation

Carroll S. Spaceitme Geometry [Pearson 2003]
Coles P., Lucchin F. Cosmology [Wiley 2000]
Kolb E., Turner M. The eraly Universe [Addison Wesley 1990]

Type of delivery of the course

The course consists of a number of face-to-face lectures, with exercises.

Type of evaluation

The exam is in written form. Questions will be asked addressing all topics in the program. There is the option of splitting it into two exams, each one covering the first and the second half of the program, to be held during and right after the course, respectively.

BRANCHINI ENZO FRANCO

teacher profile | teaching materials

Mutuazione: 20410086 ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA in Fisica LM-17 BRANCHINI ENZO FRANCO

Programme

- SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGY-MOMENTUM TENSOR.
- GENERAL RELATIVITY. UNDERLYING CONCEPTS. AFFINE CONNECTION. PARALLEL TRANSPORT. GEODESICS EQUATION.
- SYMMETRY AND KILLING VECTORS. RIEMANN TENSOR. SINGULARITY.
- EINSTEIN EQUATIONS.
- SCHWARZSCHILD METRIC.
- ORBITS IN THE SCHWARZSCHILD METRIC. MERCURY’S ORBIT.
- NON ROTATING BLACK HOLES. EVENT HORIZON AND THE CHOICE OF COORDINATES.
- KERR METRIC. ROTATING BLACK HOLES AND FRAME DRAGGING.
- INTRODUCTION TO GRAVITATIONAL WAVES.
- THE COSMOLOGICAL PRINCIPLE AND ROBERTSON-WALKER METRIC.
- FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.
- COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. CO-MOVING COORDINATES AND PROPER DISTANCE.
- LUMINOSITY DISTANCE. ANGULAR DIAMETER DISTANCE.
- OBSERVATIONAL TESTS: HUBBLE TEST, ANGULAR DIAMETER TEST, NUMBER COUNTS.
- FLUIDS RELEVANT IN COSMOLOGY: EQUATION OF STATE AND DENSITY EVOLUTION. Cosmological constant.
- THE EQUIVALENCE EPOCH.
- THERMAL HISTORY OF THE UNIVERSE: DECOUPLING. RECOMBINATION.
- MATTER/ANTIMATTER AND THE BARYON ASYMMETRY.
- PLANCK EPOCH AND QUANTUM GRAVITY.
- HORIZON PARADOX. FLATNESS PARADOX. INFLATIONARY SOLUTION. COSMIC INFLATION.
- DARK MATTER.
- A BRIEF HISTORY OF THE UNIVERSE. HADRONIC EPOCH. LEPTONIC EPOCH. RADIATIVE EPOCH.
- NEUTRINO DECOUPLING.
- COSMOLOGICAL NUCLEOSYNTHESIS. MATTER EPOCH. FIRST OBJECTS. RE-IONIZATION.
- INHOMOGENEITY AND ANISOTROPY. JEANS GRAVITATIONAL INSTABILITY AND THE GROWTH OF COSMIC STRUCTURES

Core Documentation

Carroll S. Spaceitme Geometry [Pearson 2003]
Coles P., Lucchin F. Cosmology [Wiley 2000]
Kolb E., Turner M. The eraly Universe [Addison Wesley 1990]

Type of delivery of the course

The course consists of a number of face-to-face lectures, with exercises.

Type of evaluation

The exam is in written form. Questions will be asked addressing all topics in the program. There is the option of splitting it into two exams, each one covering the first and the second half of the program, to be held during and right after the course, respectively.

BRANCHINI ENZO FRANCO

teacher profile | teaching materials

Mutuazione: 20410086 ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA in Fisica LM-17 BRANCHINI ENZO FRANCO

Programme

- SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGY-MOMENTUM TENSOR.
- GENERAL RELATIVITY. UNDERLYING CONCEPTS. AFFINE CONNECTION. PARALLEL TRANSPORT. GEODESICS EQUATION.
- SYMMETRY AND KILLING VECTORS. RIEMANN TENSOR. SINGULARITY.
- EINSTEIN EQUATIONS.
- SCHWARZSCHILD METRIC.
- ORBITS IN THE SCHWARZSCHILD METRIC. MERCURY’S ORBIT.
- NON ROTATING BLACK HOLES. EVENT HORIZON AND THE CHOICE OF COORDINATES.
- KERR METRIC. ROTATING BLACK HOLES AND FRAME DRAGGING.
- INTRODUCTION TO GRAVITATIONAL WAVES.
- THE COSMOLOGICAL PRINCIPLE AND ROBERTSON-WALKER METRIC.
- FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.
- COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. CO-MOVING COORDINATES AND PROPER DISTANCE.
- LUMINOSITY DISTANCE. ANGULAR DIAMETER DISTANCE.
- OBSERVATIONAL TESTS: HUBBLE TEST, ANGULAR DIAMETER TEST, NUMBER COUNTS.
- FLUIDS RELEVANT IN COSMOLOGY: EQUATION OF STATE AND DENSITY EVOLUTION. Cosmological constant.
- THE EQUIVALENCE EPOCH.
- THERMAL HISTORY OF THE UNIVERSE: DECOUPLING. RECOMBINATION.
- MATTER/ANTIMATTER AND THE BARYON ASYMMETRY.
- PLANCK EPOCH AND QUANTUM GRAVITY.
- HORIZON PARADOX. FLATNESS PARADOX. INFLATIONARY SOLUTION. COSMIC INFLATION.
- DARK MATTER.
- A BRIEF HISTORY OF THE UNIVERSE. HADRONIC EPOCH. LEPTONIC EPOCH. RADIATIVE EPOCH.
- NEUTRINO DECOUPLING.
- COSMOLOGICAL NUCLEOSYNTHESIS. MATTER EPOCH. FIRST OBJECTS. RE-IONIZATION.
- INHOMOGENEITY AND ANISOTROPY. JEANS GRAVITATIONAL INSTABILITY AND THE GROWTH OF COSMIC STRUCTURES

Core Documentation

Carroll S. Spaceitme Geometry [Pearson 2003]
Coles P., Lucchin F. Cosmology [Wiley 2000]
Kolb E., Turner M. The eraly Universe [Addison Wesley 1990]

Type of delivery of the course

The course consists of a number of face-to-face lectures, with exercises.

Type of evaluation

The exam is in written form. Questions will be asked addressing all topics in the program. There is the option of splitting it into two exams, each one covering the first and the second half of the program, to be held during and right after the course, respectively.

BRANCHINI ENZO FRANCO

teacher profile | teaching materials

Mutuazione: 20410086 ELEMENTI DI RELATIVITA' GENERALE, ASTROFISICA E COSMOLOGIA in Fisica LM-17 BRANCHINI ENZO FRANCO

Programme

- SPECIAL RELATIVITY. VECTORS AND TENSORS. METRIC TENSOR. ENERGY-MOMENTUM TENSOR.
- GENERAL RELATIVITY. UNDERLYING CONCEPTS. AFFINE CONNECTION. PARALLEL TRANSPORT. GEODESICS EQUATION.
- SYMMETRY AND KILLING VECTORS. RIEMANN TENSOR. SINGULARITY.
- EINSTEIN EQUATIONS.
- SCHWARZSCHILD METRIC.
- ORBITS IN THE SCHWARZSCHILD METRIC. MERCURY’S ORBIT.
- NON ROTATING BLACK HOLES. EVENT HORIZON AND THE CHOICE OF COORDINATES.
- KERR METRIC. ROTATING BLACK HOLES AND FRAME DRAGGING.
- INTRODUCTION TO GRAVITATIONAL WAVES.
- THE COSMOLOGICAL PRINCIPLE AND ROBERTSON-WALKER METRIC.
- FRIEDMAN EQUATIONS. NEWTONIAN LIMIT.
- COSMOLOGICAL REDSHIFT. COSMOLOGICAL HORIZONS. CO-MOVING COORDINATES AND PROPER DISTANCE.
- LUMINOSITY DISTANCE. ANGULAR DIAMETER DISTANCE.
- OBSERVATIONAL TESTS: HUBBLE TEST, ANGULAR DIAMETER TEST, NUMBER COUNTS.
- FLUIDS RELEVANT IN COSMOLOGY: EQUATION OF STATE AND DENSITY EVOLUTION. Cosmological constant.
- THE EQUIVALENCE EPOCH.
- THERMAL HISTORY OF THE UNIVERSE: DECOUPLING. RECOMBINATION.
- MATTER/ANTIMATTER AND THE BARYON ASYMMETRY.
- PLANCK EPOCH AND QUANTUM GRAVITY.
- HORIZON PARADOX. FLATNESS PARADOX. INFLATIONARY SOLUTION. COSMIC INFLATION.
- DARK MATTER.
- A BRIEF HISTORY OF THE UNIVERSE. HADRONIC EPOCH. LEPTONIC EPOCH. RADIATIVE EPOCH.
- NEUTRINO DECOUPLING.
- COSMOLOGICAL NUCLEOSYNTHESIS. MATTER EPOCH. FIRST OBJECTS. RE-IONIZATION.
- INHOMOGENEITY AND ANISOTROPY. JEANS GRAVITATIONAL INSTABILITY AND THE GROWTH OF COSMIC STRUCTURES

Core Documentation

Carroll S. Spaceitme Geometry [Pearson 2003]
Coles P., Lucchin F. Cosmology [Wiley 2000]
Kolb E., Turner M. The eraly Universe [Addison Wesley 1990]

Type of delivery of the course

The course consists of a number of face-to-face lectures, with exercises.

Type of evaluation

The exam is in written form. Questions will be asked addressing all topics in the program. There is the option of splitting it into two exams, each one covering the first and the second half of the program, to be held during and right after the course, respectively.