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.
Originalsprache | Englisch |
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Seiten (von - bis) | 687-707 |
Seitenumfang | 21 |
Fachzeitschrift | Advances in Theoretical and Mathematical Physics |
Jahrgang | 18 |
Ausgabenummer | 3 |
Frühes Online-Datum | 16 Aug. 2013 |
DOIs | |
Publikationsstatus | Veröffentlicht - 2014 |
ÖFOS 2012
- 103036 Theoretische Physik
- 103019 Mathematische Physik