From static to cosmological solutions of N $$ \mathcal{N} $$ = 2 supergravity

J. Gutowski (Department of Mathematics, University of Surrey, Guildford, GU2 7XH, U.K.) ; T. Mohaupt (Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, U.K.) ; G. Pope (Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, U.K.)

We obtain cosmological solutions with Kasner-like asymptotics in N $$ \mathcal{N} $$ = 2 gauged and ungauged supergravity by maximal analytic continuation of planar versions of non-extremal black hole solutions. Initially, we construct static solutions with planar symmetry by solving the time-reduced field equations. Upon lifting back to four dimensions, the resulting static regions are incomplete and bounded by a curvature singularity on one side and a Killing horizon on the other. Analytic continuation reveals the existence of dynamic patches in the past and future, with Kasner-like asymptotics. For the ungauged STU-model, our solutions contain previously known solutions with the same conformal diagram as a subset. We find explicit lifts to five, six, ten and eleven dimensions which show that in the extremal limit, the underlying brane configuration is the same as for STU black holes. The extremal limit of the six-dimensional lift is shown to be BPS for special choices of the integration constants. We argue that there is a universal correspondence between spherically symmetric black hole solutions and planar cosmological solutions which can be illustrated using the Reissner-Nordström solution of Einstein-Maxwell theory.

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      "source": "Springer", 
      "value": "We obtain cosmological solutions with Kasner-like asymptotics in   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 2 gauged and ungauged supergravity by maximal analytic continuation of planar versions of non-extremal black hole solutions. Initially, we construct static solutions with planar symmetry by solving the time-reduced field equations. Upon lifting back to four dimensions, the resulting static regions are incomplete and bounded by a curvature singularity on one side and a Killing horizon on the other. Analytic continuation reveals the existence of dynamic patches in the past and future, with Kasner-like asymptotics. For the ungauged STU-model, our solutions contain previously known solutions with the same conformal diagram as a subset. We find explicit lifts to five, six, ten and eleven dimensions which show that in the extremal limit, the underlying brane configuration is the same as for STU black holes. The extremal limit of the six-dimensional lift is shown to be BPS for special choices of the integration constants. We argue that there is a universal correspondence between spherically symmetric black hole solutions and planar cosmological solutions which can be illustrated using the Reissner-Nordstr\u00f6m solution of Einstein-Maxwell theory."
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Published on:
23 November 2019
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2019 (2019)
Issue 8
Pages 1-66
DOI:
https://doi.org/10.1007/JHEP08(2019)172
arXiv:
1905.09167
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

Fulltext files: