Unit INTRODUCTION TO GENERAL RELATIVITY
- Course
- Physics
- Study-unit Code
- GP005462
- Curriculum
- In all curricula
- Teacher
- Orlando Panella
- Teachers
-
- Orlando Panella
- Hours
- 42 ore - Orlando Panella
- CFU
- 6
- Course Regulation
- Coorte 2018
- Offered
- 2020/21
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- FIS/02
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Elements of differential geometry essential for learning the concept of essential curvature for a description of Einstein's theory of gravity. Definition of differentiable manifolds, tangent vectors and tangent space, dual and bidual spaces. Metric tensor. Algebra of tensors of arbritary rank.
Lie derivatives. Introduction to integration over manifold. Koszul connection. Compatibility of the metric with the connection. Parallel transport and its definition in terms of the connection. Riemann tensor. Equivalence principle. Pulse energy tensor, Einstein-Hilbert action. Derivation of Einstein's equations from a principle of least action. Correspondence with Newton's law of gravitation in the case of a weak and static field. Derivation of Swartzschild metric. - Reference texts
- The course does not follow a single textbook, although for a large part of the course the setting of the book of S. Carrol is prevalent.
Attendance to lessons is strongly recommended.
The reference textbooks are the following:
S. Carroll: Spacetime and Geometry (Benjamin Cummings)
B.F. Schutz: A First Course in General Relativity (Cambridge University Press)
L. Ryder: Introduction to general relativity (Cambridge University Press) R.M. Wald: General Relativity (University Of Chicago Press)
C.W. Misner, K. Thorne, J.A. Wheeler: Gravitation (Freeman)
S. Weinberg: "Gravitation and Cosmology" (Wiley) - Educational objectives
- The main objective of the course is to provide the student with a knowledge of the mathematical tools necessary to address and reproduce specific literature and calculations of general relativity. Upon completion of the course the student is able to deal with the calculations of the classical tests of general relativity (deflection of light, Perihelion of Mercury, etc ..)
- Prerequisites
- The basic calculus of elementary functions and of functions of several real variables are required. The basic notions of linear algebra are required.
- Teaching methods
- Class lectures
- Other information
- None
- Learning verification modality
- Written exam (about three hours) and oral exam.
- Extended program
- EXTENDED PROGRAM
Reminder of Special Relativity
Special Relativity Principle
Lorentz transformations and main consequences Tensor algebra in Special Relativity Maxwell's equations
Energy-momenutm tensor
Equivalence principle
Gravitation and inertia
Ideal experiments
Gravitational redshit
Differentiable varieties
General transformations of coordinates Vectors, linear forms and tensors on manifolds. Metric tensor.
Differential forms
Integration
Affine connection
Curvature
Connections and covariant derivation
Parallel and geodesic transport
The Riemann curvature tensor and its properties
Geodesic deviation
Gravitation Principle of General Covariance Physics in a curved spacetime
Einstein's equations: Lagrangian derivation
The cosmological constant
Schwarzschild's solution, Schwarzschild's metric, Birkhoff's theorem, Schwarzschild's geodesics Stars and black holes (outline)
Perturbative theory and gravitational waves Classical tests of General Relativity
Gravitational redshift. Deflection of light. Precession of perihelion
Gravitational waves (elements) Cosmology (elements)