The r-map, c-map and black hole solutions



Vaughan, Owen
The r-map, c-map and black hole solutions. Doctor of Philosophy thesis, University of Liverpool.

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Abstract

We consider various geometrical and physical aspects of the r-map and c-map, which are two maps induced by the dimensional reduction of 5d and 4d, N = 2 supergravity coupled to vector multiplets respectively. We treat reduction over a spacelike or timelike dimension on an equal footing, and prove, for the first time, that the target manifold in the image of the timelike c-map is para-quaternion Kahler. In order to do this we provide a new formulation of projective special Kahler geometry based on real Darboux coordinates, which is useful both mathematically and physically in its own right. As an application we investigate how the r-map and c-map can be used to generate new stationary black hole solutions. In four dimensions we construct new extremal non-BPS solutions, and in both four and five dimensions we construct new non-extremal solutions. We also take the first steps towards constructing new rotating solutions, though at this stage we only recover known solutions. The systematic and geometrical nature of these constructions allows us to gain a deeper understanding of many familiar properties of black holes in supergravity, such as the attractor mechanism and the transformation of BPS into non-BPS black holes using a field rotation matrix. We also observe an interesting and novel feature relating to non-extremal black holes: in order for solutions to correspond to non-extremal black holes with finite scalar fields we find that the number of integration constants must reduce by half. This suggests that non-extremal black holes always satisfy first order equations similar to their extremal counterparts. For STU-like models all calculations are performed explicitly.

Item Type: Thesis (Doctor of Philosophy)
Additional Information: Date: 2012-12-22 (completed)
Subjects: ?? QA ??
Divisions: Faculty of Science and Engineering > School of Physical Sciences > Mathematical Sciences
Depositing User: Symplectic Admin
Date Deposited: 03 Sep 2013 15:39
Last Modified: 16 Dec 2022 04:38
DOI: 10.17638/00008953
Supervisors:
  • Mohaupt, Thomas
  • Tatar, Radu
URI: https://livrepository.liverpool.ac.uk/id/eprint/8953