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Register a new userDimensional Reduction of Gravity and Relation between Static States, Cosmologies and Waves
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V.de Alfaro
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We introduce generalized dimensional reductions of an integrable 1+1-dimensional dilaton gravity coupled to matter down to one-dimensional static states (black holes in particular), cosmological models and waves. An unusual feature of these reductions is the fact that the wave solutions depend on two variables - space and time. They are obtained here both by reducing the moduli space (available due to complete integrability) and by a generalized separation of variables (applicable also to non integrable models and to higher dimensional theories). Among these new wave-like solutions we have found a class of solutions for which the matter fields are finite everywhere in space-time, including infinity. These considerations clearly demonstrate that a deep connection exists between static states, cosmologies and waves. We argue that it should exist in realistic higher-dimensional theories as well. Among other things we also briefly outline the relations existing betweenthe low-dimensional models that we have discussed hereand the realistic higher-dimensional ones. This paper develops further some ideas already present in our previous papers. We briefly reproduce here (without proof) their main results in a more concise form and give an important generalization.
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We discuss some problems related to dimensional reductions of gravity theories to two-dimensional and one-dimensional dilaton gravity models. We first consider the most general cylindrical reductions of the four-dimensional gravity and derive the corresponding (1+1)-dimensional dilaton gravity, paying a special attention to a possibility of producing nontrivial cosmological potentials from pure geometric variables (so to speak, from `nothing). Then we discuss further reductions of two-dimensional theories to the dimension one by a general procedure of separating the space and time variables. We illustrate this by the example of the spherically reduced gravity coupled to scalar matter. This procedure is more general than the usual `naive reduction and apparently more general than the reductions using group theoretical methods. We also explain in more detail the earlier proposed `static-cosmological duality (SC-duality) and discuss some unusual cosmologies and static states which can be obtained by using the method of separating the space and time variables.
We analyze the constraints on four-derivative corrections to 5d Einstein-Maxwell theory from the black hole Weak Gravity Conjecture (WGC). We calculate the leading corrections to the extremal mass of asymptotically flat 5d charged solutions as well as 4d Kaluza-Klein compactifications. The WGC bounds from the latter, interpreted as 4d dyonic black holes, are found to be strictly stronger. As magnetic graviphoton charge lifts to a NUT-like charge in 5d, we argue that the logic of the WGC should apply to these topological charges as well and leads to new constraints on purely gravitational theories.
In recent years several approaches to quantum gravity have found evidence for a scale dependent spectral dimension of space-time varying from four at large scales to two at small scales of order of the Planck length. The first evidence came from numerical results on four-dimensional causal dynamical triangulations (CDT) [Ambjorn et al., Phys. Rev. Lett. 95 (2005) 171]. Since then little progress has been made in analytically understanding the numerical results coming from the CDT approach and showing that they remain valid when taking the continuum limit. Here we argue that the spectral dimension can be determined from a model with fewer degrees of freedom obtained from the CDTs by radial reduction. In the resulting toy model we can take the continuum limit analytically and obtain a scale dependent spectral dimension varying from four to two with scale and having functional behaviour exactly of the form which was conjectured on the basis of the numerical results.
We describe a class of integrable models of 1+1 and 1-dimensional dilaton gravity coupled to scalar fields. The models can be derived from high dimensional supergravity theories by dimensional reductions. The equations of motion of these models reduce to systems of the Liouville equations endowed with energy and momentum constraints. We construct the general solution of the 1+1 dimensional problem in terms of chiral moduli fields and establish its simple reduction to static black holes (dimension 0+1), and cosmological models (dimension 1+0). We also discuss some general problems of dimensional reduction and relations between static and cosmological solutions.
We discuss the difference between n-dimensional regularization and n-dimensional reduction for processes in QCD which have an additional mass scale. Examples are heavy flavour production in hadron-hadron collisions or on-shell photon-hadron collisions where the scale is represented by the mass $m$. Another example is electroproduction of heavy flavours where we have two mass scales given by $m$ and the virtuality of the photon $Q=sqrt{-q^2}$. Finally we study the Drell-Yan process where the additional scale is represented by the virtuality $Q=sqrt{q^2}$ of the vector boson ($gamma^*, W, Z$). The difference between the two schemes is not accounted for by the usual oversubtractions. There are extra counter terms which multiply the mass scale dependent parts of the Born cross sections. In the case of the Drell-Yan process it turns out that the off-shell mass regularization agrees with n-dimensional regularization.
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