Area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory
- Author(s)
- David Fajman, Walter Simon
- Abstract
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by Dain, Jaramillo and Reiris [1] in the pure Einstein-Maxwell case without symmetries, and on the other hand from Yazadjiev's inequality [2] in the axially symmetric Einstein-Maxwell-dilaton case. The common issue in these proofs and in the present one is a functional ${\mathscr W}$ of the matter fields for which the stability condition readily yields an {\it upper} bound. On the other hand, the step which crucially depends on whether or not a dilaton field is present is to obtain a {\it lower} bound for ${\mathscr W}$ as well. We obtain the latter by first setting up a variational principle for ${\mathscr W}$ with respect to the dilaton field $\phi$, then by proving existence of a minimizer $\psi$ as solution of the corresponding Euler-Lagrange equations and finally by estimating ${\mathscr W}(\psi)$. In the special case that the normal components of the electric and magnetic fields are proportional we obtain the area bound $A \ge 8\pi P Q$ in terms of the electric and magnetic charges. In the generic case our results are less explicit but imply rigorous `perturbation' results for the above inequality. All our inequalities are saturated for a 2-parameter family of static, extreme solutions found by Gibbons [3]. Via the Bekenstein-Hawking relation $A = 4S$ our results give positive lower bounds for the entropy $S$ which are particularly interesting in the Einstein-Maxwell-dilaton case.
- Organisation(s)
- Gravitational Physics
- Journal
- Advances in Theoretical and Mathematical Physics
- Volume
- 18
- Pages
- 687-707
- No. of pages
- 21
- ISSN
- 1095-0761
- DOI
- https://doi.org/10.4310/ATMP.2014.v18.n3.a4
- Publication date
- 08-2013
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 103036 Theoretical physics, 103019 Mathematical physics
- Keywords
- ASJC Scopus subject areas
- Physics and Astronomy(all), Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/area-inequalities-for-stable-marginally-outer-trapped-surfaces-in-einsteinmaxwelldilaton-theory(5b877537-aa9d-4eb3-b74b-5f13f9944da8).html