Conformal Factor Research Articles

Holographic thermodynamics of BTZ black holes and Tsallis entropy

This paper presents a detailed study of the thermodynamics of charged BTZ black holes using the conformal holographic extended thermodynamics formalism and Tsallis statistics. The cornerstone of our thermodynamic framework is the re-scaling of CFT by the conformal factor, which is considered a thermodynamic parameter. Here, the AdS radius is distinct from the CFT radius, allowing for independent variations of the central charge and volume. Our analysis revealed that the thermodynamic behavior of charged BTZ black holes in three dimensions is characterized by the stability and absence of phase transitions, contrasting with the behavior of four-dimensional black holes. The central charge of CFT notably influences the thermal evolution of these black holes, with a smaller central charge leading to faster thermal processes. Additionally, the temperature of large black holes is proportional to their entropy. By incorporating Tsallis statistics into our study, we found that the stability of black holes depends on the Tsallis parameter. Black holes are always stable when the Tsallis parameter is less than 2. However, if this parameter is greater than 2, a first-order phase transition occurs between small stable and large unstable. Overall, our findings contribute to a deeper understanding of the holographic thermodynamics of lower-dimensional black holes and the impact of non-extensive statistics on their physical properties.

The effective potential for conformal factor and GL(4) symmetry

We revisit the issue of whether the effective potential for the conformal factor of the metric, which is generated by quantized matter fields, possesses a non-vanishing vacuum expectation value (VEV) or not. We prove that the effective potential has a vanishing vacuum expectation value on the basis of a global GL(4) symmetry. We also account for why there seems to be two different effective potentials for the conformal factor in a theory, one of which gives rise to a vanishing VEV for the conformal factor, whereas the other has a non-vanishing VEV.

K-mouflage at high k: extending the reach of Hi-COLA

The Hi-COLA (https://github.com/Hi-COLACode/Hi-COLA) code is an efficient dark matter simulation suite that flexibly handles the Horndeski family of modified gravity models. In this work we extend the scope of Hi-COLA to accommodate Horndeski theories with K-mouflage screening, allowing for the computation of matter power spectra in the non-linear regime in these models. We explore the boost of the dark matter power spectrum relative to GR-ΛCDM in K-mouflage gravity, and also discuss how large-scale structure computations change between the Einstein and Jordan frames. A dissection of the relative contributions of the modified background, linear growth, fifth force, and the conformal factor (a new inclusion to Hi-COLA) to the boost factor is presented. The ability of Hi-COLA to run with general Horndeski models and multiple screening mechanisms makes it an ideal tool for testing gravity with upcoming galaxy survey data.

Systematic Investigation on Acid-Catalyzed Truncation of N-Acylated Peptoids.

Peptoids have emerged as a useful alternative to peptides. However, N-acylated peptoids have occasionally undergone truncation at the terminal peptoid unit under acidic conditions. We previously reported on the mechanistic and electronic aspects of the acid-catalyzed truncation of N-acylated peptoids. To gain further insight, we systematically investigated the conformational and electronic effects of the terminal side chains of peptoids. The n→π* interaction, based on cis/trans-amide bond conformation, is considered to be one of the determining factors. In this study, it was demonstrated that both conformational and electronic factors contribute to this unusual truncation.

Probing the effect of time conformal factor on the particle dynamics around AdS Reissner–Nordström black hole

This study entails the effect of time on particle dynamics (both charged and uncharged) in the surrounding of the Reissner–Nordström AdS black hole in light of a general time conformal factor by acquiring Noether symmetry relation using the Lagrangian of the considered black hole spacetime. Upon acquiring the required time conformal spacetime as well as the Noether and approximated Noether symmetries along with their respective laws of conservation, the study further aims at investigating different parameters, like effective potential, effective force, and trajectories of escape velocity for the particle dynamics of the specified black hole. Additionally, in order to investigate orbit stability, the study employs the Lyapunov exponent.

Validation of factor structures of the Drinking Motives Questionnaire among the Czech young and adult general population

BackgroundAlcohol use is one of the leading public health concerns in the Czech Republic. Drinking motives play a vital role in both initiation and subsequent alcohol use. A revised version of the self-report Drinking Motives Questionnaire (DMQ-R) has been proposed to assess these motives. The present study aims to validate the DMQ-R in the Czech general population.MethodsA total sample of 1,784 Czech participants completed a national survey. For the analysis, only a sub-sample of the past 12 months alcohol users was used: N = 1,123; 52.8% male; mean (SD) age = 40.2 (13.3). Drinking motives were assessed by the adopted Czech version of the DMQ-R. Both confirmatory (CFA) and exploratory factor analysis (EFA) were conducted to examine the factorial structure of the instrument. The age of the participant was additionally considered in the analysis (15–24 years as opposed to 25–64 years).ResultsThe CFA supported the four-factor model in the 25–64 age group. The analysis supported the construct validity of the Social, Conformity, and Coping factors. The Enhancement factor retained only two items and was found to refer more to a domain of ‘Pleasant Feeling’. For the 15–24 age group, the hypothesised four-factor structure was not corroborated.ConclusionsThe Czech version of the DMQ-R was found to be a reliable measurement tool of the Social, Conformity, and Coping motives. Future research should investigate the dimensionality of the instrument items presumed to correspond to the Enhancement motives. This should be conducted particularly among adolescents and young adults aged 15–24 years, where administering the DMQ-R with a large enough sample is also needed.

The Correlation of Peer Conformity and Type of Smoking Behavior among Adolescents at a State Junior High School SMPN 3 Hamparan Perak Deli Serdang Regency

The issue of peer conformity on smoking behavior significantly affect in individuals’ self-preservation to get acceptance and avoid rejection or critism from peers. These conformity factors cause individuals to engage in deviant behaviors, such as smoking. This research method aims to explore the correlation of peer conformity and the type of smoking behavior among adolescents at SMPN 3 Hamparan Perak, Deli Serdang Regency. This is a quantitative Research method with a descriptive correlational design conducted on 30 male adolescents ages 13 - 16 years old from May to June 2024. The data are collected by distributing questionnaires on peer conformity and the type of smoking behavior. The results of the statistical test using chi-square test with α=0.05 indicate a significant correlation between peer conformity and the type of smoking behavior among male adolescents at SMPN 3 Hamparan Perak (p-value = 0,034). Based on this research, it is recommended that the school conduct routine conseling sessions and promote anti-smoking campaigns to reduce the number of smoker among adolescents.

Ultraviolet finite resummation of perturbative quantum gravity

Abstract If the metric is chosen to depend exponentially on the conformal factor, and if one works in a gauge where the conformal factor has the wrong sign propagator, perturbative quantum gravity corrections can be partially resummed into a series of terms each of which is ultraviolet finite. These new terms however are not perturbative in some small parameter, and are not individually BRST invariant, or background diffeomorphism invariant. With appropriate parametrisation, the finiteness property holds true also for a full phenomenologically relevant theory of quantum gravity coupled to (beyond the standard model) matter fields, provided massive tadpole corrections are set to zero by a trivial renormalisation.

Hodge Decomposition of Conformal Vector Fields on a Riemannian Manifold and Its Applications

For a compact Riemannian m-manifold (Mm,g),m>1, endowed with a nontrivial conformal vector field ζ with a conformal factor σ, there is an associated skew-symmetric tensor φ called the associated tensor, and also, ζ admits the Hodge decomposition ζ=ζ¯+∇ρ, where ζ¯ satisfies divζ¯=0, which is called the Hodge vector, and ρ is the Hodge potential of ζ. The main purpose of this article is to initiate a study on the impact of the Hodge vector and its potential on Mm. The first result of this article states that a compact Riemannian m-manifold Mm is an m-sphere Sm(c) if and only if (1) for a nonzero constant c, the function −σ/c is a solution of the Poisson equation Δρ=mσ, and (2) the Ricci curvature satisfies Ricζ¯,ζ¯≥φ2. The second result states that if Mm has constant scalar curvature τ=m(m−1)c>0, then it is an Sm(c) if and only if the Ricci curvature satisfies Ricζ¯,ζ¯≥φ2 and the Hodge potential ρ satisfies a certain static perfect fluid equation. The third result provides another new characterization of Sm(c) using the affinity tensor of the Hodge vector ζ¯ of a conformal vector field ζ on a compact Riemannian manifold Mm with positive Ricci curvature. The last result states that a complete, connected Riemannian manifold Mm, m>2, is a Euclidean m-space if and only if it admits a nontrivial conformal vector field ζ whose affinity tensor vanishes identically and ζ annihilates its associated tensor φ.

An inverse problem for the minimal surface equation in the presence of a riemannian metric

In this work we study an inverse problem for the minimal surface equation on a Riemannian manifold (Rn,g) where the metric is of the form g(x)=c(x)(g^⊕e) . Here g^ is a simple Riemannian metric on Rn−1 , e is the Euclidean metric on R and c a smooth positive function. We show that if the associated Dirichlet-to-Neumann maps corresponding to metrics g and c~g agree, then the Taylor series of the conformal factor c~ at xn=0 is equal to a positive constant. We also show a partial data result when n = 3.

Anisotropic conformal change of conic pseudo-Finsler surfaces, I*

Abstract The present work is devoted to investigate anisotropic conformal transformation of conic pseudo-Finsler surfaces $(M,F)$, that is, $ F(x,y)\longmapsto \overline{F}(x,y)=e^{\phi(x,y)}F(x,y)$, where the function $\phi(x,y)$ depends on both position $x$ and direction $y$, contrary to the ordinary (isotropic) conformal transformation which depends on position only. If $F$ is a pseudo-Finsler metric, the above transformation does not yield necessarily a pseudo-Finsler metric. Consequently, we find out necessary and sufficient condition for a (conic) pseudo-Finsler surface $(M,F)$ to be transformed to a (conic) pseudo-Finsler surface $(M,\overline{F})$ under the transformation $\overline{F}=e^{\phi(x,y)}F$. In general dimension, it is extremely difficult to find the anisotropic conformal change of the inverse metric tensor in a tensorial form. However, by using the modified Berwald frame on a Finsler surface, we obtain the change of the components of the inverse metric tensor in a tensorial form. This progress enables us to study the transformation of the Finslerian geometric objects and the geometric properties associated with the transformed Finsler function $\overline{F}$. In contrast to isotropic conformal transformation, we have a non-homothetic conformal factor $\phi(x,y)$ that preserves the geodesic spray. Also, we find out some invariant geometric objects under the anisotropic conformal change. Furthermore, we investigate a sufficient condition for $\overline{F}$ to be dually flat or/and projectively flat. Finally, we study some special cases of the conformal factor $\phi(x,y)$. Various examples are provided whenever the situation needs.

Substructures of the Weyl group and their physical applications

We study substructures of the Weyl group of conformal transformations of the metric of (pseudo)Riemannian manifolds. These substructures are identified by differential constraints on the conformal factors of the transformations which are chosen such that their composition is associative. Mathematically, apart from rare exceptions, they are partial associative groupoids, not groups, so they do not have an algebra of infinitesimal transformations, but this limitation can be partially circumvented using some of their properties cleverly. We classify and discuss the substructures with two-derivatives differential constraints, the most famous of which being known as the harmonic or restricted Weyl group in the physics literature, but we also show the existence of a lightcone constraint which realizes a proper subgroup of the Weyl group. We then show the physical implications that come from invariance under the two most important substructures, concentrating on classical properties of the energy-momentum tensor and a generalization of the quantum trace anomaly. We also elaborate further on the harmonic substructure, which can be interpreted as partial gauge fixing of full Weyl invariance using BRST methods. Finally, we discuss how to construct differential constraints of arbitrary higher-derivative order and present, as examples, generalizations involving scalar constraints with four and six derivatives.

The study of perturbation in magnetized Schwarzschild anti-de Sitter spacetime and dark energy profile

AbstractWe are going to investigate the geodesic motion of charged particles in the vicinity of Schwarzschild anti-de-Sitter (S-AdS) spacetime with topological defects that admit temporal perturbation. We used the approximate Noether symmetry equation to insert the time conformal factor in the black hole without losing its symmetry structure. This type of insertion is necessary because the black hole radiates its energy and momentum in the form of gravitational waves and Hawking radiation. Along with the temporal perturbation, the S-AdS black hole (BH) is immersed in an external magnetic field. We conduct an in-depth examination of the dynamics of charged particles near a weakly magnetized and time conformal S-AdS BH. Our analysis involves calculating the shift in the position of the innermost circular orbit (ISCO) caused by both temporal perturbation and the presence of a magnetic field. Furthermore, we explore the influence of dark energy (DE) and angular momentum on the stability of these orbits. Additionally, we determine the effective force and escape velocity for a charged particle orbiting around the perturbed magnetized S-AdS BH. The application of time-dependent perturbation theory can extend our understanding to investigate the quasinormal modes (QNMs) of BH mergers.

Exploring Conformal Soliton Structures in Tangent Bundles with Ricci-Quarter Symmetric Metric Connections

In this study, we investigate the tangent bundle TM of an n-dimensional (pseudo-)Riemannian manifold M equipped with a Ricci-quarter symmetric metric connection ∇˜. Our primary goal is to establish the necessary and sufficient conditions for TM to exhibit characteristics of various solitons, specifically conformal Yamabe solitons, gradient conformal Yamabe solitons, conformal Ricci solitons, and gradient conformal Ricci solitons. We determine that for TM to be a conformal Yamabe soliton, the potential vector field must satisfy certain conditions when lifted vertically, horizontally, or completely from M to TM, alongside specific constraints on the conformal factor λ and the geometric properties of M. For gradient conformal Yamabe solitons, the conditions involve λ and the Hessian of the potential function. Similarly, for TM to be a conformal Ricci soliton, we identify conditions involving the lift of the potential vector field, the value of λ, and the curvature properties of M. For gradient conformal Ricci solitons, the criteria include the Hessian of the potential function and the Ricci curvature of M. These results enhance the understanding of the geometric properties of tangent bundles under Ricci-quarter symmetric metric connections and provide insights into their transition into various soliton states, contributing significantly to the field of differential geometry.

Conformal wormholes in f(R,Lm) theory

In this study, we present a new static and conformally symmetric wormhole solution. We develop new wormhole model in f(R,Lm) gravity. Shape function of conformally symmetric f(R,Lm) wormholes, provided by homothetic vector field is obtained regarding to conformal factor. It is investigated whether the function provides a stable throat infrastructure that does not allow collapsing. Anisotropic fluid matter filled the obtained conformally symmetric traversable wormholes is discussed by examining the dynamical properties of the fluid. Constructed new wormhole model violates all energy conditions. Physical significance of the sources filled constructed wormholes is discussed using volume quantifier. It is revealed that f(R,Lm) theory allows traversable and conformally symmetric wormholes if supported by phantom field.

Alzheimer's disease diagnosis by applying Shannon entropy to Ricci flow-based surface indexing and extreme gradient boosting

Geometric surface models are extensively utilized in brain imaging to analyze and compare three-dimensional anatomical shapes. Due to the intricate nature of the brain surface, rather than examining the entire cortical surface, we are introducing a new set of signatures focused on characteristics of the hippocampal region, which is linked to aspects of Alzheimer's disease. Our approach focuses on Ricci flow as a conformal parameterization method, permitting us to calculate the conformal factor and mean curvature as conformal surface representations to identify distinct regions within a three-dimensional mesh. For the first time for such settings, we propose a simple while elegant formulation by employing the well-established concept of Shannon entropy on these well-known features. This compact while rich feature formulation turns out to lead to an efficient local surface encoding. We are validating its effectiveness through a series of preliminary experiments on 3D MRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), with the aim of diagnosing Alzheimer's disease. The feature vectors generated and inputted into the XGBoost classifier demonstrate a remarkable level of accuracy, further emphasizing their potential as a valuable additional measure for surface-based cortical morphometry in Alzheimer's disease research.

Influence of transformational and transactional leadership on agile project success

This study investigates the influence of Transformational and Transactional Leadership contribution in project accomplishment. It specifically evaluates the mediating role of Leadership for Agile project methodology. The data was collected from cross-sectional professionals such as Information Technology project Managers of various fields, Civil and Construction, Pharmaceuticals, Telecommunication, Higher Educational Institutions (HEIs) in Oman that comprised 384 valid samples. We used conformity factor analysis for reliability and validity of our measurement and it was valid and reliable. Partial Least-Squares Structural Equation Modelling (PLS-SEM) was used to analyze the theoretical framework. The results confirmed leadership enhances agile project methodology through the project excellence, improves end user satisfaction, value addition by achieving triple constraints. It was observed that leadership improves project performance in which team building, management commitment, unobstructed vision, daily standup meeting eases the influence of leadership on Agile methodologies.

Assessing the Suitability of Fifth Grade Textbooks on 'Ecosystems and Our Environment' in Lebong Elementary Schools

This descriptive-quantitative study examines the eligibility of Grade 5 student textbooks on the theme of ecosystems and the environment at Lebong Regency Elementary School, using survey and observation to collect data and analyze it quantitatively. Lebong District's 93 elementary schools, including 180 fifth-grade teachers, are sampled using regional sampling, a random selection technique taken per sub-district. The study's main data is gathered through a questionnaire and secondary data from sources like textbooks for class IV students on the theme of "Ekosistem dan Lingkungan Sahabat Kita". The results of the research show that the conformity factor of material description with KI and KD is considered quite appropriate with an average percentage of 56.76%. Then, in terms of accuracy, the material was assessed as meeting the requirements with a percentage of 62.92%. Then, in terms of learning support materials, it was also assessed as meeting the requirements with a percentage figure of 64.3%. Finally, Factors for suitability of material descriptions with KI and KD, material accuracy factors, and learning support material factors were also declared to meet the requirements after obtaining a percentage figure of 62.47%. The results of the research concluded that the feasibility of a textbook for fifth-grade students on the theme of ecosystems and the environment of Our Friends at Lebong Regency Elementary School was eligible because it met several criteria such as the suitability of the material with Core Competencies (KI) and Basic Competencies (KD), material accuracy, learning support material, suitability of material descriptions with KI and KD, material accuracy factors and learning support material factors. The study reveals positive aspects of Lebong Regency Elementary School's Grade 5 student textbooks on ecosystems, including conformity with Core Competencies, accuracy, and learning support. However, improvements include aligning with curriculum guidelines, improving content clarity, optimizing learning support materials, and continuous evaluation for better educational impact.

Uniqueness of Ricci flows from non‐atomic Radon measures on Riemann surfaces

AbstractIn previous work (Topping and Yin, https://arxiv.org/abs/2107.14686), we established the existence of a Ricci flow starting with a Riemann surface coupled with a non‐atomic Radon measure as a conformal factor. In this paper, we prove uniqueness, settling Conjecture 1.3 of Topping and Yin (https://arxiv.org/abs/2107.14686). Combining these two works yields a canonical smoothing of such rough surfaces that also regularises their geometry at infinity.

On the generalization of the Kruskal–Szekeres coordinates: a global conformal charting of the Reissner–Nordström spacetime

The Kruskal–Szekeres coordinate construction for the Schwarzschild spacetime could be interpreted simply as a squeezing of the t-line into a single point, at the event horizon r=2M . Starting from this perspective, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner–Nordström manifold, MRN . We develop a new method to construct Kruskal-like coordinates through casting the metric in new null coordinates, and find two algebraically distinct ways to chart MRN , referred to as classes: type-I and type-II within this work. We pedagogically illustrate our method by crafting two compact, conformal, and global coordinate systems labeled GKI and GKII as an example for each class respectively, and plot the corresponding Penrose diagrams. In both coordinates, the metric differentiability can be promoted to C∞ in a straightforward way. Finally, the conformal metric factor can be written explicitly in terms of the t and r functions for both types of charts. We also argued that the chart recently reported in Soltani (2023 arXiv:2307.11026) could be viewed as another example for the type-II classification, similar to GKII .