Logo

Introduction to Differential Geometry and General Relativity

Small book cover: Introduction to Differential Geometry and General Relativity

Introduction to Differential Geometry and General Relativity
by


Number of pages: 138

Description:
From the table of contents: distance, open sets, parametric surfaces and smooth functions, smooth manifolds and scalar fields, tangent vectors and the tangent space, contravariant and covariant vector fields, tensor fields, Riemannian manifolds, locally Minkowskian manifolds, covariant differentiation, geodesics and local inertial frames, the Riemann curvature tensor, comoving frames and proper time, the stress tensor and the relativistic stress-energy tensor, three basic premises of general relativity, the Einstein field equations and derivation of Newton's law, the Schwarzschild metric and event horizons, White Dwarfs, neutron stars and black holes.

Download or read it online for free here:
Download link
(1.7MB, PDF)

Similar books

Book cover: Schwarzschild and Kerr Solutions of Einstein's Field Equation: an introductionSchwarzschild and Kerr Solutions of Einstein's Field Equation: an introduction
by - arXiv
Starting from Newton's gravitational theory, we give a general introduction into the spherically symmetric solution of Einstein's vacuum field equation, the Schwarzschild solution, and into one specific stationary solution, the Kerr solution.
(7873 views)
Book cover: Spacetime and FieldsSpacetime and Fields
by - arXiv
A self-contained introduction to the classical theory of spacetime and fields. Topics: Spacetime (tensors, affine connection, curvature, metric, Lorentz group, spinors), Fields (principle of least action, action for gravitational field, matter, etc)
(9949 views)
Book cover: Recent Developments in Gravitational Collapse and Spacetime SingularitiesRecent Developments in Gravitational Collapse and Spacetime Singularities
by - arXiv
The research of recent years has provided considerable clarity and insight on stellar collapse, black holes and the nature and structure of spacetime singularities. In this text, the authors discuss several of these developments here.
(10633 views)
Book cover: An Introduction to the Theory of Rotating Relativistic StarsAn Introduction to the Theory of Rotating Relativistic Stars
by - arXiv
These notes introduce the theory of rotating stars in general relativity. The focus is on the theoretical foundations, with a detailed discussion of the spacetime symmetries, the choice of coordinates and the derivation of the equations of structure.
(11963 views)