"This introductory textbook, which is positioned at an intermediate level between the more qualitative books at the low end and the many graduate-level standard textbooks, is an accessible introduction to general relativity primarily aimed at undergraduates studying mechanics, dynamics and special relativity. The text provides structured outlines to the concepts and applications of the topic, leading the reader from the basic ideas of relativity, such as the cosmological principle to the Friedmann equation, on to some more advanced ideas such as orbits in the Schwarzschild Geometry. At the end of each chapter there are appropriate problems. A wide-range of classical and modern topics are covered, exploring observational successes and particle physics to explain many popular principles including space-time, redshift, gravity, and fascinating topics such as black holes and dark matter. This timely textbook also provides a section of advanced topics that offers more detailed mathematical approaches and advanced ideas as a basis for further studies to prepare the reader for understanding more specialised texts"-- Provided by publisher.

Preface -- Constants and Symbols -- Introducing General Relativity -- A Special Relativity Reminder -- The need for Special Relativity -- The Lorentz transformation -- Time dilation -- Lorentz-Fitzgerald contraction -- Addition of velocities -- Simultaneity, colocality, and causality -- Space-time diagrams -- Tensors in Special Relativity -- Coordinates -- 4-vectors -- 4-velocity, 4-momentum, and 4-acceleration -- 4-divergence and the wave operator -- Tensors -- Tensors in action: the Lorentz force -- Towards General Relativity -- Newtonian gravity -- Special Relativity and gravity -- Motivations for a General Theory of Relativity -- Mach's Principle -- Einstein's Equivalence Principle -- Implications of the Equivalence Principle -- Gravitational redshift -- Gravitational time dilation -- Principles of the General Theory of Relativity -- Towards curved space-time -- Curved space in two dimensions -- Tensors and Curved Space-Time -- General coordinate transformations -- Tensor equations and the laws of physics -- Partial differentiation of tensors -- The covariant derivative and parallel transport -- Christoffel symbols of a two-sphere -- Parallel transport on a two-sphere -- Curvature and the Riemann tensor -- Riemann curvature of the two-sphere -- More tensors describing curvature -- Local inertial frames and local flatness -- Describing Matter -- The Correspondence Principle -- The energy-momentum tensor -- General properties -- Conservation laws and 4-vector flux -- Energy and momentum belong in a rank-2 tensor -- Symmetry of the energy-momentum tensor -- Energy-momentum of perfect fluids -- The energy-momentum tensor in curved space-time -- The Einstein Equation -- The form of the Einstein equation -- Properties of the Einstein equation -- The Newtonian limit -- The cosmological constant -- The vacuum Einstein equation -- The Schwarzschild Space-time -- Christoffel symbols -- Riemann tensor -- Ricci tensor -- The Schwarzschild solution -- The Jebsen-Birkhoff theorem -- Geodesics and Orbits -- Geodesics -- Non-relativistic limit of geodesic motion -- Geodesic deviation -- Newtonian theory of orbits -- Orbits in the Schwarzschild space-time -- Massive particles -- Photon orbits -- Tests of General Relativity -- Precession of Mercury's perihelion -- Gravitational light bending -- Radar echo delays -- Gravitational redshift -- Binary pulsar PSR 1913+ -- Direct detection of gravitational waves -- Black Holes -- The Schwarzschild radius -- Singularities -- Radial rays in the Schwarzschild space-time -- Schwarzschild coordinate systems -- The black hole space-time -- Special orbits around black holes -- Black holes in physics and in astrophysics -- Cosmology -- Constant-curvature spaces -- The metric of the Universe -- The matter content of the Universe -- The Einstein equations -- Cosmological Models -- Simple solutions: matter and radiation -- Light travel, distances, and horizons -- Light travel in the cosmological metric -- Cosmological redshift -- The expansion rate -- The age of the Universe -- The distance-redshift relation and Hubble's law -- Cosmic horizons -- The luminosity and angular-diameter distances -- Ingredients for a realistic cosmological model -- Accelerating cosmologies -- General Relativity: The Next 100 Years -- Developing General Relativity -- Beyond General Relativity -- Into the future -- Advanced Topic A1 Geodesics in the Schwarzschild Space-Time -- Geodesics and conservation laws -- Schwarzschild geodesics for massive particles -- Schwarzschild geodesics for massless particles -- Advanced Topic A2 The Solar System Tests in Detail -- Newtonian orbits in detail -- Perihelion shift in General Relativity -- Light deflection -- Time delay -- Advanced Topic A3 Weak Gravitational Fields and Gravitational Waves -- Nearly-flat space-times -- Gravitational waves -- Sources of gravitational waves -- Advanced Topic A4 Gravitational Wave Sources and Detection -- Gravitational waves from compact binaries -- The energy in gravitational waves -- Binary inspiral -- Detecting gravitational waves -- Laser interferometers -- Pulsar timing -- Interferometers in space -- Bibliography -- Answers to selected problems -- Index.