Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity

Abstract

The scalar-tensor theories of gravity in spacetime dimensions $D+1>2$ are studied. By doing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter $\omega$. The Hamiltonian structure in both sectors are similar to the corresponding structure of 4-dimensional cases. It turns out that there is a symplectic reduction from the canonical structure of $so(D+1)$ Yang-Mills theories coupled to the scalar field to the canonical structure of the geometrical scalar-tensor theories. Therefore the non-perturbative loop quantum gravity techniques can also be applied to the scalar-tensor theories in $D+1$ dimensions based on their connection-dynamical formalism.

13 pages

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Cited by in corpus (7)

• Shadow and stability of quantum-corrected black holes
• Shadows and optical appearance of quantum-corrected black holes illuminated by static thin accretions
• Generalized Ashtekar variables for Palatini f(R) models
• Manifestly Gauge Invariant Perturbations of Scalar-Tensor Theories of Gravity
• Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
• Degenerate Limits of Scalar-Tensor Gravity
• Hamiltonian Theory: generalizations to higher dimensions, supersymmetry and modified gravity