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Register a new userOn the Einstein-Gauss-Bonnet Gravity in Four Dimension
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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.
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We report on a numerical investigation of the stability of scalarized black holes in Einstein dilaton Gauss-Bonnet (EdGB) gravity in the full dynamical theory, though restricted to spherical symmetry. We find evidence that for sufficiently small curvature-couplings the resulting scalarized black hole solutions are nonlinearly stable. For such small couplings, we show that an elliptic region forms inside these EdGB black hole spacetimes (prior to any curvature singularity), and give evidence that this region remains censored from asymptotic view. However, for coupling values superextremal relative to a given black hole mass, an elliptic region forms exterior to the horizon, implying the exterior Cauchy problem is ill-posed in this regime.
We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol. However as the merger point geometry does not approach the black hole geometry asymptotically it is not obvious that the transition is directly to a black hole phase. We also demonstrate that for another range of the Gauss-Bonnet parameter, the merger point geometry approaches the black hole geometry asymptotically when a certain parameter depending on the Gauss-Bonnet parameter $alpha$ and on the parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.
In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we focus on order-reduced Einstein dilaton Gauss-Bonnet gravity (EDGB), a higher curvature beyond-GR theory with motivations in string theory. The stability of single, rotating black holes in EDGB is unknown, but is a necessary condition for being able to simulate binary black hole systems (especially the early-inspiral and late ringdown stages) in EDGB. We thus investigate the stability of rotating black holes in order-reduced EDGB. We evolve the leading-order EDGB scalar field and EDGB spacetime metric deformation on a rotating black hole background, for a variety of spins. We find that the EDGB metric deformation exhibits linear growth, but that this level of growth exponentially converges to zero with numerical resolution. Thus, we conclude that rotating black holes in EDGB are numerically stable to leading-order, thus satisfying our necessary condition for performing binary black hole simulations in EDGB.
We compute the Hamiltonian for spherically symmetric scalar field collapse in Einstein-Gauss-Bonnet gravity in D dimensions using slicings that are regular across future horizons. We first reduce the Lagrangian to two dimensions using spherical symmetry. We then show that choosing the spatial coordinate to be a function of the areal radius leads to a relatively simple Hamiltonian constraint whose gravitational part is the gradient of the generalized mass function. Next we complete the gauge fixing such that the metric is the Einstein-Gauss-Bonnet generalization of non-static Painleve-Gullstrand coordinates. Finally, we derive the resultant reduced equations of motion for the scalar field. These equations are suitable for use in numerical simulations of spherically symmetric scalar field collapse in Gauss-Bonnet gravity and can readily be generalized to other matter fields minimally coupled to gravity.
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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