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We present a generalization of Birkhoff’s theorem in the context of six-dimensional Gauss-Bonnet theory. Contrary to what we encounter in ordinary General Relativity, the presence of the higher curvature terms leads to novel constraints on the geometry of the admissible black hole horizons. As a result, we can have static solutions which depart from spherical symmetry, but must satisfy specific constraints involving the Weyl tensor of the four-dimensional horizon. After obtaining the general profile of the static solutions in the transverse space, we give explicit examples of such black hole horizons, which are in general of an anisotropic nature. [ABSTRACT FROM AUTHOR]

We explore various aspects of dynamical black holes defined by a future outer trapping horizon in n(>=5)-dimensional Einstein-Gauss-Bonnet gravity. We assume that the spacetime has symmetries corresponding to the isometries of an (n-2)-dimensional maximally symmetric space and the Gauss-Bonnet coupling constant is non-negative. Depending on the existence or absence of the general relativistic limit, solutions are classified into GR and non-GR branches, respectively. Assuming the null energy condition on matter fields, we show that a future outer trapping horizon in the GR branch possesses the same properties as that in general relativity. In contrast, that in the non-GR branch is shown to be non-spacelike with its area non-increasing into the future. On the other hand, the entropy of a future outer trapping horizon is shown to be non-decreasing in both branches along its generator. [ABSTRACT FROM AUTHOR]

The current acceleration of the universe leads us to investigate higher dimensional gravity theory, which is able to explain acceleration from a theoretical view point without the need of introducing dark energy by hand. We argue that the terms containing higher dimensional metric coefficients produce an extra negative pressure that apparently drives an acceleration of the 3D space, tempting us to suggest that the accelerating universe seems to act as a window to the existence of extra spatial dimensions. Interesting to point out that in this case our cosmology apparently mimics the well known quintessence scenario fuelled by a generalised Chaplygin-type of fluid where a smooth transition from a dust dominated model to a de Sitter like one takes place. Correspondence to models generated by a tachyonic form of matter is also briefly discussed. [ABSTRACT FROM AUTHOR]

We study the short distance behaviour of euclidean quantum gravity in the light of Weinberg’s asymptotic safety scenario. Implications of a non-trivial ultraviolet fixed point are reviewed. Based on an optimised renormalisation group, we provide analytical flow equations in the Einstein-Hilbert truncation. A non-trivial ultraviolet fixed point is found for arbitrary dimension. We discuss a bifurcation pattern in the spectrum of eigenvalues at criticality, and the large dimensional limit of quantum gravity. Implications for quantum gravity in higher dimensions are indicated. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]