![]() ![]() ![]() A straightforward answer to both questions is to simply say that as the number of dimensions grows, the number of degrees of freedom of the gravitational field also increases, but more specific, yet intuitive, answers are possible.ĭoes not, since rotation is confined to a plane. Īt the risk of anticipating results and concepts that will be developed only later in this review, in the following we try to give simple answers to two frequently asked questions: 1) why should one expect any interesting new dynamics in higher-dimensional general relativity, and 2) what are the main obstacles to a direct generalization of the four-dimensional techniques and results. Arguably, two advances are largely responsible for this perception: the discovery of dynamical instabilities in extended black-hole horizons and the discovery of black-hole solutions with horizons of nonspherical topology that are not fully characterized by their conserved charges. There is a growing awareness that the physics of higher-dimensional black holes can be markedly different, and much richer, than in four dimensions. At the very least, this study will lead to a deeper understanding of classical black holes and of what spacetime can do at its most extreme. One would like to know which of these are peculiar to four-dimensions, and which hold more generally. For instance, four-dimensional black holes are known to have a number of remarkable features, such as uniqueness, spherical topology, dynamical stability, and to satisfy a set of simple laws - the laws of black hole mechanics. ![]() Just as the study of quantum field theories, with a field content very different than any conceivable extension of the Standard Model, has been a very useful endeavor, throwing light on general features of quantum fields, we believe that endowing general relativity with a tunable parameter - namely the spacetime dimensionality d - should also lead to valuable insights into the nature of the theory, in particular into its most basic objects: black holes. These, however, refer to applications of the subject - important though they are - but we believe that higher-dimensional gravity is also of intrinsic interest. As mathematical objects, black-hole spacetimes are among the most important Lorentzian Ricci-flat manifolds in any dimension. ![]()
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