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Register a new userQuantum spacetime and the renormalization group: Progress and visions
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Authors
Antonio D. Pereira
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The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental interactions. In this contribution we briefly review two approaches to quantum gravity, namely, asymptotically safe quantum gravity and tensor models, based on different theoretical assumptions. Nevertheless, the main goal is to find a universal continuum limit for such theories and we explain how coarse-graining techniques should be adapted to each case. Finally, we argue that although seemingly different, such approaches might be just two sides of the same coin.
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The problem of finding null geodesics in a stationary Lorentzian spacetime is known to to be equivalent to finding the geodsics of a Randers-Finlser structure. This latter problem is equivalent to finding the motion of charged particles moving on a Riemannian manifold in a background magnetic field or equivalently, by a generalization of Fermats principle, to Zermelos problem of extremizing travel time of an aeroplane in the presence of a wind. In this paper this triad of equivalences is extended to include recent model of the spread of a forest fire which uses form of Huyghens principle. The construction may also be used to solve a problem in quantum control theory in which one seeks a control Hamiltonia taking an initial state of a quantum mechanical system with its own Hamiltonian to a desired final state in least time. The associated stationary spacetime may be thought of as defined on an extended quantum phase space (Souriaus evolution space), the space of quantum stares being complex projective space equipped with its Fubini-Study Kahler metric. It is possible that this spacetime view point may provide insights relevant for our understanding of quantum gravity.
We consider a model involving a self-interacting complex scalar field minimally coupled to gravity and emphasize the cylindrically symmetric classical solutions. A general ansatz is performed which transforms the field equations into a system of differential equations. In the generic case, the scalar field depends on the four space-time coordinates. The underlying Einstein vacuum equations are worth studying by themselve and lead to numerous analytic results extending the Kasner solutions. The solutions of the coupled system are -static as well as stationnary- gravitating Q-tubes of scalar matter which deform space-time.
We review some of the recent results which can be useful for better understanding of the problem of stability of vacuum and in general classical solutions in higher derivative quantum gravity. The fourth derivative terms in the purely gravitational vacuum sector are requested by renormalizability already in both semiclassical and complete quantum gravity theories. However, because of these terms the spectrum of the theory has unphysical ghost states which jeopardize the stability of classical solutions. At the quantum level ghosts violate unitarity, and and thus ghosts look incompatible with the consistency of the theory. The `dominating or `standard approach is to treat higher derivative terms as small perturbations at low energies. Such an effective theory is supposed to glue with an unknown fundamental theory in the high energy limit. We argue that the perspectives for such a scenario are not clear, to say the least. On the other hand, recently there was certain progress in understanding physical conditions which can make ghosts not offensive. We survey these results and discuss the properties of the unknown fundamental theory which can provide these conditions satisfied.
The transformation which adds (or removes) NUT charge when it is applied to electrovacuum, axisymmetric and stationary space-times is studied. After analysing the Ehlers and the Reina-Treves transformations we propose a new one, more precise in the presence of the Maxwell electromagnetic field. The enhanced Ehlers transformation proposed turns out to act as a gravitomagnetic duality, analogously to the electromagnetic duality, but for gravity: it rotates the mass charge into the gravomagnetic (or NUT) charge. As an example the Kerr-Newman-NUT black hole is obtained with the help of this enhanced transformation. Moreover a new analytical exact solution is built adding the NUT charge to a double charged black hole, at equilibrium. It describes the non-extremal generalisation of the Majumdar-Papapetrou-NUT solution. From the near-horizon analysis, its microscopic entropy, according to the Kerr/CFT correspondence, is found and the second law of black hole thermodynamics is discussed.
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