Critical Collapse in Einstein-Gauss-Bonnet Gravity in Five and Six
  Dimensions

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Abstract

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.

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Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---

, , (2009)

A scenario is presented, based on renormalization group (linear perturbation) ideas, which can explain the self-similarity and scaling observed in a numerical study of gravitational collapse of radiation fluid. In particular, it is shown that the critical exponent \(\beta\) and the largest Lyapunov exponent \({\rm Re\, } \kappa\) of the perturbation is related by \(\beta= ({\rm Re\, } \kappa) ^{-1}\). We find the relevant perturbation mode numerically, and obtain a fairly accurate value of the critical exponent \(\beta \simeq 0.3558019\), also in agreement with that obtained in numerical simulation.

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Critical Behaviour in Gravitational Collapse of a Yang-Mills Field

Tadeusz Chmaj, Piotr Bizoń, Matthew W. Choptuik (1996)

We present results from a numerical study of spherically-symmetric collapse of a self-gravitating, SU(2) gauge field. Two distinct critical solutions are observed at the threshold of black hole formation. In one case the critical solution is discretely self-similar and black holes of arbitrarily small mass can form. However, in the other instance the critical solution is the n=1 static Bartnik-Mckinnon sphaleron, and black hole formation turns on at finite mass. The transition between these two scenarios is characterized by the superposition of both types of critical behaviour.

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Final fate of spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity

Hideki Maeda (2006)

We give a model of the higher-dimensional spherically symmetric gravitational collapse of a dust cloud in Einstein-Gauss-Bonnet gravity. A simple formulation of the basic equations is given for the spacetime \(M \approx M^2 \times K^{n-2}\) with a perfect fluid and a cosmological constant. This is a generalization of the Misner-Sharp formalism of the four-dimensional spherically symmetric spacetime with a perfect fluid in general relativity. The whole picture and the final fate of the gravitational collapse of a dust cloud differ greatly between the cases with \(n=5\) and \(n \ge 6\). There are two families of solutions, which we call plus-branch and the minus-branch solutions. Bounce inevitably occurs in the plus-branch solution for \(n \ge 6\), and consequently singularities cannot be formed. Since there is no trapped surface in the plus-branch solution, the singularity formed in the case of \(n=5\) must be naked. In the minus-branch solution, naked singularities are massless for \(n \ge 6\), while massive naked singularities are possible for \(n=5\). In the homogeneous collapse represented by the flat Friedmann-Robertson-Walker solution, the singularity formed is spacelike for \(n \ge 6\), while it is ingoing-null for \(n=5\). In the inhomogeneous collapse with smooth initial data, the strong cosmic censorship hypothesis holds for \(n \ge 10\) and for \(n=9\) depending on the parameters in the initial data, while a naked singularity is always formed for \(5 \le n \le 8\). These naked singularities can be globally naked when the initial surface radius of the dust cloud is fine-tuned, and then the weak cosmic censorship hypothesis is violated.