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Register a new userDerivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions
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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 Lovelocks theorem. We discuss issues concerning the equivalence between our new regularized theory and the original.
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To ensure the existence of a well defined linearized gravitational wave equation, we show that the spacetimes in the so-called Einstein-Gauss-Bonnet gravity in four dimension have to be locally conformally flat.
In this paper we study the observational constraints that can be imposed on the coupling parameter, $hat alpha$, of the regularized version of the 4-dimensional Einstein-Gauss-Bonnet theory of gravity. We use the scalar-tensor field equations of this theory to perform a thorough investigation of its slow-motion and weak-field limit, and apply our results to observations of a wide array of physical systems that admit such a description. We find that the LAGEOS satellites are the most constraining, requiring $| hat alpha | lesssim 10^{10} ,{rm m}^2$. This constraint suggests that the possibility of large deviations from general relativity is small in all systems except the very early universe ($t<10^{-3}, {rm s}$), or the immediate vicinity of stellar-mass black holes ($Mlesssim100, M_{odot}$). We then consider constraints that can be imposed on this theory from cosmology, black hole systems, and table-top experiments. It is found that early universe inflation prohibits all but the smallest negative values of $hat alpha$, while observations of binary black hole systems are likely to offer the tightest constraints on positive values, leading to overall bounds $0 lesssim hat alpha lesssim 10^8 , {rm m}^2$.
Einstein-Gauss-Bonnet gravity (EGB) provides a natural higher dimensional and higher order curvature generalization of Einstein gravity. It contains a new, presumably microscopic, length scale that should affect short distance properties of the dynamics, such as Choptuik scaling. We present the results of a numerical analysis in generalized flat slice co-ordinates of self-gravitating massless scalar spherical collapse in five and six dimensional EGB gravity near the threshold of black hole formation. Remarkably, the behaviour is universal (i.e. independent of initial data) but qualitatively different in five and six dimensions. In five dimensions there is a minimum horizon radius, suggestive of a first order transition between black hole and dispersive initial data. In six dimensions no radius gap is evident. Instead, below the GB scale there is a change in the critical exponent and echoing period.
In this paper, we investigate the photon sphere, shadow radius and quasinormal modes of a four-dimensional charged Einstein-Gauss-Bonnet black hole. The perturbation of a massless scalar field in the black holes background is adopted. The quasinormal modes are gotten by the $6th$ order WKB approximation approach and shadow radius, respectively. When the value of the Gauss-Bonnet coupling constant increase, the values of the real parts of the quasinormal modes increase and those of the imaginary parts decrease. The coincidence degrees of quasinormal modes derived by the two approaches increases with the increase of the values of the Gauss-Bonnet coupling constant and multiple number. It shows the correspondence between the shadow and test field in the four-dimensional Einstein-Gauss-Bonnet-Maxwell gravity. The radii of the photon sphere and shadow increase with the decrease of the Gauss-Bonnet coupling constant.
We investigate the $Drightarrow 4$ 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 $Drightarrow 4$ 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.
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