Symmetries and conformal bridge in Schwarschild-(A)dS black hole mechanics

We show that the Schwarzschild-(A)dS black hole mechanics possesses a hidden symmetry under the three-dimensional Poincaré group. This symmetry shows up after having gauge-fixed the diffeomorphism invariance in the symmetry-reduced homogeneous Einstein-Λ model and stands as a physical symmetry of the system. It dictates the geometry both in the black hole interior and exterior regions, as well as beyond the cosmological horizon in the Schwarzschild-dS case. It follows that one can associate a set of non-trivial conserved charges to the Schwarzschild-(A)dS black hole which act in each causally disconnected regions. In T-region, they act on fields living on spacelike hypersurface of constant time, while in R-regions, they act on time-like hypersurface of constant radius. We find that while the expression of the charges depend explicitly on the location of the hypersurface, the charge algebra remains the same at any radius in R-regions (or time in T-regions). Finally, the analysis of the Casimirs of the charge algebra reveals a new solution-generating map. The $$ \mathfrak{sl}\left(2,\mathrm{\mathbb{R}}\right) $$ sl 2 ℝ Casimir is shown to generate a one-parameter family of deformation of the black hole geometry labelled by the cosmological constant. This gives rise to a new conformal bridge allowing one to continuously deform the Schwarzschild-AdS geometry to the Schwarzschild and the Schwarzschild-dS solutions.

Proper time reparametrization in cosmology: Möbius symmetry and Kodama charges

It has been noticed that for a large class of cosmological models, the gauge fixing of the time-reparametrization invariance does not completely fix the clock. Instead, the system enjoys a surprising residual Noether symmetry under a Möbius reparametrization of the proper time, which maps gauge-inequivalent solutions to the Friedmann equations onto each other. In this work, we provide a unified treatment of this hidden conformal symmetry and its realization in the homogeneous and isotropic sector of the Einstein-Scalar-Λ system. We consider the flat Friedmann-Robertson-Walker (FRW) model, the (A)dS cosmology and provide a first treatment of the model with spatial constant curvature. We derive the general condition relating the choice of proper time and the conformal weight of the scale factor, and give a detailed analysis of the conserved Noether charges generating this physical symmetry. Our approach allows us to identify new realizations of this symmetry while recovering previous results in a unified manner. We also present the general mapping onto the conformal particle and discuss the solution-generating nature of the transformations beyond the Möbius symmetry. Finally, we show that, at least in a restricted context, this hidden conformal symmetry is intimately related to the Kodama charges of spherically symmetric gravity. This new connection suggests that the Möbius invariance of cosmology is only the corner of a larger symmetry structure which could be relevant beyond cosmological models.

Local invertibility and sensitivity of atomic structure-feature mappings

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety of representations that can be used to convert them into a finite set of symmetric descriptors or features. Methods: Here, we analyze the sensitivity of the mapping to atomic displacements, using a singular value decomposition of the Jacobian of the transformation to quantify the sensitivity for different configurations, choice of representations and implementation details. Results: We show that the combination of symmetry and smoothness leads to mappings that have singular points at which the Jacobian has one or more null singular values (besides those corresponding to infinitesimal translations and rotations). This is in fact desirable, because it enforces physical symmetry constraints on the values predicted by regression models constructed using such representations. However, besides these symmetry-induced singularities, there are also spurious singular points, that we find to be linked to the incompleteness of the mapping, i.e. the fact that, for certain classes of representations, structurally distinct configurations are not guaranteed to be mapped onto different feature vectors. Additional singularities can be introduced by a too aggressive truncation of the infinite basis set that is used to discretize the representations. Conclusions: These results exemplify the subtle issues that arise when constructing symmetric representations of atomic structures, and provide conceptual and numerical tools to identify and investigate them in both benchmark and realistic applications.

Symmetries of the black hole interior and singularity regularization

We reveal an \mathfrak{iso}(2,1)𝔦𝔰𝔬(2,1) Poincar'e algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincar'e group ISO(2,1)(2,1), which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS{}_22. At the Lagrangian level, this symmetry corresponds to M"obius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger \textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)BMS3=Diff(S1)⋉Vect(S1) group, where S^1S1 is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincar'e symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.

Edge modes of gravity. Part I. Corner potentials and charges

This is the first paper in a series devoted to understanding the classical and quantum nature of edge modes and symmetries in gravitational systems. The goal of this analysis is to: i) achieve a clear understanding of how different formulations of gravity provide non-trivial representations of different sectors of the corner symmetry algebra, and ii) set the foundations of a new proposal for states of quantum geometry as representation states of this corner symmetry algebra. In this first paper we explain how different formulations of gravity, in both metric and tetrad variables, share the same bulk symplectic structure but differ at the corner, and in turn lead to inequivalent representations of the corner symmetry algebra. This provides an organizing criterion for formulations of gravity depending on how big the physical symmetry group that is non-trivially represented at the corner is. This principle can be used as a “treasure map” revealing new clues and routes in the quest for quantum gravity. Building up on these results, we perform a detailed analysis of the corner pre-symplectic potential and symmetries of Einstein-Cartan-Holst gravity in [1], use this to provide a new look at the simplicity constraints in [2], and tackle the quantization in [3].

MHMIC Six-port Interferometer for W-band Transceivers: Design and Characterization

The study has presented an extensive analysis of an integrated millimeter wave six-port interferometer, operating over a 10 GHz band, from 80 to 90 GHz. It has covered both semi-unlicensed point-to-point links (81-86 GHz), and imaging sensor system frequencies (above 85 GHz). An in-house process is used to fabricate miniaturized hybrid millimeter wave integrated circuits on a very thin ceramic substrate. Two-port S-parameter measurements are performed on a minimum number of circuits integrated on the same die, exploiting the circuit’s physical symmetry and chosen to collect enough data for full-port characterization. Based on these measurements on an integrated prototype, a six-port circuit computer model implemented and advanced system simulations performed for circuit analysis. Interferometer performances evaluated using several methods: analysis of harmonic balance, qi points’, homodyne quadrature demodulation, and error vector modulation (EVM). The analysis showed that this circuit can directly perform, without any calibration, the demodulation of various PSK and QAM signals over the 10 GHz band, with very good results.

The Factor of Visual Symmetry Perception in Aesthetic Experience

The article deals with the formation of aesthetic experience in connection with the perception of physical symmetry of objects and their images. An overview of modern works on the psychology of aesthetic perception in the context of the problem of the perception of symmetry is presented. The phenomenon of symmetry preference in visual perception is illustrated by arguments in its favor and data on its situationality. The ecological context of symmetry in animals and plants is touched in connection with the phenomenon of fluctuating asymmetry as an undirected deviation in the symmetry of a two-sided structure normally distributed in the population. Mathematical models of symmetry of forms and their multiscale representation are discussed. The analysis of the study of the Zen stone garden perceptual peculiarities from the position of the medial axes’ model is carried out.On the basis of the provisions of the transcendental psychology of perception, a hypothesis is advanced about the meta-sensory origin of the aesthetic sense, based on the process of interrelation of the internal symmetrical mechanisms of visual perception and the cognitive processes of creating figurative representations. The relation to the principle of symmetry in the context of the transcendental psychology of perception is shown.

PHYSICAL SYMMETRY AND VIRTUAL PLANE-BASED REDUCTION REFERENCE: A PRELIMINARY STUDY FOR ROBOT-ASSISTED PELVIC FRACTURE REDUCTION

Traditional pelvis fracture reduction suffers from some disadvantages. Robot-assisted pelvis fracture reduction offers some promise in solving these problems. However, the reduction reference to guide robot motion is a key issue that must be resolved. In this paper, we propose a physical symmetry and virtual plane-based reduction reference and adopt the method of registration to calculate the virtual plane for the reference, which were verified via experiments. The results of the position symmetry experiments of the original pelvis and virtual plane-based position symmetry experiments were similar; both showed that the symmetry errors of the pelvis were less than 4[Formula: see text]mm and 2.5[Formula: see text]. The results indicated that the proposed method could be used as a reference for robot-assisted pelvis fracture reduction.