Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2204.12826

ADM formulation and Hamiltonian analysis of $f(Q)$ gravity

Kun Hu·Taishi Katsuragawa·Taotao Qiu
View original source ↗Read source document ↗Export metadata ↓

Abstract

$f(Q)$ gravity is an extension of the symmetric teleparallel equivalent to general relativity. We demonstrate the Hamiltonian analysis of $f(Q)$ gravity with fixing the coincident gauge condition. Using the standard Dirac-Bergmann algorithm, we show that $f(Q)$ gravity has 8 physical degrees of freedom. This result reflects that the diffeomorphism symmetry of $f(Q)$ gravity is completely broken due to the gauge fixing. Moreover, in terms of the perturbations, we discuss the possible mode decomposition of these degrees of freedom.

Explore related subjects

gr-qcastro-ph.COhep-phhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Kun Hu, Taishi Katsuragawa, Taotao Qiu. 2022-08-11. ADM formulation and Hamiltonian analysis of $f(Q)$ gravity. https://doi.org/10.1103/physrevd.106.044025

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Loop Quantum Kaluza-Klein Cosmology and Inflation

We present the detailed analyses of five-dimensional loop quantum Kaluza-Klein cosmology based on the symmetric reduction of the connection formulation of the full theory. The previous results in a particular scenario are extended to more general cases. The effective scalar constraint for the geometric sector of the model is derived by the systematic semi-classical analysis in both the canonical and path-integral formulations, incorporating the quantum fluctuations as a subleading-order correction. The resulting effective scalar constraint not only exhibits the correct classical limit of the quantum system, but also serves as the basis for investigating the following three distinct effective scenarios through the incorporation of matter contributions: (i) vacuum, (ii) minimally coupling with a scalar field, and (iii) coupling with the dust. In all the three effective scenarios, the big bang and potential past big rip singularities in the classical model are naturally resolved by including the leading-order quantum correction of holonomies. Moreover, the visible universe undergoes a super-inflationary phase after overcoming the classical big bang singularity, during which the phenomenologically desired 55 e-folds can be achieved by appropriate initial conditions. In the case where the subleading-order quantum fluctuation term is included as a constant, the evolutions of the five-dimensional universe in all the three effective scenarios not only achieve sufficient inflation in the visible dimensions, but also exhibit re-collapse behaviors at certain large scales. Hence the cosmic inflation may originate from the interplay between compact extra dimensions and quantum geometric effects.

gr-qc↗
arXiv2026

Charged black string immersed in a quintessence fluid and string cloud

We present a new static solution describing a charged black string immersed in a Kiselev-type quintessence fluid and a string cloud. The metric and field equations are solved for a general quintessence state parameter, with explicit results provided for the physically relevant case $w_q = -2/3$. We analyze the event-horizon structure and the Kretschmann scalar, verify energy-condition constraints, and derive thermodynamic properties including the Hawking temperature and heat capacity and the Helmholtz free energy. Finally, we investigate the existence of an exterior photon cylinder for circular null geodesics, finding that, under the parameter assumptions adopted here, no such cylinder occurs outside the outer horizon. The solution generalizes known charged black-string spacetimes by simultaneously including quintessence and a string-cloud parameter.

gr-qc↗
arXiv2026

Extended parameterized spin expansion formalism for ringdown analysis with GW250114

Parameterized descriptions of black-hole quasinormal-mode spectra are essential for testing gravity with ringdown observations. We extend the Parameterized Spin Expansion Coefficients (ParSpec) formalism by simultaneously sampling the characteristic length scale $\tilde{\ell}$ and the scaling index $\tilde{p}$, rather than fixing $\tilde{p}$ to a theory-motivated integer and constraining $\tilde{\ell}$. Physically, this extension promotes the scaling of the spectral corrections coming from higher-curvature operators to an observable quantity. Methodologically, it enables us to investigate the enlarged ParSpec parameter space and identify the prior geometry induced by conditions on the effective coupling $γ$. We examine the robustness of the framework by using the $220$ and $220+221$ ringdown models over different start times with informative priors on mass and luminosity for GW250114, and further study a joint constraint with GW231123. We pointed out that $γ<1$ avoids an artificial correlation between $\tilde{p}$ and $\tilde{\ell}$ among the coupling prescriptions considered, and the choices of ringdown starting time and QNM mode content in the ParSpec framework should be matched to the information content and resolving power of the data. Higher-SNR ringdowns and hierarchical analyses of a larger event population will be required to break the $\tilde{p}$-$\tilde{\ell}$ degeneracy and directly probe the scaling structure of corrections to GR.

gr-qc↗