Holography of accelerating black holes

This project falls within EPSRC "mathematical physics" and "geometry and topology" research areas.

A wide area of interest within high energy theoretical physics is concerned with the study of black holes. These objects constitute a particularly interesting field of work because the extreme gravitational regimes they give rise to can be exploited as a playground for studying some of the features of quantum gravity. Moreover, despite being rather simple objects, some of their fundamental aspects are little understood still today, particularly those relative to their thermodynamical behaviour (e.g. microscopic description, information paradox). One particular class of black holes that has received a remarkable attention lately is that of asymptotically AdS black holes. Though they do not have an explicit connection to reality as far as we know, they are interesting because they allow to be studied through a very powerful tool: the holographic principle. Following this idea, one can attempt to provide a microscopic description of the statistical degrees of freedom underlying the black hole thermodynamics in terms of the CFT living on the boundary of AdS which is dual to the black hole solution. This strategy has indeed been applied with success in a wide variety of cases, yet many others are still to be studied.

The aim of the project is to construct new general classes of black holes in low dimensional supergravity and try to understand more systematically their microscopic description from the full string theory perspective.
With this wide picture in mind, we will start by considering a family of black holes in four dimensions with asymptotic AdS_4 geometry and five different parameters: mass, electric and magnetic charges, angular momentum, and acceleration. Despite being known since long ago, this solution of the Einstein-Maxwell theory has not been studied much up to nowadays. The starting point of our project will be to correctly identify its boundary geometry and then reproduce the Bekenstein-Hawking entropy of such a black hole through a holographic computation.

The main new ingredient we will add to the usual charged and rotating AdS_4 black holes studied in literature is the presence of a non-vanishing acceleration. Remarkably, this amounts to considering a metric which displays conical singularities and therefore identifies with a weighted projective space. Due to technical reasons related to the holographically dual field theory, we will focus on BPS black holes i.e. black holes that are both supersymmetric and extremal. These requirements impose constraints on the free parameters, reducing the number of independent ones from five down to two. On the other hand, at zero temperature the near horizon geometry is essentially an infinite throat and the quantum statistical relation that connects the entropy of the black hole with the renormalised on-shell action is not valid a priori. The standard procedure in these cases foresees a regularisation of the problem by means of analytical continuation of some of the parameters to the complex plane, followed by taking the BPS limit along a supersymmetric trajectory in the parameter space. Through this procedure it should be possible to recover a form of the quantum statistical relation which is valid also at zero temperature. Our strategy will be to apply this BPS limiting procedure and identify the boundary geometry, that is how the parameters entering the black hole solution influence the asymptotic geometry. With this result in our hand we will then consider an SCFT living on such a boundary and try to reproduce the Bekenstein-Hawking entropy of the black hole through an exact computation of the partition function. Lately, a lot of effort was put on the systematic study of supersymmetric theories on curved spaces, and our work will land precisely in this framework.