Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions

Abstract

We propose a regularization procedure for the novel Einstein-Gauss-Bonnet theory of gravity, which produces a set of field equations that can be written in closed form in four dimensions. Our method consists of introducing a counter term into the action, and does not rely on the embedding or compactification of any higher-dimensional spaces. This counterterm is sufficient to cancel the divergence in the action that would otherwise occur, and exactly reproduces the trace of the field equations of the original formulation of the theory. All other field equations display an extra scalar gravitational degree of freedom in the gravitational sector, in keeping with the requirements of Lovelock's theorem. We discuss issues concerning the equivalence between our new regularized theory and the original.

6 pages + 2 pages with references; V2: Published in Physical Review D

References in corpus (34)

• Modified Gravity and Cosmology
• The Confrontation between General Relativity and Experiment
• On Renormalization Group Flows in Four Dimensions
• Einstein-Gauss-Bonnet gravity in 4-dimensional space-time
• Horndeski theory and beyond: a review
• Testing General Relativity in Cosmology
• Charged Black Holes in AdS Spaces in $4D$ Einstein Gauss-Bonnet Gravity
• Horndeski Gravity as $D\to 4$ Limit of Gauss-Bonnet
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?
• Extended thermodynamics and microstructures of four-dimensional charged Gauss-Bonnet black hole in AdS space
• Black Holes in Gravity with Conformal Anomaly and Logarithmic Term in Black Hole Entropy
• Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4-D Einstein-Gauss-Bonnet Gravity
• The $D\to 2$ Limit of General Relativity
• Einstein gravity with Gauss-Bonnet entropic corrections
• Black holes in the four-dimensional Einstein-Lovelock gravity
• Grey-body factors and Hawking radiation of black holes in $4D$ Einstein-Gauss-Bonnet gravity
• Thermodynamic geometry of the novel 4-D Gauss Bonnet AdS Black Hole
• Amplitudes and 4D Gauss-Bonnet Theory
• Thermodynamics of Conformal Anomaly Corrected Black Holes in AdS Space
• Thin Accretion Disk around a four-dimensional Einstein-Gauss-Bonnet Black Hole
• Twenty Five Years of Asymptotic Freedom
• Regularized Lovelock gravity
• Dimensionally Dependent Tensor Identities by Double Antisymmetrisation
• BTZ black holes with higher curvature corrections in the 3D Einstein-Lovelock theory
• Bending of light in novel 4$D$ Gauss-Bonnet-de Sitter black holes by Rindler-Ishak method
• On Useful Conformal Tranformations In General Relativity
• Classification of shift-symmetric Horndeski theories and hairy black holes
• Gravity in Two Spacetime Dimensions
• Quasinormal modes of the Dirac field in the novel 4D Einstein-Gauss-Bonnet gravity
• Novel cosmological and black hole solutions in Einstein and higher-derivative gravity in two dimensions
• Superradiance and stability of the novel 4D charged Einstein-Gauss-Bonnet black hole
• Stability of the Einstein Static Universe in $4D$ Gauss-Bonnet Gravity
• Two Dimensional Quantum Gravity Coupled to Matter

Cited by in corpus (137)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity and its shadow
• The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review
• Gravitational lensing by black holes in the $4D$ Einstein-Gauss-Bonnet gravity
• A consistent theory of $D\to 4$ Einstein-Gauss-Bonnet gravity
• A note on the novel 4D Einstein-Gauss-Bonnet gravity
• Charged 4D Einstein-Gauss-Bonnet-AdS Black Holes: Shadow, Energy Emission, Deflection Angle and Heat Engine
• Gravitational lensing by charged black hole in regularized $4D$ Einstein-Gauss-Bonnet gravity
• Thermodynamic geometry of the novel 4-D Gauss Bonnet AdS Black Hole
• Amplitudes and 4D Gauss-Bonnet Theory
• Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity
• (In)stability of black holes in the 4D Einstein-Gauss-Bonnet and Einstein-Lovelock gravities
• 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
• Observational Constraints on the Regularized 4D Einstein-Gauss-Bonnet Theory of Gravity
• Thin Accretion Disk around a four-dimensional Einstein-Gauss-Bonnet Black Hole
• Gravity with a generalized conformal scalar field: Theory and solutions
• Quark Stars in 4D Einstein-Gauss-Bonnet gravity with an Interacting Quark Equation of State
• Regularized Lovelock gravity
• Electrically Charged Quark Stars in $4D$ Einstein-Gauss-Bonnet Gravity
• Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes
• BTZ black holes with higher curvature corrections in the 3D Einstein-Lovelock theory
• Vacua and Exact Solutions in Lower-$D$ Limits of EGB
• Relativistic stars in 4D Einstein-Gauss-Bonnet gravity
• Black holes with primary scalar hair
• 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
• Bardeen Black Holes in the Regularized $4D$ Einstein--Gauss--Bonnet Gravity
• Astrophysical constraints on compact objects in 4D Einstein-Gauss-Bonnet gravity
• Strange Quark Stars in 4D Einstein-Gauss-Bonnet Gravity
• Testing the nature of Gauss-Bonnet gravity by four-dimensional rotating black hole shadow
• Effect of the magnetic charge on weak deflection angle and greybody bound of the black hole in Einstein-Gauss-Bonnet gravity
• Applicability of Modified Gauss-Bonnet Gravity Models on the Existence of Stellar Structures
• Rotating Gauss-Bonnet BTZ Black Holes
• 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
• Nonsingular Black Holes in $4D$ Einstein--Gauss--Bonnet Gravity
• Traversable wormholes in beyond Horndeski theories
• A new approach and code for spinning black holes in modified gravity
• Theoretical and observational constraints on regularized 4$D$ Einstein-Gauss-Bonnet gravity
• Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime
• $D\to 4$ Einstein-Gauss-Bonnet Gravity and Beyond
• Phase Transitions in 4D Gauss-Bonnet-de Sitter Black Holes
• Quasibound States, Stability and Wave Functions of the Test Fields in the Consistent 4D Einstein-Gauss-Bonnet Gravity
• Canonical variational completion and 4D Gauss-Bonnet gravity
• Instability of regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes
• Quark stars with a unified interacting equation of state in regularized 4D Einstein-Gauss-Bonnet gravity
• Unruh-DeWitt detector in dimensionally-reduced static spherically symmetric spacetimes
• Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity
• Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence
• Compact objects of spherical symmetry in beyond Horndeski theories
• Conformally coupled theories and their deformed compact objects: from black holes, radiating spacetimes to eternal wormholes
• Cosmology and gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• Null Geodesics and Thermodynamic Phase Transition of Four-Dimensional Gauss-Bonnet AdS Black Hole
• Rotating black holes in semiclassical gravity
• Neutron stars in 4D Einstein-Gauss-Bonnet gravity
• Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms
• On the "Einstein-Gauss-Bonnet Gravity in Four Dimension"
• Distinguishing modified gravity with just two tensorial degrees of freedom from general relativity: Black holes, cosmology, and matter coupling
• Long-lived quasinormal modes and echoes in the Einstein-Gauss-Bonnet-Proca theory
• Proca theory of four-dimensional regularized Gauss-Bonnet gravity and black holes with primary hair
• Traversable Thin-shell Wormhole in the 4D Einstein-Gauss-Bonnet Theory
• Thermodynamics, Phase Transition and Joule Thomson Expansion of 4-D Gauss-Bonnet AdS Black Hole
• Page Curve and Island in EGB gravity
• Three Dimensional Modified Gravities as Holographic Limits of Lancsoz-Lovelock Theories
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Black Holes in $4D$ AdS Einstein Gauss Bonnet Gravity With Power- Yang Mills Field
• Cosmological Constraints on 4-Dimensional Einstein-Gauss-Bonnet Gravity
• Regular BTZ black holes from an infinite tower of corrections
• White dwarfs in regularized 4D Einstein-Gauss-Bonnet gravity
• Non-linear charged planar black holes in four-dimensional Scalar-Gauss-Bonnet theories
• Asymptotic structure of Einstein-Gauss-Bonnet theory in lower dimensions
• On the gravitational collapse in 4-dimensional Einstein-Gauss-Bonnet gravity
• Einstein-Gauss-Bonnet gravity with rational nonlinear electrodynamics
• Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and (in)-stability
• Stability of asymptotically de Sitter and anti-de Sitter black holes in $4D$ regularized Einstein-Gauss-Bonnet theory
• Theory and phenomenology of a four dimensional string-corrected black hole
• Singularity resolution and inflation from an infinite tower of regularized curvature corrections
• Charged AdS black holes with finite electrodynamics in 4D Einstein-Gauss-Bonnet gravity
• Exploring the shear viscosity in four-dimensional planar black holes beyond General Relativity
• 3D Lovelock Gravity and the Holographic c-Theorem
• Quasibound states of scalar fields in the consistent 4D Einstein-Gauss-Bonnet-(Anti-)de Sitter gravity
• A new class of regular Black Holes in Einstein Gauss Bonnet gravity with localized sources of matter
• Radiation from Einstein-Gauss-Bonnet de Sitter Black Hole via Tunneling Process
• Primary hairs may create echoes
• Generalized Lense--Thirring metrics: higher-curvature corrections and solutions with matter
• 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
• Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity with backreactions
• Lower-dimensional Limits of Cubic Lovelock Gravity
• Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity
• Eikonal quasinormal modes, photon sphere and shadow of a charged black hole in the 4D Einstein-Gauss-Bonnet 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
• Stability of neutron stars in Horndeski theories with Gauss-Bonnet couplings
• Generalized gravitational phase transition in novel 4D Einstein-Gauss-Bonnet gravity
• Conformal/Poincaré Coset, Cosmology, and Descendants of Lovelock Terms
• Double shadow of a 4D Einstein-Gauss-Bonnet black hole and their connection between with quasinormal modes
• Massive scalar field perturbations of 4D de Sitter Einstein-Gauss-Bonnet black holes
• No logarithmic corrections to entropy in shift-symmetric Gauss-Bonnet gravity
• Charged Wormhole Solutions in 4D Einstein-Gauss-Bonnet Gravity
• Dyonic Born-Infeld black hole in four-dimensional Horndeski gravity
• Emergent Cosmology in 4D Einstein Gauss Bonnet Theory of Gravity
• Microscopic entropy of static black holes in 3d Lovelock gravities
• Primary Proca Hair and the Double-Peak Optics of Black Holes
• An exact five dimensional Weyl-Geometry Gauss-Bonnet Black Hole
• The Stringy Origins of Galileons and their Novel Limit
• Can Bekenstein's area law prevail in modified theories of gravity?
• Slowly Rotating Black Holes in 4D Einstein Gauss-Bonnet Gravity
• Scaling symmetry, Smarr relation, and the extended first law in lower-dimensional Lovelock gravity
• Magnetic black holes in 4$D$ Einstein--Gauss--Bonnet massive gravity coupled to nonlinear electrodynamics
• Dimensional aspects of Lovelock-Lanczos gravity
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• Shadow of axisymmetric, stationary and asymptotically flat black holes in the presence of plasma
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• One-Dimensional Relativistic Self-Gravitating Systems
• Deflection of charged massive particles by a four-dimensional charged Einstein-Gauss-Bonnet black hole
• Strong coupling and instabilities in singularity-free inflation from an infinite sum of curvature corrections
• Global and local thermodynamics of the (2+1)-dimensional rotating Gauss-Bonnet black hole
• Shadow of black holes with a plasma environment in 4D Einstein-Gauss-Bonnet gravity
• Regular AdS${}_3$ black holes from regularized Gauss-Bonnet coupling
• Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations
• Surface gravity in spherically symmetric collapsing stars
• Impact of hyperons on structural properties of neutron stars and hybrid stars within the regularized four-dimensional Einstein-Gauss-Bonnet gravity
• Dynamical 4-D Gauss-Bonnet action from matter-graviton interaction at one-loop
• Periodic Orbits and Gravitational Wave Radiation of Black Hole in EGB gravity
• Instability of regular planar black holes in four dimensions arising from an infinite sum of curvature corrections
• Theoretical filters for shift-symmetric Horndeski gravities
• Stellar modeling within regularized 4D Einstein-Gauss-Bonnet gravity in light of current astrophysical constraints
• Internal structure and its connection with thermodynamics and dynamics in black holes
• Image of the thin accretion disk around compact objects in the Einstein-Gauss-Bonnet gravity
• The Interior MOTSs of Spherically Symmetric Black Holes
• Lower-dimensional Gauss-Bonnet gravity black holes with quintessence
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity
• Cosmic acceleration from string induced Galileons
• Regularized Black Hole Solution from a New String Cloud Source
• Black Holes in 4D Einstein-Gauss-Bonnet gravity with exponential electrodynamics