ADM formulation and Hamiltonian analysis of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>Q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity
Kun Hu, Taishi Katsuragawa, Taotao Qiu
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.
Topics & Concepts
Mathematical physicsHamiltonian (control theory)PhysicsGauge (firearms)General relativityMathematicsArchaeologyMathematical optimizationHistoryCosmology and Gravitation TheoriesBlack Holes and Theoretical PhysicsNoncommutative and Quantum Gravity Theories