Low-temperature Holographic Screens Correspond to Einstein-Rosen Bridges

Recent conjectures on the complexity of black holes suggest that their evolution manifests in the structural properties of Einstein-Rosen bridges, like the length and volume. The complexity of black holes relates to the computational complexity of their dual, namely holographic, quantum systems identified via the Gauge/Gravity duality framework. Interestingly, the latter allows us to study the evolution of a black hole as the transformation of a qubit collection performed through a quantum circuit. In this work, we focus on the complexity of Einstein-Rosen bridges. More in detail, we start with a preliminary discussion about their computational properties, and then we aim to assess whether an Ising-like model could represent their holographic dual. In this regard, we recall that the Ising model captures essential aspects of complex phenomena such as phase transitions and, in general, is deeply related to information processing systems. To perform this assessment, which relies on a heuristic model, we attempt to describe the dynamics of information relating to an Einstein-Rosen bridge encoded in a holographic screen in terms of dynamics occurring in a spin lattice at low temperatures. We conclude by discussing our observations and related implications.Comment: 17 pages, 5 figure

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context

Holographic non-computers

We introduce the notion of holographic non-computer as a system which exhibits parametrically large delays in the growth of complexity, as calculated within the Complexity-Action proposal. Some known examples of this behavior include extremal black holes and near-extremal hyperbolic black holes. Generic black holes in higher-dimensional gravity also show non-computing features. Within the $1/d$ expansion of General Relativity, we show that large-$d$ scalings which capture the qualitative features of complexity, such as a linear growth regime and a plateau at exponentially long times, also exhibit an initial computational delay proportional to $d$. While consistent for large AdS black holes, the required `non-computing' scalings are incompatible with thermodynamic stability for Schwarzschild black holes, unless they are tightly caged.Comment: 23 pages, 7 figures. V3: References added. Figures updated. New discussion of small black holes in the canonical ensembl