Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2011-09-28
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
extensions, corrections and revision of presentation (including change of title)
Scientific paper
We sharpen the known inequalities $A \Lambda \le 4\pi (1-g)$ and $A\ge 4\pi Q^2$ between the area $A$ and the electric charge $Q$ of a stable marginally outer trapped surface (MOTS) of genus g in the presence of a cosmological constant $\Lambda$. In particular, instead of requiring stability we include the principal eigenvalue $\lambda$ of the stability operator. For $\Lambda^{*} = \Lambda + \lambda > 0$ we obtain a lower and an upper bound for $ \Lambda^{*} A$ in terms of $ \Lambda^{*} Q^2$ as well as the upper bound $ Q \le 1/(2\sqrt{\Lambda^{*}})$ for the charge, which reduces to $ Q \le 1/(2\sqrt{\Lambda})$ in the stable case $\lambda \ge 0$. For $\Lambda^{*} < 0$ there remains only a lower bound on $A$. In the spherically symmetric, static, stable case one of the area inequalities is saturated iff the surface gravity vanishes. We also discuss implications of our inequalities for "jumps" and mergers of charged MOTS.
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