Lecture Notes on General Relativity

Abstract

These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.

238 pages, numerous figures. Individual chapters, and potentially updated versions, can be found at http://itp.ucsb.edu/~carroll/notes/

References in corpus (3)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Quintessence, Cosmic Coincidence, and the Cosmological Constant
• Quintessence and the Rest of the World

Cited by in corpus (135)

• Extra force in $f(R)$ modified theories of gravity
• Chern-Simons Modified General Relativity
• Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity
• Non-local gravity and dark energy
• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Wormhole geometries supported by a nonminimal curvature-matter coupling
• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Spectral Analysis of the Volume Operator in Loop Quantum Gravity
• Quantum mechanics: Myths and facts
• Quantum radiative corrections to slow-roll inflation
• Light Rays, Singularities, and All That
• The Structure of the Gravitational Action and its relation with Horizon Thermodynamics and Emergent Gravity Paradigm
• Can scale-dependent cosmology alleviate the $H_0$ tension?
• The irreversible thermodynamics of curved lipid membranes
• A review on analytical studies in Gravitational Lensing
• The End of a Black Hole's Evaporation -- Part I
• Arbitrary Lagrangian--Eulerian finite element method for curved and deforming surfaces. I. General theory and application to fluid interfaces
• ADM formulation and Hamiltonian analysis of $f(Q)$ gravity
• Shadows of Exact Binary Black Holes
• Gravitational field of global monopole within the Eddington-inspired Born-Infeld theory of gravity
• Fate of scalar dark matter solitons around supermassive galactic black holes
• Information Geometry and Quantum Phase Transitions in the Dicke Model
• Force-Free Electrodynamics around Extreme Kerr Black Holes
• Gravity particles from Warped Extra Dimensions, predictions for LHC
• Metric-Affine Gravity and Cosmology/Aspects of Torsion and non-Metricity in Gravity Theories
• Generalized Symmetries of the Graviton
• A Geometric Approach to CP Violation: Applications to the MCPMFV SUSY Model
• Geometry and entanglement in the scattering matrix
• Hamiltonian formulation of an effective modified gravity with nondynamical background fields
• Basics of M-Theory
• Capture of bulk geodesics by brane-world black holes
• Geometric inequivalence of metric and Palatini formulations of General Relativity
• Generalised Boundary Terms for Higher Derivative Theories of Gravity
• A graviton propagator for inflation
• The alpha-prime stretched horizon in the Heterotic string
• On the Stability of Planetary Circular Orbits in Noncommutative Spaces
• Weak field limit and gravitational waves in higher-order gravity
• Coordinate families for the Schwarzschild geometry based on radial timelike geodesics
• Lattice ${\varphi }^4$ Field Theory on Riemann Manifolds: Numerical Tests for the 2-d Ising CFT on ${\mathbb{S}}^2$
• Polonyi Inflation
• TASI Lectures: Cosmology for String Theorists
• Raychaudhuri equation in $k$-essence geometry: conditional singular and non-singular cosmological models
• Social aspects of collision avoidance: A detailed analysis of two-person groups and individual pedestrians
• Toward General-Relativistic Magnetohydrodynamics Simulations in Stationary Non-Vacuum Spacetimes
• Path Integrals for Causal Diamonds and the Covariant Entropy Principle
• CMB acoustic scale in the entropic-like accelerating universe
• Covariant canonical formulations of classical field theories
• The Einstein-Vlasov-Maxwell(EVM) System with Spherical Symmetry
• Expanding space, quasars and St. Augustine's fireworks
• Quintessence in the Weyl-Gauss-Bonnet model
• Black holes as spherically-symmetric horizon-bound objects
• Gravity theory on Poisson manifold with $R$-flux
• An eikonal equation approach to thermodynamics and the gradient flows in information geometry
• Particle motion in circularly polarized vacuum pp waves
• Black hole evolution in quantum-gravitational framework
• 3+1 decomposition in modified gravities within the Palatini formalism and some applications
• FLRW cosmology in Weyl-Integrable Space-Time
• Two Dimensional Horava-Lifshitz Black Hole Solutions
• Weak field and slow motion limits in energy-momentum powered gravity
• Space-time anisotropy: theoretical issues and the possibility of an observational test
• A simpler solution of the non-uniqueness problem of the covariant Dirac theory
• Influence of cosmological expansion in local experiments
• K-essence scalar dark matter solitons around supermassive black holes
• Gravitational Collapse in Scale-Dependent Gravity
• A way to get rid of cosmological constant and zero point energy problems of quantum fields through metric reversal symmetry
• Quantum Emulation of Gravitational Waves
• Kac-Moody Algebras in M-theory
• Constraints on $f(R_{ijkl}{R}^{ijkl})$ gravity: An evidence against the covariant resolution of the Pioneer anomaly
• Generalization of Einstein's gravitational field equations
• Non-vacuum AdS cosmology and comments on gauge theory correlator
• Generalized particle dynamics: modifying the motion of particles and branes
• Self-supporting wormholes with massive vector field
• Electromagnetism in Curved Spacetimes: Coupling of the Doppler and Gravitational Redshifts
• Emergent dual holographic description as a non-perturbative generalization of the Wilsonian renormalization group
• Cosmological evolution of generalized non-local gravity
• Black Holes with Abelian and Non-Abelian Charges and Their Impact on Matter Accretion Flows
• New considerations on Hilbert action and Einstein equations in anisotropic spaces
• Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities
• Gravitational Waves: An Introduction
• Evolving Geometries in General Relativity
• Quantum Gravity from the Composition of Spacetime Constructed through Generalised Proper Time
• Causality and dimensionality in geometric scattering
• Stability of white holes revisited
• A WDM model for the evolution of galactic halos
• Curvature properties of interior black hole metric
• On the particle collisions during gravitational collapse of Vaidya spacetimes
• Classical geodesics from the canonical quantisation of spacetime coordinates
• Supertranslations: redundancies of horizon data, and global symmetries at null infinity
• Gauge-Field-Induced Torsion and Cosmic Inflation
• Moving mirrors and event horizons in non-flat background geometry
• Uniform position alignment estimate of spherical flocking model with inter-particle bonding forces
• Wormhole solutions of RDM model
• Penrose process in charged axion-dilaton coupled black hole
• Gravitational systems in asymptotically anti-de Sitter space-times
• Ray-Wave Duality of Electromagnetic Fields: A Feynman Path integral Approach to Classical Vectorial Imaging
• Binary Black Hole Information Loss Paradox & Future Prospects
• Quantum Black Holes
• Lagrangian formalism in the theory of relativistic vector fields
• RDM-stars and galactic rotation curves
• Particle propagation on spacetime manifolds with static defects
• Killing vectors of FLRW metric (in comoving coordinates) and zero modes of the scalar Laplacian
• Renormalization of Electromagnetic Quantities in Small Josephson Junctions
• A pedagogical review of gravity as a gauge theory
• Quasi-Local 3D Quantum Gravity : Exact Amplitude and Holography
• Energy estimates for minimizers to a class of elliptic systems of Allen-Cahn type and the Liouville property
• Propagators and WKB-exactness in the plane wave limit of AdSxS
• The Universe at the MeV era: neutrino evolution and cosmological observables
• n-dimensional Weyl conformal tensor in a 4-index gravitational field theory
• Wormholes and Teleporters
• Absolute Time and Temperature in Quantum and Classical Relativistic Mechanics
• A Keplerian Limit to Static Spherical Spacetimes in Curvature Coordinates
• Gravitational fermion creation during an anisotropic phase of cosmological expansion
• Galactic model with a phase transition from dark matter to dark energy
• Quantum Gravity Wormholes and Topological Teleporter
• About Boundary Terms in Higher Order Theories
• Universal thermalization dynamics in (1+1)d QFTs
• RDM-stars and related topics
• Uniformly Area Expanding Flows in Spacetimes
• Hawking modes and the optimal disperser : Holographic lessons from the observer's causal-patch unitarity
• Quantum Geometrodynamics of Higher Derivative Theories with and without Conformal Symmetry
• A Simple Introduction to Particle Physics Part II
• Phenomenology and Cosmology of Supersymmetric Grand Unified Theories
• Bouncing and coasting universe with exact quantum-classical correspondence
• The Entropic Dynamics of Relativistic Quantum Fields in Curved Space-time
• Applications of Cosmological Perturbation Theory in the Late Universe
• Quantum Physics in Space
• Polyakov's string classical mechanics
• An Evolving Spacetime Metric Induced by a `Static' Source
• The dual behavior of quantum Fields and the big Bang
• Production of Primordial Gravitational Waves in Teleparallel Gravity
• Towards an Efficient Use of the BLAS Library for Multilinear Tensor Contractions
• Lepton Flavor Violating Radion Decays in the Randall-Sundrum Scenario: The Thesis
• Mass Creation From Extra Dimensions
• Gravity as Classical Effect in Generalized Relativistic Quantum Mechanics on Flat Background