Area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory

Autor(en)

David Fajman, Walter Simon

Abstrakt

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(en)

Gravitationsphysik

Journal

Advances in Theoretical and Mathematical Physics

Band

18

Seiten

687-707

Anzahl der Seiten

21

ISSN

1095-0761

DOI

https://doi.org/10.4310/ATMP.2014.v18.n3.a4

Publikationsdatum

08-2013

Peer-reviewed

Ja

ÖFOS 2012

103036 Theoretische Physik, 103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie, Allgemeine Mathematik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/5b877537-aa9d-4eb3-b74b-5f13f9944da8