Energy Conditions Research Articles

Conservative wormholes in generalized [formula omitted]- function

We present an exhaustive study of wormhole configurations in κ(R,T) gravity with linear and non-linear functions. The model assumed Morrison-Thorne spacetime where the redshift and shape functions linked with the matter contain and geometry of the spacetime through non-covariant conservation equation of the stress-energy tensor. The first solution was explored assuming a constant redshift function that leads to a wormhole (WH) which is asymptotically non-flat. The remaining solutions were explored in two cases. Firstly, assuming a linear equation of state p(r)=ωρ(r) along with different forms of κ(R,T)-function. This proved enough to derive a shape function of the form b(r)=r0(r0r)1/ω. Secondly, by assuming specific choices of the shape function consistent with the wormhole configuration requirements. All the solutions fulfill flare-out condition, asymptotically flat and supported by phantom energy. Further, the embedding surface and its revolution has been generated using numerical method to see how the length of the throat is affected of the coupling parameters through κ(R,T) function. At the end, we have also calculated the average null energy condition, which is satisfied by all the WH models signifying minimum exotic matter is required to open the WH throats.

Strong cosmic censorship in de Sitter spacetimes with dark matter

After imposing the weak energy condition on dark matter, we find that even in the absence of charge, a spherically symmetric de Sitter black hole with perfect fluid dark matter may still possess a Cauchy horizon. This paper investigates the stability of the Cauchy horizon in such a black hole under perturbations from a massless scalar field. Through numerical calculations of the massless scalar field's quasinormal modes, we discover that in this spacetime, when the black hole approaches extremality, i.e., when the dark-matter parameter b approaches its maximum value bmax, the Strong Cosmic Censorship (SCC) conjecture may be violated. This is the first instance of classical SCC violation observed in a spherically symmetric, uncharged black hole. Additionally, we explore the region of SCC violation within the parameter space ΛM2−b/bmax. Our findings indicate that as the cosmological constant increases, the violation region initially expands and then contracts.

Disentanglement as a strong cosmic censor

If entanglement builds spacetime, then conversely, disentanglement ought to destroy spacetime. From the quantum null energy condition and quantum focusing conjecture, we obtain disentanglement criteria which necessitate infinite energies and strong spacetime singularities. We apply our results to the strong cosmic censorship proposal, where singularities at the Cauchy horizons in black holes are desirable. Using our disentanglement criteria and without resorting to any detailed calculations, we provide an exceedingly general and physically transparent discussion of strong cosmic censorship in semiclassical black holes. We argue that strong cosmic censorship is enforced in asymptotically flat and de Sitter black holes by disentanglement and describe how similar disentanglement might be avoided in some anti-de Sitter cases.

Phantom Matter: A Challenging Solution to the Cosmological Tensions

The idea of composite dark energy (DE) is quite natural since on general grounds we expect that the vacuum energy density (associated with the cosmological term Λ) may appear in combination with other effective forms of DE, denoted X. Here we deal with model wXCDM, a simplified version of the old ΛXCDM model, and exploit the possibility that X behaves as “phantom matter” (PM), which appears in stringy versions of the running vacuum model (RVM). Unlike phantom DE, the PM fluid satisfies the strong energy condition like usual matter, hence bringing to bear positive pressure at the expense of negative energy. Bubbles of PM may appear in the manner of a transitory “phantom vacuum” tunneled into the late Universe before it heads toward a new de Sitter era, thereby offering a crop field for the growing of structures earlier than expected. Using Type Ia supernovae, cosmic chronometers, transversal baryon acoustic oscillations (BAO 2D), large-scale structure data, and the full cosmic microwave background likelihood from Planck 2018, we find that the H 0 and growth tensions virtually disappear, provided that BAO 2D are the only source of BAO data used in the fit. In contrast, our preliminary analysis using exclusively anisotropic BAO (BAO 3D) indicates that the ability to ease the H 0 tension is significantly reduced as compared to the scenario with BAO 2D, despite the fact that the overall fit to the cosmological data is still better than in the ΛCDM. Finally, our approach with BAO 2D favors quintessence-like behavior of the DE below z ≃ 1.5 at ≳3σ confidence level, which is compatible with the recent DESI measurements.

Phase space properties of cosmological models in f(Q, T) gravity

The Weyl type f(Q, T) gravity is the modification of f(Q) gravity and f(Q, T) theories, where non-metricity is denoted by Q and T is the trace of the energy–momentum tensor. Together with a geometric explanation for dark energy, the theory can provide an exact interpretation of the transformation of the late-time Universe and the observable data. In this study, we present an accelerated cosmic model of the Universe in f(Q, T) gravity. We consider the model of f(Q, T) gravity as, f(Q,T)=-Q+ϕ(Q,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(Q,T) = -Q+\\phi (Q,T)$$\\end{document}. We examine the energy condition for the model of f(Q, T) gravity and find out that our model satisfies the null and strong energy conditions at the same time, it violates the weak and dominant energy conditions. After that, we perform the phase-space study of our cosmological model with and without interaction independently. In case of the absence of interaction, we get six critical points out of which three critical points are stable critical points while the rest three critical points are saddle. When we perform the stability analysis in the presence of interaction, we get three critical points out of which one critical point is stable while the rest two are saddle points. The phase-plot analysis also shows the cosmological models in f(Q, T) gravity.

Study on the Performances of Toughening UV-LED-Cured Epoxy Electronic Encapsulants

This study aims to investigate the effects of three toughening agents—core–shell rubber particles (CSR), nano-silica particles (NSPs), and epoxidized polybutadiene (EPB)—on the performance of UV-LED-cured epoxy electronic encapsulants. By systematically comparing the curing behavior, thermomechanical properties, and impact resistance of different toughening agents in alicyclic epoxy resins, their potential applications in more environmentally friendly UV-cured electronic encapsulation are evaluated. The results show that NSP and CSR toughened samples have fast cured speed under 365 nm UV-LED light, but it affects the depth of curing under low energy conditions. They maintain high Tg, high modulus, and low thermal expansion coefficient (CTE), especially in the NSP-toughened sample. The EPB-toughened sample has good transparency for LED, but it has negative effects on Tg and CTE. This research provides essential theoretical and experimental data to support the development of high-performance UV-LED-cured epoxy encapsulation materials.

Traversable wormhole solutions utilizing the Karmarkar condition in f(R,G) gravity

The main objective of this paper is to reveal the evolving traversable wormhole solutions in the context of modified f(R,G) gravity, which affects the gravitational interaction. These results are derived by applying the Karmarkar condition, which creates wormhole geometry that meets the necessary conditions and connects two asymptotically flat areas of spacetime. The proposed study’s main goal is to construct the wormhole structures by splitting the f(R,G) gravity model into two forms Firstly, we split the model into an exponential-like f(R) gravity model and a power law f(G) gravity model, and secondly, we consider the Starobinsky f(R) gravity model along with a power law f(G) gravity model. Besides, we address the feasibility of shape functions and the structural analysis of wormhole structures for specific models. These models are then confined to be compatible with current experimental evidence. Further, the energy conditions of the wormhole are geometrically probed, and it is proven that they adhere to the null energy conditions in areas close to the throat. Moreover, the fascinating aspect of this study involves conducting an examination and comparison of evolving wormhole geometries in the vicinity of the throat in our chosen models, utilizing two- and three-dimensional graphical representations. We observe that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter, correlating to the proper choice of f(R,G) gravity models and acceptable free parameter values. In summary, we conclude that our findings meet all the criteria for the existence of wormholes, affirming the viability and consistency of our study.

Theoretical insights and implications of bouncing cosmology in f(R,T2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal {R},\ extrm{T}^2)$$\\end{document} theory

In this paper, we explore cosmological bouncing solutions to investigate the cosmic evolution in the framework of energy-momentum squared gravity. We consider flat Friedmann–Robertson–Walker spacetime with a perfect matter distribution. We assume two different functional forms of f(R,T2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal {R},T^2)$$\\end{document} gravity model to examine the impact of this modified framework in the evolution of the universe. Furthermore, we consider a specific scale factor to investigate different cosmological parameters, analyzing the evolutionary behavior of the universe in this gravity. We also perform stability analysis using the perturbation technique. Our findings indicate that the null energy condition violates at the bounce point and equation of state parameter exhibits characteristics of a quintessence era or phantom regimes. These aspects highlight the complex interplay between energy conditions and stability in bouncing cosmological model. We conclude that the f(R,T2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal {R},T^2)$$\\end{document} theory successfully provides viable alternatives to the standard cosmological scenarios, offering insights into the early universe and the nature of gravity.

Existence of traversable wormholes in the minimally coupled gravity model

The objective of this study is to examine the possible existence of traversable wormhole geometries within the context of [Formula: see text] gravity. To meet this objective, we employ the Karmarkar condition to construct the shape function that aids in identifying the wormhole configurations. This developed function is found to satisfy the essential conditions and provides a link between two asymptotically flat spacetime regions. We then assume the Morris–Thorne line element that expresses the wormhole configuration and formulate the anisotropic gravitational equations for a particular minimal matter-spacetime coupled model of the modified theory. Afterward, we develop three solutions and determine their viability by analyzing whether they violate the null energy conditions. Different stability methods are applied to the resulting geometries to explore the acceptance of the considered modified model. We conclude that the developed wormhole structures potentially fulfill the required criteria and thus exist in this modified gravity under all choices of the matter Lagrangian density.

NEC violation in [formula omitted] gravity in the context of a non-canonical theory via modified Raychaudhuri equation

In this work, we develop the Raychaudhuri equation in f(R̄,T̄) gravity in the setting of a non-canonical theory, namely K-essence theory. We solve the modified Raychaudhuri equation for the additive form of f(R̄,T̄), which is f1(R̄)+f2(T̄). For this solution, we employ two different scale factors to give two types of f(R̄,T̄) solutions. The ongoing debate between Fisher et al. and Harko et al. in 2020 regarding the additive form of f(R̄,T̄) may provide a resolution within the modified f(R̄,T̄) gravity theory. By conducting a viability test and analyzing energy conditions, we have determined that in the first scenario, the null energy condition (NEC) is violated between two regions where the NEC is satisfied. Additionally, we have observed that this violation of the NEC exhibits a symmetric property during the phase transition. These observations indicate that bouncing events may occur as a result of the symmetrical violation of the NEC during the expansion of the universe. Moreover, this model indicates that resonant-type quantum tunneling may take place during the period when the NEC is violated. The findings of NEC violation through the power law of scale factor may have empirical relevance in contemporary observations. In the second scenario, our model indicates that the strong energy condition is violated, but the NEC and weak energy conditions are satisfied. The effective energy density decreases and is positive, while the effective pressure and equation of state parameters are negative. This suggests that the universe is expanding with acceleration and is dominated by dark energy.

Viable Wormhole Structures and Energy Conditions in f(Q,T) Theory

Abstract This paper explores static wormhole solutions in
$f(\textmd{Q},\textmd{T})$ theory, where $\textmd{Q}$ is the
non-metricity and $\textmd{T}$ is the trace of energy-momentum
tensor. We derive the field equations that describe gravitational
phenomena in the existence of non-metricity and matter source terms.
We examine different models of this theory to determine the explicit
expressions of matter contents, which are useful for analyzing the
wormhole structures. We investigate the existence of feasible
traversable wormhole solutions for constant and variable redshift
functions. To determine whether physically viable wormhole geometry
exists, we examine the graphical interpretation of energy
constraints for different values of model parameters. It is found
that realistic traversable and stable wormhole solutions exist only
for the first model of this gravity.

Space–Time Forecasting of Heating & Cooling Energy Needs as an Energy Poverty Measure in Romania

Lack of access to basic energy services, known as energy poverty, remains felt in the country, with seasonal changes and an economic divide. The frameworks to measure energy poverty differ spatially and temporally, with climate change and behavioral culture being the essential influencing factors. This paper is focused on heating and cooling energy demands, which can be defined as an energy poverty metric for the propensity to be at risk of energy poverty caused by climate regime. Employing sophisticated statistical space–time forecasting tools, we build a model incorporating spatial and temporal energy consumption volatility across Romanian regions at the NUTS3 level. The model considers climatic conditions and raw data from 45 years (1979–2023) of cooling and heating degree days to determine local trajectories for the next nine years. Identifying high-energy-poverty-risk areas in our research can provide valuable insights for policymakers, enabling them to develop targeted plans for eliminating energy poverty and ensuring equitable access to heating and cooling. The results underline the necessity of differentiated approaches in energy policies and add value to the general understanding of energy poverty issues and conditions, considering the Romanian climatic and socio-economic context.

Self-gravitating matter in stationary and axisymmetric black hole spacetimes

Abstract All black holes (BHs) in nature are expected to be described by the Kerr vacuum solution of general relativity. However, the Kerr BH interior contains several problematic features such as a Cauchy horizon, a curvature singularity, and a causality-violating region. Non-Kerr BH models, which are used to examine the genericity of these features, typically contain nontrivial matter content. When such self-gravitating matter is minimally-coupled to Einstein–Hilbert gravity, the Einstein equations can be directly used to investigate its physical properties. We examine here the properties of matter in a broad class of stationary and axisymmetric, geodesically-integrable BH spacetimes, and how they are linked to various features of the spacetime geometry. In these spacetimes, we find the matter to typically flow along timelike Killing orbits in the BH exterior, usually exhibiting differential rotation but sometimes additionally also non-rigid rotation. At a horizon, the matter rest-frame energy density, ε, and principal normal pressure, pn , are shown to necessarily satisfy p n = − ϵ , implying that only specific types of matter can thread stationary event horizons (e.g. electromagnetic fields but not massless real scalar fields). Furthermore, we introduce Boyer–Lindquist-like coordinates for the nonstationary regions in the BH interior, which show the matter to be comoving with the interior cosmology. We also obtain simple expressions for the expansions of the ingoing and outgoing zero angular momentum null congruences and comment on the light-focussing behavior of the cosmology. Finally, we verify above results explicitly by working with a representative set of well-known BH spacetimes which contain various types of matter—scalar fields, electromagnetic fields, anisotropic fluids. Some spacetimes have singularities while others have regular interiors. In the exterior, the matter satisfies the weak energy condition. The framework developed here can be extended to cover more general spacetimes.

A five-dimensional vacuum-defect wormhole space-time

In this study, we present a novel extension to the Klinkhamer vacuum-defect model by incorporating a fifth spatial dimension. This modification results in the formulation of a comprehensive five-dimensional wormhole space-time. Crucially, this extension preserves its classification as a vacuum solution to the field equations, thereby automatically satisfying all energy conditions. We demonstrate that this five-dimensional vacuum-defect space-time can be expressed in a pure canonical form, and thus, locally reduces to five-dimensional Minkowski space. Finally, we explore the geodesic equations in the vicinity of this five-dimensional vacuum-defect wormhole, offering insights into its intriguing properties.

The Green Economy in the Energy Transformation Process—Comparative Analysis of the European Union Member States

The article mainly examines spatial diversification of the green economy in EU countries in 2014 and 2021 in the context of the energy transformation process. In the theoretical part of the work, the green economy concept, with reference to the conditions of the green energy, was analyzed. The research procedure used in the article is based on multidimensional comparative analysis. The empirical verification was conducted using green economy indicators that are published periodically by the OECD and Eurostat. Based on 21 indicators, a synthetic green economy index was designed for 27 EU member states. In the selected set of detailed indicators, those related to green energy economy played an important role. This approach allowed for the creation of rankings and comparisons between EU countries in 2014 and 2021, i.e., the implementation period of the Europe 2020 Strategy. In this period, the priority areas of EU development were: the low-carbon economy, including the use of renewable energy sources and improvement of energy efficiency, as well as the introduction of eco-innovation. Green energy should be the basis for the functioning of highly developed countries and socio-economic progress in the case of developing countries. Based on the analysis, a large discrepancy in terms of green economy was observed in the examined countries. Particular attention was paid to disproportions in the area of green energy. The average value of the synthetic measure of the green economy in the EU countries increased in the studied years from 0.4488 to 0.4529, which can be interpreted as a slight acceleration in the greening processes. The added value of the research presented in the paper and its novelty is the analysis of the current patterns of green transformation in EU member states, with particular emphasis on energy factors.

Matter bounce cosmology within Finsler-Randers geometry: A comprehensive study of anisotropic influences

In this study, we explore the dynamics of matter bounce cosmology within the framework of Finsler-Randers geometry, focusing on the role of the Finslerian correction term η(t). By integrating Finsler geometry into cosmological models, we introduce anisotropic effects that significantly impact the evolution of the universe, particularly during the bounce phase. The research examines various cosmological parameters, including the deceleration (qη(t)), jerk (jη(t)), and snap (sη(t)) parameters, highlighting the influence of the Finsler correction on these key indicators. Our results demonstrate that the Finslerian framework leads to more complex and abrupt transitions in the universe's expansion dynamics compared to traditional Riemannian models. The study also reveals that the Finslerian correction intensifies the violations of energy conditions, such as the null energy condition (NEC), which are crucial for the occurrence of a successful bounce. Furthermore, the analysis of the squared sound speed vs2 indicates that the model's stability is highly sensitive to the choice of the Finslerian parameters, with certain configurations leading to instability during the bounce. Our findings underscore the unique contributions of Finsler geometry to cosmological models, offering deeper insights into the behavior of the universe under anisotropic influences and providing a potential avenue for addressing longstanding challenges in cosmology.

Study of cosmic evolution admitting thermodynamic analysis

This article examines the cosmic evolution in the framework of symmetric teleparallel theory, characterized by the function of non-metricity scalar (Q)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mathcal {Q})$$\\end{document}. We use the e-folding number and reconstruction method with a suitable parametrization of the scale factor to obtain the functional form of symmetric teleparallel theory. Using this reconstructed model, we examine the behavior of different cosmographic parameters to demonstrate the bouncing scenarios of the cosmos by considering the contraction and expansion phases of cosmos before and after the bouncing point, respectively. It is found that the null energy condition is violated which shows that the singularity issue can be resolved in this extended theoretical framework. Moreover, we observe that the acceleration occurs near the bouncing point and the reconstructed model aligns with the current cosmic expansion. Finally, we check the validity of second law of thermodynamics in the bouncing framework of our model.

A new class of traversable wormhole metrics

In this work, we have formulated a new class of traversable wormhole metrics. Initially, we have considered a wormhole metric in which the temporal component is an exponential function of r but the spatial components of the metrics are fixed. Following that, we have again constructed a generalized wormhole metric in which the spatial component is an exponential function of r, but the temporal component is fixed. Finally, we have considered the generalized wormhole metric in which both the temporal and spatial components are generalized exponential functions of r. We have also studied some of their properties including throat radius, stability, and energy conditions, examined singularity, the metric in curvature coordinates, effective refractive index, innermost stable circular orbit (ISCO) and photon sphere, Regge–Wheeler potential and their quasinormal modes, gravitational entropy, and determined the curvature tensor. The radius of the throat is found to be consistent with the properties of wormholes and does not contain any types of singularities. Most interestingly, we find that their throat radius is the same for the same spatial component and the same range of values of m. In addition to these, they also violate the Null Energy Condition (NEC) near the throat. These newly constructed metrics form a new class of traversable wormholes.

Quark Stars in $f(R,T)$ Gravity: Mass-to-Radius Profiles and Observational Data

Abstract In this paper, we explore the $f(R,T)$ gravity theory, which introduces a coupling between matter and curvature, through the simplest linear functional form $f(R,T)= R + 2\beta T$. We derive the modified Einstein field equations and conservation equations for this theory. We then apply this framework to study the structural properties of quark stars (QSs) composed of interacting quark matter, considering perturbative QCD corrections and color superconductivity. By solving the modified Tolman-Oppenheimer-Volkoff equations, we investigate the mass-radius relation, stability criteria, and energy conditions of QSs. Our results indicate that the $f(R,T)$ gravity significantly influences the properties of QSs, leading to deviations from General Relativity. The analysis shows consistency with recent observational data, suggesting that the modified gravity framework could provide viable models for the study of compact stars.

Modified F(R,T2)-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

In the present research note, we discuss the energy–momentum squared gravity model F(R,T2) coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the F(R,T2)-gravity model. Furthermore, we deal with the energy–momentum squared gravity model F(R,T2) coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to F(R,T2)-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential Un with hyperbolic Ricci solitons in the F(R,T2)-gravity model coupled with perfect fluid and a phantom barrier.