Fluid Distribution Research Articles

Study of Isotropic Stellar Models via Durgapal-Lake Solutions in Rastall System

Abstract This manuscript is dealt with the influences of Rastall factor on the physical aspects of isotropic celestial models. In this scenario, both the ideal fluid distribution and static spherically symmetry are taken into consideration. In specifically, the Durgapal-Lake solutions are taken into consideration to analyze the different characteristics of several specific compact star models like Her X-1, Vela X-1, LMC X-4 and RXJ 1856-37. Due to its innovative combination of two methodologies, this solution is a significant advancement on Durgapal-Fuloria and Lake's previous ansatz in enormous crucial eras. Using observed estimates of radii and masses of certain specific star objects, the undefined parameters in Durgapal-Lake ansatz are derived by matching conditions. The consistency of the adopted solutions is examined through the visual interpretation of matter constituents, equation of state factor, energy conditions, mass function and stability criteria corresponding to distinct choices of Rastall factor. The radially symmetric graphs of matter variables as well as the mass function are also displayed. Moreover, We present the graphical analysis for vanishing Rastall factor. It is concluded that in the context of Rastall theory, the stars under examination exhibit stable compositions with Durgapal-Lake solution, while in the context of general relativity, they exhibit instability.

Injected phase change seismic source construction and monitoring experiment

Scientific assessment of the transport channels and distribution of oil, gas, water, and other fluids is the key to enhancing oil and gas production capacity and ensuring the safe and efficient development of mineral resources. Traditional microseismic monitoring has been suffering from limitations such as ambiguous attribute characteristics of the seismic source and low signal-to-noise ratios of the data, leading to poor location accuracy and large uncertainties. We develop a phase change seismic source monitoring method that allows for a detailed characterization of the spatial distribution of subsurface fluid transport by accurately locating the equivalent seismic source within supportive fractures. A phase change seismic source is developed and constructed based on the phase change material, enabling control over phase change temperature, source energy, and source scale through the principle of phase change energy storage. The source introduces an active approach to seismic signal generation, diverging from the conventional passive method reliant on rock rupture. Then, 3D homogeneous models are constructed for ground monitoring and in-well monitoring using impulse source propagation theory. The numerical simulation of the wavefield uses the finite-difference method, and the equivalence of discrete sources is confirmed using the Pearson correlation function. The reliability of the monitoring method is verified through a seismic monitoring experiment and comprehensive feasibility analysis.

Bioinspired Moisture‐Driven Soft Robotic Actuator

Multifunctional materials in nature, utilizing atmospheric water content, offer solutions to challenges in soft‐actuating materials research. The leaf of Arundo donax, an invasive plant, showcases exceptional properties: structural integrity, passive actuation, tunability, load‐bearing capacity, longevity, and an integrated battery‐free fluid generation and distribution mechanism. These functions coexist within a thin (≈130 μm) and lightweight structure with simple compositions. The study investigates material composition, passive fluid transport, water harvesting structures, and mechanical properties, revealing unexpected correlations between surface and internal structures. Additionally, tunable actuation, suitable for origami‐based mechanisms, is explored. Testing an energy‐free, moisture‐triggered soft robotic gripper, its ability to lift over 50 times its weight while maintaining sufficient softness for delicate tasks is demonstrated. This unit‐wise structure‐based actuation offers promise for soft robotics, with favorable fabrication possibilities and motion manipulation.

Manifold geometry optimization and flow distribution analysis in commercial-scale proton exchange membrane fuel cell stacks

The manifold structure in high-power Proton Exchange Membrane Fuel Cell (PEMFC) stacks critically influences airflow distribution, thereby affecting stack performance, temperature uniformity, and longevity. Therefore, this paper explores how manifold geometry affects fluid distribution within the manifold of a fuel cell stack. In addition, a new step-shaped manifold structure is established to improve the manifold flow field structure and enhance the uniformity of gas flow distribution in each single cell. In our study, each cell within the stack is modeled as a porous medium. We examine how varying the height at different positions within the manifold impacts the uniformity of gas flow distribution, focusing on different length ratios and heights. Our results demonstrate that adjusting the manifold shape improves airflow uniformity, with length ratios having a more pronounced impact than height variations. Specifically, the mass flow coefficient of variation decreased by 22.62 % and 23.07 % for cases 9 and 12, respectively. Similarly, the velocity inhomogeneity coefficient in the inlet manifold decreased by 21.22 % and 21.34 % for cases 9 and 12, respectively. Additionally, pressure distribution in case 9 showed greater uniformity. Our findings indicate that a manifold shape with a length ratio of 2/3 and a height of 2.5 mm delivers optimal performance.

Evolution of Self-Gravitating Fluid Spheres Involving Ghost Stars

Exact solutions are presented which describe, either the evolution of fluid distributions corresponding to a ghost star (vanishing total mass), or describing the evolution of fluid distributions which attain the ghost star status at some point of their lives. The first two solutions correspond to the former case, they admit a conformal Killing vector (CKV) and describe the adiabatic evolution of a ghost star. Other two solutions corresponding to the latter case are found, which describe evolving fluid spheres absorbing energy from the outside, leading to a vanishing total mass at some point of their evolution. In this case the fluid is assumed to be expansion–free. In all four solutions the condition of vanishing complexity factor was imposed. The physical implications of the results, are discussed.

Effect of different injection strategies considering intravenous injection on combination therapy of magnetic hyperthermia and thermosensitive liposomes

Abstract The combination therapy of magnetic hyperthermia and thermosensitive liposomes (TSL) is an emerging and effective cancer treatment method. The heat generation of magnetic nanoparticles (MNPs) due to an external alternating magnetic field can not only directly damage tumor cells, but also serves as a triggering factor for the release of doxorubicin from TSL. The aim of this study is to investigate the effects in the degree of tumor cell damage of two proposed injection strategies that consider intravenous administration. Since both MNPs and TSL enter the tumor region intravenously, this study establishes a biological geometric model based on an experiment-based vascular distribution. Furthermore, this study derives the flow velocity of interstitial fluid after coupling the pressure distribution inside blood vessels and the pressure distribution of interstitial fluid, which then provides the convective velocity for the calculation of subsequent nanoparticle concentration. Different injection strategies for the proposed approach are evaluated by drug delivery result, temperature distribution, and tumor cell damage. Simulation results demonstrate that the proposed delayed injection strategy after optimization can not only result in a wider distribution for MNPs and TSL due to the sufficient diffusion time, but also improves the distribution of the temperature and drug concentration fields for the overall efficacy of combination therapy.

A coupled displacement-pressure model for elastic waves induce fluid flow in mature sandstone reservoirs

Elastic (seismic) wave stimulation is considered one of the unconventional enhanced oil recovery (EOR) methods. Increasing water quantity in the high permeability layer of a mature oil reservoir is highly challenging and can significantly decrease the ultimate recovery due to the reservoir heterogeneity. Using seismic waves can be considered low-cost, environmentally friendly, and illuminates the entire reservoir size compared to conventional EOR methods. A numerical model is developed by extending the Quintal approach for seismic attenuation due to wave-induced fluid flow (WIFF) to incorporate capillary pressure in partially saturated porous media and shift undrained boundary conditions to exclude external flow stress for drained boundary conditions. Therefore, the fluid distribution due to the capillary effect makes the developed finite element method (FEM) u-p model more widely applicable for oil recovery in mature reservoirs. A two-layer partially saturated media was subjected to compressive seismic stress at low frequency (3 Hz). The results indicated that the vertical displacement gradients of the bottom and upper layers decline with excitation time for both fully and partially saturated media. On the other hand, partially saturated pore pressure gradients of both the upper and bottom layers have higher amplitudes with excitation time than fully saturated pore pressure gradients due to the influence of capillar pressure. The cumulative crossflow oil volume for 180 days of continuous stimulation was 1176 bbl, 1032 bbl, and 648 bbl in low permeability layers: 200 md, 100 md, and 50 md, respectively. Therefore, the developed model has the potential for field-scale EOR applications. The study also suggests coupling elastic EOR with CO2 flooding to recover more oil due to increasing fluid mobility and relative permeability to oil in low-permeability reservoirs or tight formations.

A petrophysically driven seismic inversion method for the total organic carbon content of source rocks

Organic carbon content is the main index for evaluating organic matter abundance of source rocks, and it is still difficult to quantitatively predict total organic carbon (TOC) in source rocks based on seismic data. The study of seismic fluid identification driven by petrophysics can help to understand the fluid characteristics and distribution patterns of subsurface oil and gas reservoirs. First, this paper clarifies the sweet spot parameters (parameters characterizing hydrocarbon enrichment) and sensitive elastic parameters (a parameter characterizing the nature of an ideal elastic body) of source rocks through theoretical petrophysical modeling. Next, the paper establishes the relationship between sensitive elastic parameters and sweet spot parameters TOC and constructs a statistical petrophysical model that can characterize the relationship between the two on this basis. And then we construct the joint distribution of TOC and elastic impedance through the Bayesian theoretical framework to obtain the maximum posterior probability estimate as the final TOC inversion results of source rocks. Our method successfully predicts the spreading of high-quality source rocks in the Wen4 Section of Lufeng 13 Subsag, and the inversion results are within an uncertainty range of ±14 m for well data, which proves the reliability of the method. The prediction results show that the organic matter abundance of source rocks in the Wen4 Section is high, and the organic carbon content is generally higher than 2%, which provides a reliable basis for the further implementation of the resource scale of the depression and the clarification of the hydrocarbon-rich area, which provides technical support for the evaluation of the source rocks of the new depression in the new area.

Low-field MRI study of the 1H distribution and migration in porous sediments during natural gas conversion from methane hydrate

Gas hydrates, crystalline compounds formed from water and guest molecules like methane, are gaining attention as a promising clean energy source. While research has extensively focused on the extraction and transport of natural gas hydrates from offshore marine sediments, the dynamic processes in the porous sediments remain under explored. This study employs low-field Magnetic Resonance Imaging (MRI) to investigate the in-situ formation and dissociation of methane hydrate within a partially saturated stack of glass beads. By integrating advanced MRI techniques, including 1D dhk SPRITE, bulk T1 distribution, and 2D spatial T2 imaging, this research provides a comprehensive analysis of fluid distribution and migration during phase transitions in the porous sediments. Three key findings emerged from the study. First, SE-SPI measurements successfully quantified hydrate and residual water saturation, aligning with previous X-ray CT and high-field MRI studies and validating low-field MRI for hydrate research. Secondly, this study introduced a volumetric approach to T1 and T2 measurements, distinguishing between free and bound water, with characteristic relaxation times for each, confirming the technique's capability to differentiate types of residual water. Finally, spatially resolved T2 relaxation time distributions revealed vertical fluid migration within the pore spaces, identifying an equilibrium zone where inflow and outflow rates were balanced. Overall, this study underscores the effectiveness of low-field MRI as a noninvasive tool for analyzing hydrate-bearing sediments. The findings lay the groundwork for further exploration of hydrate in porous sediments, enhancing our understanding of gas production dynamics in hydrate-rich environments.

Complexity factor for a static self-gravitating sphere in Rastall–Rainbow gravity

We generalized Herrera’s definition of complexity factor for static spherically symmetric fluid distributions to Rastall–Rainbow theory of gravity. For this purpose, an energy-dependent equation of motion is employed in accordance with the principle of gravity’s rainbow. It is found that the complexity factor appears in the orthogonal splitting of the Riemann curvature tensor, and measures the deviation of the value of the active gravitational mass from the simplest system under the combined corrections of Rastall and rainbow. In the low-energy limit, all the results we have obtained reduce to the counterparts of general relativity when the non-conserved parameter is taken to be one. We also demonstrate how to build an anisotropic or isotropic star model using complexity approach. In particular, the vanishing complexity factor condition in Rastall–Rainbow gravity is exactly the same as that derived in general relativity. This fact may imply a deeper geometric foundation for the complexity factor.

Parametric model and experimental investigation of a distribution header to relieve heat sink coolant maldistribution

Coolant maldistribution has obvious negative effects on the liquid cooled heat sink (LCHS) performance. This work proposed a distribution header parametric model to improve flow distribution and compared with conventional I-type LCHS. The distribution header was a symmetrical S-shaped structure with a drop-shaped baffle. The S-shaped outline was obtained through a streamlined design to reduce the flow resistance. The structure characteristics of the drop-shaped baffle, which first expands and then contracts, were conducive to change the flow direction and relieve flow maldistribution. The experimental and numerical results indicate that the S-shaped outline parameters exhibited small impact on fluid distribution improvement, but distinctly affected pressure drop. The parameters of the drop-shaped baffle had significant influence on the fluid distribution. Notably, compared with conventional I-type LCHS, the LCHS with distribution header can improve the heat transfer, fluid distribution and flow performance. The maximum temperature of the measuring points was significantly decreased by 12.12 %−14.62 %, pressure drop was reduced by 2.78 %–4.44 %, and the flow distribution was improved by 68.32 %. The conclusions proved that the distribution header is based on a simple design with lower energy consumption, and which can be used into LCHS to relieve the flow maldistribution.

Using noninvasive imaging to assess manual lymphatic drainage on lymphatic/venous responses in a spaceflight analog

This retrospective case series (clinicaltrials.gov NCT06405282) used noninvasive imaging devices (NIID) to assess the effect of manual lymphatic drainage (MLD) on dermal/venous fluid distribution, perfusion, and temperature alterations of the head, neck, upper torso, and legs while in the 6-degree head-down tilt validated spaceflight analog. A lymphatic fluid scanner measured tissue dielectric constant levels. Near-infrared spectroscopy assessed perfusion, by measuring tissue oxygenation saturation. Long-wave infrared thermography measured tissue temperature gradients. Fifteen healthy, university students participated. NIID assessments were taken 1 minute after assuming the HDT position and then every 30 minutes, with MLD administered from 180 to 195 minutes. Subjects returned to the sitting position and were assessed at post-225 min NIID demonstrated significant changes from baseline (p < 0.01), although these changes at areas of interest varied. MLD had a reverse effect on all variables. NIID assessment supported the potential use of MLD to mitigate fluid shifts during a spaceflight analog.

Transient temperature and pressure coupling model of cementing injection stage in ultra deep wells considering segmental rheological model, casing eccentricity and U-tube effect

The geological environments of ultra deep wells such as high temperature and high pressure (HTHP), narrow safety density window pose significant challenges to cementing operation. Considering segmental rheological model and density model, casing eccentricity, U-tube effect and viscous dissipation, this paper established a transient temperature and pressure coupling model during cementing injection stage of ultra deep wells. The segmental rheological model can describe the rheological properties of cementing fluids under HTHP much better. Considering casing eccentricity and viscous dissipation can accurately model the variation of temperature and pressure profiles. Taking U-tube effect into the model, the formation process of vacuum section at top of the casing can be simulated. The fully implicit finite-difference approach was used to solve the coupling model, and the calculation results were compared with field measurement data and simulation data to verify its accuracy. The calculation errors of the developed model are respectively 10% and 5% compared to field measurement data and Wellplan’s simulation data. Numerical simulations were conducted to reveal the cementing fluid distribution, transient temperature distribution and pressure distribution during the cementing injection stage. The simulation results show that the variety of cementing fluids with different density, rheological properties and thermophysical parameters complicates the change mechanism of temperature and pressure. The temperature and pressure distributions both present unsteady characteristics during cementing injection stage, which puts forward higher requirements of pressure control for narrow safety density window formation. The influence of temperature and pressure on rheology of cementing fluids cannot be ignored, and segmental rheological model should be considered for accurate pressure prediction. Also the casing eccentricity cannot be ignored for cementing pressure calculation in deviated or horizontal wells. Managed pressure cementing (MPC) has a greater advantage in dealing with narrow density window formation. The synergistic control of cementing fluid density and back pressure can keep the equivalent circulating density (ECD) within the safe density window. Through the application of the transient temperature and pressure coupling model, we can simulate the variations of key dynamic parameters during cementing injection stage and optimize the cementing parameters.

Population Pharmacokinetic Model of Intravenous Immunoglobulin in Patients Treated for Various Immune System Disorders

Intravenous immunoglobulin (IVIG) is used to treat various immune system disorders, but the factors influencing its disposition are not well understood. This study aimed to estimate the population pharmacokinetic parameters of IVIG and to investigate the effect of genetic polymorphism of the FCGRT gene encoding the neonatal Fc receptor (FcRn) and clinical variability on the pharmacokinetic properties of IVIG in patients with immune system disorders. Patients were recruited from 4 hospitals in Malaysia. Clinical data were recorded, and blood samples were taken for pharmacokinetic and genetic studies. Population pharmacokinetic parameters were estimated by nonlinear mixed-effects modeling in Monolix. Age, weight, baseline immunoglobulin G concentration, ethnicity, sex, genotype, disease type, and comorbidity were investigated as potential covariates. Models were evaluated using the difference in objective function value, goodness-of-fit plots, visual predictive checks, and bootstrap analysis. A total of 292 blood samples were analyzed from 79 patients. The IVIG concentrations were best described by a 2-compartment model with linear elimination. Weight was found to be an important covariate for volume of distribution in the central compartment (Vc), volume of distribution in the peripheral compartment (Vp), and clearance in the central compartment, whereas disease type was found to be an important covariate for Vp. Goodness-of-fit plots indicated that the model fit the data adequately. Genetic polymorphism of the FCGRT gene encoding the neonatal Fc receptor did not affect the pharmacokinetic properties of IVIG. This study supports the use of dosage based on weight as per current practice. The study findings highlight that Vp is significantly influenced by the type of disease being treated with IVIG. This relationship suggests that different disease types, particularly inflammatory and autoimmune conditions, may alter tissue permeability and fluid distribution due to varying degrees of inflammation. Increased inflammation can lead to enhanced permeability and retention of IVIG in peripheral tissues, reflecting higher Vp values.

Review on spontaneous imbibition mechanisms in gas-water systems: Impacts on unconventional gas production and CO2 geo-sequestration

Spontaneous imbibition, a fundamental process in porous media, involves the displacement of a non-wetting phase by a wetting phase driven by capillary pressure. It plays a key role in various applications, particularly in unconventional gas production and greenhouse gas geo-sequestration. Despite extensive research in this area, conflicting results and explanations persist regarding imbibition phenomena, particularly in gas-water systems. This paper aims to address this gap by providing a comprehensive review of basic concepts, mechanical analyses, pore-filling patterns, front evolutions, and influencing factors associated with spontaneous imbibition. Mechanical factors including capillary force, viscous force, gravitational force, hydrostatic force, inertial force, capillary back force, and dead end force, play crucial roles in water imbibition with different boundary types. The pore-filling pattern significantly affects microscopic fluid distribution and front evolution during the imbibition process. To resolve conflicting findings, we systematically analyze the influencing factors of spontaneous imbibition within gas-water systems, encompassing rock properties, fluid characteristics, rock-fluid interactions, and reservoir properties. Furthermore, we present an in-depth discussion on the imbibition and trapping mechanisms relevant to unconventional gas production and CO2 geo-sequestration, providing insights into force analyses and influencing factors. Gas production strategies and favorable conditions for CO2 capillary trapping are proposed. Finally, we outline existing knowledge gaps and suggest potential directions for future research. This review thus provides useful insights and suggestions for advancing our understanding of spontaneous imbibition within gas-water systems and optimizing unconventional gas production and CO2 geo-sequestration practices.

Improving fluid identification in well logging using Continuous Wavelet Transform and Vision Transformers: An innovative approach

Well logging fluid prediction is one of the key steps in assessing oil and gas reserves. By analyzing downhole logging data, different types of fluids contained in underground rocks, such as crude oil, natural gas, and water, can be determined. This information is crucial for assessing the abundance and recoverable reserves of oil and gas resources and helps guide oil and gas exploration and development work. We have introduced a novel model called CWT (Continuous Wavelet Transform)-ViT (Vision Transformer). CWT can simultaneously provide frequency information at different scales, enabling the model to analyze downhole logging data more comprehensively and accurately at different scales. Underground rock structures often exhibit features at multiple scales, and CWT can effectively capture these features, aiding in better differentiation of different types of fluids. The ViT model utilizes the Transformer architecture, allowing for global attention over input sequences without being limited by sequence length. This enables the model to comprehensively understand the overall information of downhole logging data and extract richer features. For complex geological structures and fluid distributions in geological exploration, the global attention mechanism helps the model better grasp the overall situation, thereby improving the accuracy of fluid prediction. When we used the CWT-ViT method for well logging fluid prediction, we achieved a high accuracy rate of 97.50% in the first dataset, which further improved to 97.77% in the second dataset. These results demonstrate the significant robustness and efficiency of the CWT-ViT method in lithology prediction using well logging data. We also conducted blind well experiments, and our CWT-ViT model outperformed other models, achieving a blind well prediction accuracy of 97.36%. Therefore, the experiments indicate that the key to improving accuracy in well logging fluid prediction with CWT lies in its multiscale analysis capability, effectively capturing different fluid characteristic frequencies. Additionally, CWT enhances signal features and removes noise, increasing the precision of fluid identification. Finally, the integration with ViT further optimizes fluid prediction performance, making it outstanding in complex geological environments. The advantages of ViT in fluid prediction include its excellent sequence modeling capability, effective handling of long-distance dependencies, and enhanced ability to capture fluid characteristics in complex well logging data.

Performance and energy consumption study of a dual-evaporator loop heat pipe for chip-level cooling

The dual-evaporator loop heat pipe (DeLHP) exhibits more applications than a single-evaporator loop heat pipe in a chip-level cooling field. However, increasing the evaporators leads to a complex pipeline structure. This study focuses on developing and investigating a new parallel structure for the DeLHP. Experimental research was conducted to analyze the startup characteristics of DeLHP under single-load and dual-load conditions, and its operational characteristics under various variable power conditions. Numerical simulation was employed to analyze the fluid distribution and flow characteristics. The results indicate that heating the evaporator near the vapor pipeline achieves faster startup and more stable temperatures under a single load. Under dual loads, DeLHP exhibits a faster startup compared to a single load. When the thermal load near the vapor pipeline is greater than the load on the evaporator near the liquid pipeline, DeLHP starts faster and maintains a lower stable temperature. Under a maximum total load of 300 W, the heating surface temperature stabilizes below 80 ℃. The numerical simulation results indicate that when evaporator 1 near the liquid pipeline is individually heated, the temperatures, vapor fractions, and fluid velocities of the two evaporators are more balanced. The power usage effectiveness reaches a minimum value of 1.09 at 150 W. These research findings provide reliable and substantive support for the performance optimization of DeLHPs in practical applications.

Role of decoupling process on the configurations of compact stars induced by Thomas-Fermi dark matter with null complexity in f(T) gravity

Our goal in this work is to find an anisotropic solution for a self-bound compact object composed of dark matter with a null complexity factor in f(T)-gravity theory. We use a well-known gravitational decoupling via complete geometric deformation (CGD) technique to examine the role of decoupling parameters on the configuration of compact objects. Initially, we derive the null complexity condition for f(T)-gravity decoupled system which leads to a relation between gravitational potentials. Next, we apply the CGD approach to split the decoupled system into two subsystems. The initial system refers to a pure f(T) gravity system consisting of an isotropic fluid distribution, where the isotropy criterion is equivalent to the condition in Einstein's gravity. The solution of the first system is solved through the Vlasenk-Pronin space-time metrics while the second system associated with the deformation function is solved by the density constraints method by mimicking a new source with Thomas-Fermi dark matter density profile that generates the anisotropy in the decoupled system. The physical validity of the anisotropic solution is checked by the graphical analysis of the pressure, density, energy, and stability conditions. We have also shown the effect of torsion and decoupling parameters on the configuration of anisotropic compact objects. The energy exchange (ΔE) of fluid distribution is also discussed. We found that ΔE is positive throughout the stellar configuration, which implies that energy is effectively transmitted to the surrounding environment.

Comprehensive discussion of Krori–Barua Bardeen compact stars on modified f(R) theories of gravity with scalar potential

The objective of this paper is to deal with physical features of charged anisotropic compact objects in the framework of [Formula: see text] modified theory of gravity. To accomplish the desired objective, we consider a spherically symmetric spacetime with charged anisotropic fluid distribution. In addition, we utilize the Krori–Barua metric, i.e. [Formula: see text] and [Formula: see text] for exploring the field equations. Moreover, we compare the interior boundary to the bardeen model as an exterior geometry to calculate the unknown constrains. Further, to check the existence of bardeen stellar structure, we discuss the behavior of physical properties such as energy density, pressure components, anisotropy, equation of state parameters, stability analysis, energy bounds, equilibrium condition, adiabatic index, compactness factor and surface redshift. Conclusively, all the obtained results show that the system under consideration is physically stable, free from singularity and viable.

A new perspective on gravitational collapse: a comprehensive analysis using Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} parametrization

In this article, we have studied some new facets of gravitational collapse, beyond conventional notions of black holes, and naked singularities. The present work is focused on the unresolved problems of theoretical physics concerning the final fate of the gravitational collapse of any massive star. By generalizing the foundational work of Oppenheimer and Snyder (Phys Rev 56:455, 1939), we have considered the homogeneous gravitational collapsing system filled with perfect fluid distributions (devoid of dust fluid) within the framework of GR theory. The article investigates a homogeneous gravitational collapsing system using a parametrization scheme for the expansion-scalar (Θ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Theta )$$\\end{document} and determining the exact solution of field equations. Further, by employing the known Darmois–Israel boundary condition, we have discussed the solution in more detail, and the model’s physical and geometrical quantities are obtained in terms of stellar mass (M), making it crucial for astrophysical applications. To assess the astrophysical viability of our model, we consider a massive star-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}Canis Majoris and throughout this study we have presented a detailed numerical and graphical analysis of our model. The analysis of singularities in the models is conducted through the examination of the apparent horizon. Our findings demonstrate that the star continues to collapse indefinitely in co-moving time, ultimately leading to a space-time singularity-this represents a case of continuous gravitational collapse. We propose that this scenario describes an “Eternal Collapsing Object,” which may be treated as a “mathematical black hole without any finite equilibrium state.” Our presented models undergo rigorous physical tests to ensure their regularity, causality, and stability, and to satisfy the necessary energy conditions.