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Einstein-Gauss-Bonnet gravity (EGB) provides a natural higher dimensional and higher order curvature generalization of Einstein gravity.
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J. Bland, B. Preston, M. Becker, G. Kunstatter, and V. Husain, “Dimension Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse,” Classical and Quantum Gravity, vol. 22, no. 24, pp. 5355-5364, 2005
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