A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity

Abstract

We investigate the $D\to 4$ limit of the $D$-dimensional Einstein-Gauss-Bonnet gravity, where the limit is taken with $\tilde{\alpha }=(D-4)\alpha$ kept fixed and $\alpha$ is the original Gauss-Bonnet coupling. Using the ADM decomposition in $D$ dimensions, we clarify that the limit is rather subtle and ambiguous (if not ill-defined) and depends on the way how to regularize the Hamiltonian or/and the equations of motion. To find a consistent theory in $4$ dimensions that is different from general relativity, the regularization needs to either break (a part of) the diffeomorphism invariance or lead to an extra degree of freedom, in agreement with the Lovelock theorem. We then propose a consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity with two dynamical degrees of freedom by breaking the temporal diffeomorphism invariance and argue that, under a number of reasonable assumptions, the theory is unique up to a choice of a constraint that stems from a temporal gauge condition.

arXiv comment8 pages, no figures, published version

References in corpus (20)

• Quantum Gravity at a Lifshitz Point
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• General Covariance in Quantum Gravity at a Lifshitz Point
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• xTras: a field-theory inspired xAct package for Mathematica
• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
• A note on the novel 4D Einstein-Gauss-Bonnet gravity
• Renormalization of Horava Gravity
• The $D\to 2$ Limit of General Relativity
• Amplitudes and 4D Gauss-Bonnet Theory
• Minimal theory of massive gravity
• A Class of Minimally Modified Gravity Theories
• An Alternative Approach for General Covariant Horava-Lifshitz Gravity and Matter Coupling
• Minimally Modified Gravity: a Hamiltonian Construction
• Vacua and Exact Solutions in Lower-$D$ Limits of EGB
• Novel matter coupling in general relativity via canonical transformation
• Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity

Cited by in corpus (112)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• Comment on "Einstein-Gauss-Bonnet Gravity in 4-Dimensional Space-Time''
• Thermodynamic geometry of the novel 4-D Gauss Bonnet AdS Black Hole
• Amplitudes and 4D Gauss-Bonnet Theory
• Charged black hole in $4D$ Einstein-Gauss-Bonnet gravity: Particle motion, plasma effect on weak gravitational lensing and centre-of-mass energy
• Spinning test particle in four-dimensional Einstein-Gauss-Bonnet Black Hole
• Shadow, deflection angle and quasinormal modes of Born-Infeld charged black holes
• Thin Accretion Disk around a four-dimensional Einstein-Gauss-Bonnet Black Hole
• Gravity with a generalized conformal scalar field: Theory and solutions
• Regularized Lovelock gravity
• Electrically Charged Quark Stars in $4D$ Einstein-Gauss-Bonnet Gravity
• Relativistic stars in 4D Einstein-Gauss-Bonnet gravity
• Black hole with confining electric potential in scalar-tensor description of regularized 4-dimensional Einstein-Gauss-Bonnet gravity
• Bending of light in novel 4$D$ Gauss-Bonnet-de Sitter black holes by Rindler-Ishak method
• Strange Quark Stars in 4D Einstein-Gauss-Bonnet Gravity
• Anisotropic Stars in 4D Einstein-Gauss-Bonnet Gravity
• Thin accretion disks around rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity
• Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter
• Quasinormal spectrum of $(2+1)$-dimensional asymptotically flat, dS and AdS black holes
• Minimally Modified Gravity fitting Planck data better than $\Lambda$CDM
• $4D$ AdS Einstein-Gauss-Bonnet black hole with Yang-Mills field and its thermodynamics
• Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction
• A new approach and code for spinning black holes in modified gravity
• Nonsingular Black Holes in $4D$ Einstein--Gauss--Bonnet Gravity
• Possibility of the Traversable Wormholes in the Galactic Halos within $4D$ Einstein-Gauss-Bonnet Gravity
• Quasinormal Modes and Phase Structure of Regular $AdS$ Einstein-Gauss-Bonnet Black Holes
• Quasibound States, Stability and Wave Functions of the Test Fields in the Consistent 4D Einstein-Gauss-Bonnet Gravity
• Quasinormal modes of Einstein--scalar--Gauss--Bonnet black holes
• Canonical variational completion and 4D Gauss-Bonnet gravity
• Stability of asymptotically flat (2+1)-dimensional black holes with Gauss-Bonnet corrections
• VCDM and Cuscuton
• Weakening gravity for dark matter in a type-II minimally modified gravity
• Einstein-Gauss-Bonnet gravity with nonlinear electrodynamics
• Thermodynamic properties, thermal image and phase transition of Einstein-Gauss-Bonnet black hole coupled with nonlinear electrodynamics
• Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity
• Polarized image of an equatorial emitting ring around a 4D Gauss-Bonnet black hole
• Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence
• Page Curves of Reissner-Nordström Black Hole in HD Gravity
• Black hole solution and thermal properties in $4D$ AdS Gauss-Bonnet massive gravity
• Tidal effects in 4D Einstein-Gauss-Bonnet Black Hole Spacetime
• Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• Constraints on parity and Lorentz violations in gravity from GWTC-3 through a parametrization of modified gravitational wave propagations
• On the "Einstein-Gauss-Bonnet Gravity in Four Dimension"
• Charged 4D Einstein-Gauss-Bonnet Black Hole: Vacuum solutions, Cauchy Horizon, Thermodynamics
• Non-uniqueness of massless transverse-traceless graviton
• Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
• Optical features of AdS black holes in the novel 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics
• Traversable Thin-shell Wormhole in the 4D Einstein-Gauss-Bonnet Theory
• 4D Einstein-Gauss-Bonnet gravity: Massless particles and absorption of planar spin-0 waves
• Thermodynamics, Phase Transition and Joule Thomson Expansion of 4-D Gauss-Bonnet AdS Black Hole
• Page Curve and Island in EGB gravity
• Black Holes in $4D$ AdS Einstein Gauss Bonnet Gravity With Power- Yang Mills Field
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Non-linear charged planar black holes in four-dimensional Scalar-Gauss-Bonnet theories
• Einstein-Gauss-Bonnet gravity with rational nonlinear electrodynamics
• Dynamical analysis in regularized $4D$ Einstein-Gauss-Bonnet gravity with non-minimal coupling
• On the gravitational collapse in 4-dimensional Einstein-Gauss-Bonnet gravity
• The Integrated Sachs-Wolfe Effect in 4D Einstein-Gauss-Bonnet Gravity
• Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and (in)-stability
• Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity
• Simply rotating higher dimensional black holes in Einstein-Gauss-Bonnet theory
• Non-linear dynamics of the minimal theory of massive gravity
• Joule-Thomson Expansion of Born-Infeld AdS Black Holes in 4D Einstein-Gauss-Bonnet gravity
• Holographic Consistency and the Sign of the Gauss-Bonnet Parameter
• Charged AdS black holes with finite electrodynamics in 4D Einstein-Gauss-Bonnet gravity
• The correspondence between shadow and test field in a four-dimensional charged Einstein-Gauss-Bonnet black hole
• 3D Lovelock Gravity and the Holographic c-Theorem
• Quasibound states of scalar fields in the consistent 4D Einstein-Gauss-Bonnet-(Anti-)de Sitter gravity
• Dynamical Dark Energy in Minimally Modified Gravity
• Particle-antiparticle in 4D charged Einstein-Gauss-Bonnet black hole
• Topological Corrections and Conformal Backreaction in the Einstein Gauss-Bonnet/Weyl Theories of Gravity at D=4
• Lower-dimensional Limits of Cubic Lovelock Gravity
• Radiation from Einstein-Gauss-Bonnet de Sitter Black Hole via Tunneling Process
• A new class of regular Black Holes in Einstein Gauss Bonnet gravity with localized sources of matter
• Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity with backreactions
• Accretion onto a Charged Black Hole in Consistent 4D Einstein-Gauss-Bonnet Gravity
• New model of 4D Einstein--Gauss--Bonnet gravity coupled with nonlinear electrodynamics
• Eikonal quasinormal modes, photon sphere and shadow of a charged black hole in the 4D Einstein-Gauss-Bonnet gravity
• Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity
• Power Spectra of Slow-Roll inflation in the consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• 4D Einstein-Gauss-Bonnet Gravity From Non-Einsteinian Phase
• Cosmic evolution in novel-Gauss Bonnet Gravity
• Double shadow of a 4D Einstein-Gauss-Bonnet black hole and their connection between with quasinormal modes
• Minimal exponential measure model in the post-Newtonian limit
• Gravitational collapse and formation of a black hole in a type II minimally modified gravity theory
• Massive scalar field perturbations of 4D de Sitter Einstein-Gauss-Bonnet black holes
• Anisotropy in constraint 4D Gauss-Bonnet gravity
• Gauss-Bonnet holographic superconductors in lower-dimensions
• Minimally modified gravity with auxiliary constraints formalism
• Einstein Gauss-Bonnet Theories as Ordinary, Wess-Zumino Conformal Anomaly Actions
• The Stringy Origins of Galileons and their Novel Limit
• A new constant behind the rotational velocity of galaxies
• Holographic entanglement entropy and subregion complexity for excited states of holographic superconductors
• Dimensional aspects of Lovelock-Lanczos gravity
• Effective field theory of coupled dark energy and dark matter
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• Lorentzian quantum cosmology in novel Gauss-Bonnet gravity from Picard-Lefschetz methods
• Quantum State Dependence of Thermodynamic Phase Transition in 4D AdS Gauss-Bonnet Quantum Black Holes Surrounded With Cloud of Strings
• Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole
• 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics
• Absence of isolated critical points with nonstandard critical exponents in the four-dimensional regularization of Lovelock gravity
• Thermodynamics of 4D dS/AdS Gauss-Bonnet black holes from consistent gravity theory in presence of cloud of strings
• Strong coupling and instabilities in singularity-free inflation from an infinite sum of curvature corrections
• Black Holes with Global Monopoles in 4D Noncommutative Einstein Gauss Bonnet Gravity
• Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations
• Compact Objects in 4D Einstein Gauss Bonnet Gravity A Data Based Perspective
• Periodic Orbits and Gravitational Wave Radiation of Black Hole in EGB gravity
• Internal structure and its connection with thermodynamics and dynamics in black holes
• Dynamical 4-D Gauss-Bonnet action from matter-graviton interaction at one-loop
• Analytical study of holographic superconductor with backreaction in $4d$ Gauss-Bonnet gravity
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity