The 4D Einstein-Gauss-Bonnet Theory of Gravity: A Review

Abstract

We review the topic of 4D Einstein-Gauss-Bonnet gravity, which has been the subject of considerable interest over the past two years. Our review begins with a general introduction to Lovelock's theorem, and the subject of Gauss-Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss-Bonnet term in four space-time dimensions by re-scaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well-defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity. We show that 4D Einstein-Gauss-Bonnet gravity exhibits a number of interesting phenomena in each of these areas.

57 pages, 2 figures

References in corpus (92)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• The Confrontation between General Relativity and Experiment
• Quantum Gravity at a Lifshitz Point
• GW190814: Gravitational Waves from the Coalescence of a 23 M${}_{\odot }$ Black Hole with a 2.6 M${}_{\odot }$ Compact Object
• An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
• GW170608: Observation of a 19-solar-mass Binary Black Hole Coalescence
• Tests of general relativity from timing the double pulsar
• Dark Energy after GW170817: dead ends and the road ahead
• INTEGRAL Detection of the First Prompt Gamma-Ray Signal Coincident with the Gravitational Wave Event GW170817
• Strong constraints on cosmological gravity from GW170817 and GRB 170817A
• Observation of gravitational waves from two neutron star-black hole coalescences
• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• Horndeski theory and beyond: a review
• Rotating Black Holes in Dilatonic Einstein-Gauss-Bonnet Theory
• Spontaneously scalarised Kerr black holes
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Spin-induced scalarized black holes
• Shadows of Einstein-dilaton-Gauss-Bonnet black holes
• On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions
• Spin-induced black hole scalarization in Einstein-scalar-Gauss-Bonnet theory
• The Lovelock Black Holes
• Swampland Implications of GW170817-compatible Einstein-Gauss-Bonnet Gravity
• Thermodynamics and P-v criticality of Bardeen-AdS Black Hole in 4-D Einstein-Gauss-Bonnet Gravity
• Quasinormal modes of Einstein-Gauss-Bonnet-dilaton black holes
• Comment on "Einstein-Gauss-Bonnet Gravity in 4-Dimensional Space-Time''
• Accurate Measurement in the Field of the Earth of the General-Relativistic Precession of the LAGEOS II Pericenter and New Constraints on Non-Newtonian Gravity
• The basic physics of the binary black hole merger GW150914
• Charged black hole in $4D$ Einstein-Gauss-Bonnet gravity: Particle motion, plasma effect on weak gravitational lensing and centre-of-mass energy
• Thermodynamics of Conformal Anomaly Corrected Black Holes in AdS Space
• Shadow, deflection angle and quasinormal modes of Born-Infeld charged black holes
• Charged particle and epicyclic motions around $4D$ Einstein-Gauss-Bonnet black hole immersed in an external magnetic field
• Comment on "Einstein-Gauss-Bonnet Gravity in Four-Dimensional Spacetime"
• Conformally Coupled Scalars, Instantons and Vacuum Instability in AdS_4
• Gravity with a generalized conformal scalar field: Theory and solutions
• Dust collapse in 4D Einstein-Gauss-Bonnet gravity
• Lower-dimensional Gauss-Bonnet Gravity and BTZ Black Holes
• Electrically Charged Quark Stars in $4D$ Einstein-Gauss-Bonnet Gravity
• Einstein-Gauss-Bonnet gravity coupled to bumblebee field in four dimensional spacetime
• On the quasi-linearity of the Einstein- "Gauss-Bonnet" gravity field equations
• Astrophysical constraints on compact objects in 4D Einstein-Gauss-Bonnet gravity
• Motion of Particles and Gravitational Lensing Around (2+1)-dimensional BTZ black holes in Gauss-Bonnet Gravity
• Anisotropic Stars in 4D Einstein-Gauss-Bonnet Gravity
• Nonlinear magnetically charged black holes in 4D Einstein-Gauss-Bonnet gravity
• Classification of shift-symmetric Horndeski theories and hairy black holes
• Thin accretion disks around rotating black holes in $4D$ Einstein-Gauss-Bonnet gravity
• Inflationary gravitational waves in consistent $D\to 4$ Einstein-Gauss-Bonnet gravity
• Shadow cast and center of mass energy in a charged Gauss-Bonnet-AdS black hole
• Hawking evaporation of Einstein-Gauss-Bonnet AdS black holes in $D⩾4$ dimensions
• Black Holes in the Scalar-Tensor Formulation of 4D Einstein-Gauss-Bonnet Gravity: Uniqueness of Solutions, and a New Candidate for Dark Matter
• Dynamical Evolution of the Shock Cone around $4D$ Einstein-Gauss Bonnet Rotating Black Hole
• Static black hole solutions with a self interacting conformally coupled scalar field
• Limits on stellar structures in Lovelock theories of gravity
• Bondi-Hoyle Accretion around the Non-rotating Black Hole in 4D Einstein-Gauss-Bonnet Gravity
• $4D$ AdS Einstein-Gauss-Bonnet black hole with Yang-Mills field and its thermodynamics
• Minimally modified gravity with an auxiliary constraint: a Hamiltonian construction
• 4D Einstein-Lovelock black holes: Hierarchy of orders in curvature
• Novel cosmological and black hole solutions in Einstein and higher-derivative gravity in two dimensions
• Plebanski-Demianski solutions in Quadratic gravity with conformally coupled scalar fields
• Canonical variational completion and 4D Gauss-Bonnet gravity
• Einstein-Gauss-Bonnet gravity with nonlinear electrodynamics
• Isotropic compact stars in 4D Einstein-Gauss-Bonnet gravity
• 4D Gauss-Bonnet gravity: cosmological constraints, $H_0$ tension and large scale structure
• Null geodesics and shadow of 4$D$ Einstein-Gauss-Bonnet black holes surrounded by quintessence
• Stability of the Einstein Static Universe in $4D$ Gauss-Bonnet Gravity
• Tidal effects in 4D Einstein-Gauss-Bonnet Black Hole Spacetime
• Null Geodesics and Thermodynamic Phase Transition of Four-Dimensional Gauss-Bonnet AdS Black Hole
• Phase transition and Quasinormal modes for Charged black holes in 4D Einstein-Gauss-Bonnet gravity
• Triple points and phase diagrams of Born-Infeld AdS black holes in 4D Einstein-Gauss-Bonnet gravity
• Optical features of AdS black holes in the novel 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics
• 4D Einstein-Gauss-Bonnet gravity: Massless particles and absorption of planar spin-0 waves
• Growth of matter density perturbations in 4D Einstein-Gauss-Bonnet gravity
• Einstein-Gauss-Bonnet gravity with rational nonlinear electrodynamics
• The Integrated Sachs-Wolfe Effect in 4D Einstein-Gauss-Bonnet Gravity
• Magnetized particle motion around 4-D Einstein-Gauss-Bonnet Black Hole
• Particle-antiparticle in 4D charged Einstein-Gauss-Bonnet black hole
• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
• The correspondence between shadow and test field in a four-dimensional charged Einstein-Gauss-Bonnet black hole
• Radiation from Einstein-Gauss-Bonnet de Sitter Black Hole via Tunneling Process
• Nonsingular black holes and nonsingular universes in the regularized Lovelock gravity
• Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity with backreactions
• New model of 4D Einstein--Gauss--Bonnet gravity coupled with nonlinear electrodynamics
• Black holes in 4D Einstein-Maxwell-Gauss-Bonnet gravity coupled with scalar fields
• Thermodynamics with pressure and volume of 4D Gauss-Bonnet AdS Black Holes under the scalar field
• Cosmic evolution in novel-Gauss Bonnet Gravity
• Conformal/Poincaré Coset, Cosmology, and Descendants of Lovelock Terms
• Dyonic Born-Infeld black hole in four-dimensional Horndeski gravity
• Energy and entropy compensation, phase transition and kinetics of four dimensional charged Gauss-Bonnet Anti-de Sitter black holes on the underlying free energy landscape
• Non-exotic wormholes in 4-D Einstein-Gauss-Bonnet gravity
• The Stringy Origins of Galileons and their Novel Limit
• Dimensional aspects of Lovelock-Lanczos 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

Cited by in corpus (92)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Quasinormal modes of Schwarzschild black holes in projective invariant Chern-Simons modified gravity
• Applicability of Modified Gauss-Bonnet Gravity Models on the Existence of Stellar Structures
• Fast and accurate predictions of the nonlinear matter power spectrum for general models of Dark Energy and Modified Gravity
• Landau damping for gravitational waves in parity-violating theories
• A new approach and code for spinning black holes in modified gravity
• Torsional birefringence in metric-affine Chern-Simons gravity: gravitational waves in late-time cosmology
• The Galactic Center as a laboratory for theories of gravity and dark matter
• Possibility of the Traversable Wormholes in the Galactic Halos within $4D$ Einstein-Gauss-Bonnet Gravity
• Bottom-Up Reconstruction of Viable GW170817 Compatible Einstein-Gauss-Bonnet Theories
• Black hole hairs in scalar-tensor gravity and the lack thereof
• Charged $AdS$ Black Holes in $4D$ Einstein--Gauss--Bonnet Massive Gravity
• Quark stars with a unified interacting equation of state in regularized 4D Einstein-Gauss-Bonnet gravity
• Black hole perturbations in Maxwell-Horndeski theories
• WGC as WCCC protector: The Synergistic Effects of various Parameters in Identifying WGC candidate Models
• Page Curves of Reissner-Nordström Black Hole in HD Gravity
• Compact objects of spherical symmetry in beyond Horndeski theories
• Anisotropic solution for polytropic stars in 4D Einstein-Gauss-Bonnet gravity
• Conformally coupled theories and their deformed compact objects: from black holes, radiating spacetimes to eternal wormholes
• Neutron stars in 4D Einstein-Gauss-Bonnet gravity
• Exploring the Small Mass Limit of Stationary Black Holes in Theories with Gauss-Bonnet Terms
• Rotating black holes in semiclassical gravity
• Proca theory of four-dimensional regularized Gauss-Bonnet gravity and black holes with primary hair
• Selecting Horndeski theories without apparent symmetries and their black hole solutions
• Global Monopoles in the Extended Gauss-Bonnet Gravity
• Gauss-Bonnet Dark Energy and the Speed of Gravitational Waves
• Cosmological Constraints on 4-Dimensional Einstein-Gauss-Bonnet Gravity
• Phase Transitions and Critical Phenomena for the FRW Universe in an Effective Scalar-Tensor Theory
• Regular BTZ black holes from an infinite tower of corrections
• Quintessence in the Weyl-Gauss-Bonnet model
• Non-linear charged planar black holes in four-dimensional Scalar-Gauss-Bonnet theories
• White dwarfs in regularized 4D Einstein-Gauss-Bonnet gravity
• Reviving Horndeski after GW170817 by Kaluza-Klein compactifications
• On the gravitational collapse in 4-dimensional Einstein-Gauss-Bonnet gravity
• Naked singularity in 4D Einstein-Gauss-Bonnet novel gravity: Echoes and (in)-stability
• Shape of Dark Energy: Constraining Its Evolution with a General Parametrization
• Geometric and topological corrections to Schwarzschild black hole
• Insight into the Microstructure of FRW Universe from a $P$-$V$ Phase Transition
• Singularity resolution and inflation from an infinite tower of regularized curvature corrections
• Ultraviolet Unitarity Violations in Non-minimally Coupled Scalar-Starobinsky Inflation
• Exploring the shear viscosity in four-dimensional planar black holes beyond General Relativity
• On the Lagrangian Holographic Relation at $D\to 2$ and $4$ Limits of Gravity
• Interacting Models of Dark Energy and Dark Matter in Einstein scalar Gauss Bonnet Gravity
• Lower-dimensional Limits of Cubic Lovelock Gravity
• Eikonal quasinormal modes, photon sphere and shadow of a charged black hole in the 4D Einstein-Gauss-Bonnet gravity
• Black Hole Shadows in Einstein-Bel-Robinson Gravity
• Charged Wormhole Solutions in 4D Einstein-Gauss-Bonnet Gravity
• Higher derivative SVT theories from Kaluza-Klein reductions of Horndeski theory
• Dark energy from topology change induced by microscopic Gauss-Bonnet wormholes
• Slow-rotating black holes with potential in dynamical Chern-Simons modified gravitational theory
• Regular black holes from pure gravity in four dimensions
• Observational Feasibility of 4D Einstein-Gauss-Bonnet Cosmology: Bouncing and Non-Bouncing Universes
• Minimally modified gravity with auxiliary constraints formalism
• A new 2D formulation of modified General Relativity
• Bulk-Boundary Thermodynamics of Charged Black Holes in Higher Derivative Theory
• Emergent Cosmology in 4D Einstein Gauss Bonnet Theory of Gravity
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities
• Non-Singular Bouncing cosmology from Phantom Scalar-Gauss-Bonnet Coupling: Reconstruction with Observational Insights
• Solar system tests and neutron stars in $f(R)$ gravity revisited
• Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem
• Slowly Rotating Black Holes in 4D Einstein Gauss-Bonnet Gravity
• Hubble Tension and Dark Energy in Teleparallel Gauss-Bonnet Gravity: New Constraints from DESI BAO, Pantheon${}^{+}$ and Hubble Data
• A Post-Newtonian Analysis of Regularized 4D-EGB Theory: Complete Set of PPN Parameters and Observational Constraints
• AdS${}_3$ black holes with primary Proca hair from a regularized Gauss-Bonnet coupling
• D-dimensional black holes in extended Gauss-Bonnet gravity
• Cosmic acceleration in Lovelock quantum gravity
• Thermodynamics of Flat 4D Einstein-Gauss-Bonnet Black Hole with Rényi Entropy: An RPST-like formalism
• Gauss-Bonnet-induced symmetry breaking/restoration during inflation
• Cosmological Time Crystals from Gauss-Bonnet Gravity in Four Dimensions
• Black Holes with Global Monopoles in 4D Noncommutative Einstein Gauss Bonnet Gravity
• Absence of curvature singularities in symmetric perfect fluid spacetimes in Einstein-Gauss-Bonnet Gravity
• Compact stars in Einstein-scalar-Gauss-Bonnet gravity: regular and divergent scalar field configurations
• Sensitivity forecasts for gravitational-wave detectors to dark matter decaying into gravitons
• Holographic Anisotropic Background in 5D Einstien-Gauss-Bonnet Gravity
• Cosmological Constraints on 4D Einstein-Gauss-Bonnet Gravity and Kaniadakis Holographic Dark Energy: Implications for Black Hole Shadows
• Black hole physics within $f(R)$ gravity: Quasi-normal spectra and greybody factors
• Absence of isolated critical points with nonstandard critical exponents in the four-dimensional regularization of Lovelock gravity
• 4D Einstein--Gauss--Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics
• $\Lambda$CDM-like evolution in Einstein-scalar-Gauss-Bonnet gravity
• Stellar modeling within regularized 4D Einstein-Gauss-Bonnet gravity in light of current astrophysical constraints
• Periodic Orbits and Gravitational Wave Radiation of Black Hole in EGB gravity
• Friedmann's Universe Controlled by Gauss-Bonnet Modified Gravity
• Dynamical 4-D Gauss-Bonnet action from matter-graviton interaction at one-loop
• Anisotropic Spacetimes in $f(G)$-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies
• Compact Objects in 4D Einstein Gauss Bonnet Gravity A Data Based Perspective
• Lower-dimensional Gauss-Bonnet gravity black holes with quintessence
• Spectral Bifurcations in Quasinormal Modes of Regular BTZ Black Holes
• Black Holes in 4D Einstein-Gauss-Bonnet gravity with exponential electrodynamics
• Thin Accretion Disks around Rotating Charged Black Holes in an Effective Higher-Curvature Spacetime
• New brane-like solutions in modified four-dimensional Einstein-Gauss-Bonnet gravity
• The Penrose inequality in spherical symmetry with charge and in Gauss-Bonnet gravity
• A Brief Thermodynamic Study For Four Dimensional Einstein Gauss Bonnet Black Holes Using Fractalised Barrow Entropy