Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity
Canonical methods are a powerful mathematical tool within the field of gravitational research, both theoretical and experimental, and have contributed to a number of recent developments in physics. Providing mathematical foundations as well as physical applications, this is the first systematic explanation of canonical methods in gravity. The book discusses the mathematical and geometrical notions underlying canonical tools, highlighting their applications in all aspects of gravitational research from advanced mathematical foundations to modern applications in cosmology and black hole physics. The main canonical formulations, including the Arnowitt-Deser-Misner (ADM) formalism and Ashtekar variables, are derived and discussed. Ideal for both graduate students and researchers, this book provides a link between standard introductions to general relativity and advanced expositions of black hole physics, theoretical cosmology or quantum gravity.
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1-forms action asymptotic Bianchi black holes boundary term canonical classical coefﬁcients components compute conformal congruence conjugate connection 1-forms constant constraint surface coordinate cosmology covariant derivative curves deﬁned deﬁnition deth diffeomorphism constraint differential dynamics Einstein’s equation energy equations of motion evolution Example extrinsic curvature fermions ﬁnite ﬁrst ﬁrst-class ﬁxed ﬂat ﬂow formulation gauge transformations geodesic geometry Hamiltonian constraint homogeneous hyperbolic implies integration inverse isotropic lapse function Lie algebra Lie algebroid Lie derivative line element linear manifold matter Minkowski space models momenta momentum normal null obtained parameter perturbations phase-space Poisson brackets Poisson manifold Poisson tensor primary constraints provides quantization quantum gravity region Ricci scalar satisﬁed Schwarzschild singularity solutions solved space-time space-time metric spacelike spatial metric spatial slices speciﬁc stress-energy stress-energy tensor symmetry symplectic tetrad timelike trapped surfaces triad vanish variables vector ﬁeld