Metric Theories of Gravity: Perturbations and Conservation Laws (de Gruyter Studies in Mathematical Physics) (de Gruyter Studies in Mathematical Physics, 38)

By focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity. THE SERIES: DE GRUYTER STUDIES IN MATHEMATICAL PHYSICS The series is devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply, and develop further, with sufficient rigor, mathematical methods to given problems in physics. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels. * First monograph devoted to introduction and comparison of methods of pertubations in general relativity * Explicitly covers conservation laws and the study of symmetries for theories of gravity 2.2.4 Gauge transformations and their properties -- 2.2.5 Differential conservation laws -- 2.2.6 Different variants of the field-theoretical formulation in general relativity -- 2.2.7 The background as an auxiliary structure -- 2.3 Metric perturbations as compensating fields -- 2.3.1 "Localization" of background Killing vectors -- 2.3.2 The total action -- 2.3.3 Discussion of the results -- 2.4 The Babak-Grishchuk gravity with a non-zero graviton mass -- 2.4.1 Second derivatives in the energy-momentum tensor -- 2.4.2 Modified Lagrangian and equations -- 2.4.3 Non-zero masses of gravitons -- 2.4.4 Black holes and cosmology in massive gravity -- 2.4.5 Gauge invariance in the Babak-Grishchuk modifications -- 3. Asymptotically flat spacetime in the field-theoretical formulation -- 3.1 The Arnowitt-Deser-Misner formulation of general relativity -- 3.1.1 The ADM action principle -- 3.1.2 Asymptotically flat spacetime at spatial infinity in general relativity -- 3.1.3 The ADM definition of conserved quantities -- 3.1.4 The Regge-Teitelboim modification -- 3.2 An isolated system in the Lagrangian description -- 3.2.1 Asymptotically flat spacetime as a field configuration -- 3.2.2 Global conserved quantities -- 3.2.3 The parity conditions -- 3.2.4 Gauge invariance of the motion integrals -- 3.2.5 Concluding remarks -- 3.3 An isolated system in the Hamiltonian description -- 3.3.1 The difference between the canonical and symmetric currents -- 3.3.2 Phase variables and their asymptotic behaviour -- 3.3.3 Global conserved integrals -- 3.3.4 Gauge invariance of global integrals -- 4. Exact solutions of general relativity in the field-theoretical formalism -- 4.1 The Schwarzschild solution -- 4.1.1 The total energy -- 4.1.2 The energy distribution for the Schwarzschild black hole

By focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity.

THE SERIES: DE GRUYTER STUDIES IN MATHEMATICAL PHYSICS

The series is devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply, and develop further, with sufficient rigor, mathematical methods to given problems in physics. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

By focusing on the most popular pertubation methods this monograph aspires to give a unified overview and comparison of ways to construct conserved quantities and study symmetries in general relativity.