Bounds on area and charge for marginally trapped surfaces with cosmological constant

Abstract

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 ${\Lambda }^{\ast }=\Lambda +\lambda >0$ we obtain a lower and an upper bound for ${\Lambda }^{\ast }A$ in terms of ${\Lambda }^{\ast }{Q}^2$ as well as the upper bound $Q\le 1/(2\sqrt{{\Lambda }^{\ast }})$ for the charge, which reduces to $Q\le 1/(2\sqrt{\Lambda })$ in the stable case $\lambda \ge 0$. For ${\Lambda }^{\ast }<0$ 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.

minor corrections to previous version and to published version

References in corpus (5)

• Biaxially symmetric solutions to 4D higher-spin gravity
• The area of horizons and the trapped region
• The time evolution of marginally trapped surfaces
• Area-charge inequality for black holes
• Black hole Area-Angular momentum-Charge inequality in dynamical non-vacuum spacetimes

Cited by in corpus (12)

• The 1965 Penrose singularity theorem
• Area products for stationary black hole horizons
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Black hole Area-Angular momentum-Charge inequality in dynamical non-vacuum spacetimes
• Proof of the area-angular momentum-charge inequality for axisymmetric black holes
• Area-angular momentum-charge inequality for stable marginally outer trapped surfaces in 4D Einstein-Maxwell-dilaton theory
• A Young-Laplace law for black hole horizons
• Geometric relations for rotating and charged AdS black holes
• Horizon area-angular momentum-charge-magnetic fluxes inequalities in 5D Einstein-Maxwell-dilaton gravity
• Min-max minimal surfaces, horizons and electrostatic systems
• Mass angular momentum and charge inequalities for black holes in Einstein-Maxwell-axion-dilaton gravity
• Ultra-massive spacetimes in 2+1 dimensions with positive Λ