Abstract
The recent holographic deduction of the Penrose inequality only assumes the null energy condition, while a weak or dominant energy condition is required in the usual geometric proof. We take a step toward filling the gap between these two approaches. For planar or spherically symmetric asymptotically Schwarzschild anti-de Sitter (AdS) black holes, we give a purely geometric proof for the Penrose inequality by assuming the null energy condition. We also point out that two naive generalizations of the charged Penrose inequality are generally not true, and we propose two new candidates. When the spacetime is asymptotically AdS but not Schwarzschild-AdS, the total mass is defined according to holographic renormalization and depends on the scheme of quantization. In this case, the holographic argument implies that the Penrose inequality should still be valid, but we use a concrete example to show that whether the Penrose inequality holds or not will depend on what kind of quantization scheme we employ.
- Received 19 August 2022
- Accepted 23 December 2022
DOI:https://doi.org/10.1103/PhysRevD.107.026013
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society