Milutin Blagojevic

Gravitation and Gauge Symmetries

Preface Space, Time and Gravitation Relativity of space and time Gravitation and geometry Spacetime Symmetries Poincare symmetry Conformal symmetry Poincare Gauge Theory Poincare gauge invariance Geometric interpretation Gravitational dynamics Weyl Gauge Theory Weyl gauge invariance Weyl-Cartan geometry Dynamics Hamiltonian Dynamics Constrained Hamiltonian dynamics The gravitational Hamiltonian Specific models Symmetries and Conservation Laws Gauge symmetries Conservation laws-EC theory Conservation laws-the teleparallel theory Chern-Simons gauge theory in D = 3 Gravity in Flat Spacetime Theories of long range forces Attempts to build a realistic theory Nonlinear Effects in Gravity Nonlinear effects in Yang-Mills theory Scalar theory of gravity Tensor theory of gravity The first order formalism Supersymmetry and Supergravity Supersymmetry Representations of supersymmetry Supergravity Kaluza-Klein Theory Basic ideas Five-dimensional KK theory Higher-dimensional KK theory String Theory Classical bosonic strings Oscillator formalism First quantization Covariant field theory General remarks Appendices A: Local internal symmetries B: Differentiable manifolds C: De Sitter gauge theory D: The scalar-tensor theory E: Ashtekars formulation of GR F: Constraint algebra and gauge symmetries G: Covariance, spin and interaction of massless particles H: Lorentz group and spinors I: Poincare group and massless particles J: Dirac matrices and spinors K: Symmetry groups and manifolds L: Chern-Simons gravity in three dimensions M: Fourier expansion Bibliography Notations and Conventions Index

Gauge theories of gravitation : a reader with commentaries

The Rise of Gauge Theory of Gravity Up to 1961: From Special to General Relativity Theory Analyzing General Relativity Theory A Fresh Start by Yang - Mills and Utiyama Poincare Gauge Theory: Einstein - Cartan( - Sciama - Kibble) Theory as a Viable Gravitational Theory General Structure of Poincare Gauge Theory (Including Quadratic Lagrangians) Translational Gauge Theory Fallacies About Torsion Extending the Gauge Group of Gravity: Poincare Group Plus Scale Transformations: Weyl - Cartan Gauge Theory of Gravity From the Poincare to the Affine Group: Metric-Affine Gravity Conformal Gauge Theory of Gravity (Anti-)de Sitter Gauge Theory of Gravity From the Square Root of Translations to the Super-Poincare Group Specific Subjects of Metric-Affine Gravity and Poincare Gauge Theory: Hamiltonian Structure Equations of Motion for Matter Cosmological Models Exact Solutions Poincare Gauge Theory in Three Dimensions Dislocations and Torsion The Yang Episode: A Historical Case Study.

Asymptotic structure of topologically massive gravity in spacelike stretched AdS sector

We introduce a natural set of asymptotic conditions in the spacelike stretched AdS sector of topologically massive gravity. The Poisson bracket algebra of the canonical generators is shown to have the form of the semi-direct sum of a u(1) Kac-Moody and a Virasoro algebra, with central charges. Using the Sugawara construction, we prove that the asymptotic symmetry coincides with the conformal symmetry, described by two independent Virasoro algebras with central charges. The result is in complete agreement with the hypothesis made in [6].

Hamiltonian analysis of BHT massive gravity

We study the Hamiltonian structure of the Bergshoeff-Hohm-Townsend (BHT) massive gravity with a cosmological constant. In the space of coupling constants (Λ0, m2), our canonical analysis reveals the special role of the condition Λ0/m2 ≠ −1. In this sector, the dimension of the physical phase space is found to be N∗ = 4, which corresponds to two Lagrangian degree of freedom. When applied to the AdS asymptotic region, the canonical approach yields the conserved charges of the BTZ black hole, and central charges of the asymptotic symmetry algebra.

Gauge symmetries of the teleparallel theory of gravity

We study gauge properties of the general teleparallel theory of gravity, defined within the framework of Poincare gauge theory. It is found that the general theory is characterized by two kinds of gauge symmetries: a specific gauge symmetry that acts on Lagrange multipliers, and the standard Poincare gauge symmetry. The canonical generators of these symmetries are explicitly constructed and investigated.

Extra gauge symmetries in BHT gravity

We study the canonical structure of the Bergshoeff-Hohm-Townsend massive gravity, linearized around a maximally symmetric background. At the critical point in the space of parameters, defined by Λ0/m2 = −1, we discover an extra gauge symmetry, which reflects the existence of the partially massless mode. The number of the Lagrangian degrees of freedom is found to be 1. We show that the canonical structure of the theory at the critical point is unstable under linearization.

Black hole entropy in 3D gravity with torsion

The role of torsion in three-dimensional quantum gravity is investigated by studying the partition function of the Euclidean theory in Riemann–Cartan spacetime. The entropy of the black hole with torsion is found to differ from the standard Bekenstein–Hawking result, but its form is in complete agreement with the first law of black hole thermodynamics.

Conservation laws in the teleparallel theory of gravity

We study the conservation laws associated with the asymptotic Poincare symmetry of spacetime in the general teleparallel theory of gravity. Demanding that the canonical Poincare generators have well defined functional derivatives in a properly defined phase space, we obtain the improved form of the generators, containing certain surface terms. These terms are shown to represent the values of the related conserved charges: energy-momentum and angular momentum.

Holography in 3D AdS gravity with torsion

A bstractBasic aspects of the AdS/CFT correspondence are studied in the framework of 3-dimensional gravity with torsion. After choosing a consistent holographic ansatz, we formulate an improved approach to the Noether-Ward identities for the boundary theory. The method is applied first to the topological Mielke-Baekler model, and then to the more interesting (parity-preserving) 3-dimensional gravity with propagating torsion. In both cases, we find the finite holographic energy-momentum and spin currents and obtain the associated (anomalous) Noether-Ward identities.

Conserved charges in 3D gravity

The covariant canonical expression for the conserved charges, proposed by Nester, is tested on several solutions in three-dimensional gravity with or without torsion and topologically massive gravity. In each of these cases, the calculated values of energy momentum and angular momentum are found to satisfy the first law of black hole thermodynamics.