Stiff Fluid Research Articles

Thin-shell gravastar model in f(Q, T) gravity* *SP & PKS acknowledges the National Board for Higher Mathematics (NBHM) under the Department of Atomic Energy (DAE), Govt. of India for financial support to carry out the Research project No.: 02011/3/2022 NBHM(R.P.)/R & D II/2152 Dt.14.02.2022. PKS thanks Transilvania University of Brasov for Transilvania Fellowship for Visiting Professors

In the last few decades, gravastars have been proposed as an alternative to black holes. The stability of a gravastar has been examined in many modified theories of gravity along with Einstein's GR. The gravity, a successfully modified theory of gravity for describing the current accelerated expansion of the universe, has been used in this study to examine gravastar in different aspects. According to Mazur and Mottola [Proc. Natl. Acad. Sci. 101, 9545 (2004); Gravitational condensate stars: An alternative to black holes, I12-011, (2002)], a gravastar has three regions with three different equations of state. In this study, we examined the interior of a gravastar by considering EoS to describe the dark sector for the interior region. The next region is a thin shell of ultrarelativistic stiff fluid, in which we investigated several physical properties, including proper length, energy, entropy, and surface energy density. Additionally, we examined the surface redshift and speed of sound to check the potential stability of our proposed thin-shell gravastar model. Furthermore, we used the entropy maximization technique to verify the stability of the gravastar model. A gravastar's outer region is a complete vacuum described by exterior Schwarzschild geometry. Finally, we presented a stable gravastar model, which is singularity-free and devoid of any incompleteness in classical black hole theory.

Cosmological models in scale-independent energy-momentum squared gravity

Scale-independent EMSG is a particular model of energy–momentum squared gravity (EMSG) in which the new terms in the Einstein field equations arising from the EMSG theory enter with the same power as the usual terms from Einstein–Hilbert part of the action. However, the model violates the local energy–momentum conservation and matter-current conservation in general and hence, permits a process of matter creation/annihilation in an expanding universe. Consequently, the scale factor dependencies of the energy densities are modified by the dimensionless model parameter α. We revisit some nostalgias such as static universes and de Sitter/steady state universes. We reproduce the original ones, moreover, present some novelties, e.g., a spatially flat static universe, de Sitter expansion by negative vacuum energy, steady state universes in the presence of arbitrary fluids with constant equation of state (EoS) parameter other than dust, etc. We also investigate the possible dynamics of dust dominated and radiation dominated universes. Depending on the value of α, dust/radiation dominated universe exhibits power-law accelerated/decelerated expansion, corresponds to a steady state model or may end in a big rip. In the framework of anisotropic cosmology, we reproduce Barrow’s quiescent universe in the presence of stiff fluid and extend it to fluids with arbitrary constant EoS parameter. We also relax the condition for isotropic initial singularity (big bang) owing to that EMSG effectively allows ultra-stiff EoS parameters.

Compact stellar structures in Weyl geometric gravity

We consider the structure and physical properties of specific classes of neutron, quark, and Bose-Einstein condensate stars in the conformally invariant Weyl geometric gravity theory. The basic theory is derived from the simplest conformally invariant action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To keep the theory conformally invariant the trace condition is imposed on the matter energy-momentum tensor. The field equations are derived by varying the action with respect to the metric tensor, Weyl vector field and scalar field. By adopting a static spherically symmetric interior geometry, we obtain the field equations, describing the structure and properties of stellar objects in Weyl geometric gravity. The solutions of the field equations are obtained numerically, for different equations of state of the neutron and quark matter. More specifically, constant density stellar models, and models described by the stiff fluid, radiation fluid, quark bag model, and Bose-Einstein condensate equations of state are explicitly constructed numerically in both general relativity and Weyl geometric gravity, thus allowing an in depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, Weyl geometric gravity stars are more massive than their general relativistic counterparts. As a possible astrophysical application of the obtained results we suggest that the recently observed neutron stars, with masses in the range of $2{M}_{\ensuremath{\bigodot}}$ and $3{M}_{\ensuremath{\bigodot}}$, respectively, could be in fact conformally invariant Weyl geometric neutron or quark stars.

Friedmann-like universes with non-metricity

We study the potential effects of spacetime non-metricity in cosmology. In the spirit of Einstein–Cartan gravity, but with non-metricity replacing torsion, we consider the Einstein–Hilbert action and assume zero torsion. Adopting certain hyperfluid models, with non-vanishing hypermomentum that can source spacetime non-metricity, we add a matter component into the action and derive the field equations, along with the conservation laws. Applying our formulae to cosmology, we generalize the Friedmann and the Raychaudhuri equations in the presence of non-metricity. Our results show that, in a number of cases, non-metricity can mimic the effects of matter with unconventional equation of state. For instance, specific types of hypermomentum are found to act as an effective stiff fluid, thus opening the possibility that non-metricity could have played a significant role in the early stages of the universe’s evolution. Alternative forms of hypermomentum can dominate the universal dynamics at late times. In either case, the equilibrium moment depends on the initial conditions and it is determined by a simple relation between the matter component and the hyperfluid.

Gravastar in the framework of symmetric teleparallel gravity* *SP & PKS acknowledges the National Board for Higher Mathematics (NBHM) under the Department of Atomic Energy (DAE) of the government of India for financial support to carry out the research project (02011/3/2022 NBHM(R.P.)/R & D II/2152 Dt.14.02.2022)

We present a novel gravastar model based on the Mazur-Mottola (2004) method with an isotropic matter distribution in gravity. The gravastar, which is a hypothesized substitute for a black hole, is built using the Mazur-Mottola mechanism. This approach allows us to define the gravastar as having three stages. The first one is an inner region with negative pressure; the next region is a thin shell that is made up of ultrarelativistic stiff fluid, and we studied the proper length, energy, entropy, and surface energy density for this region. Additionally, we demonstrated the possible stability of our suggested thin shell gravastar model through the graphical study of the surface redshift. The exterior Schwarzschild geometry describes the outer region of the gravastar. In the context of gravity, we discovered analytical solutions for the interior of gravastars that are free of any type of singularity and the event horizon.

Qualitative aspects of Kantowski–Sachs cosmologies with cosmological constant and stiff fluid

Qualitative aspects of Kantowski–Sachs cosmologies with cosmological constant and stiff fluid

Torsional dark energy

Dark energy from kinetic torsion is discussed. The torsion incorporated in the Einstein–Cartan (EC) Lagrangian is assumed to be totally anti-symmetric, represented by a timelike axial vector [Formula: see text]. The dynamics of torsion is invoked by a novel kinetic term that gives rise to dark energy, while the massive quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing term.

Role of stiffness and physico-chemical properties of tumour microenvironment on breast cancer cell stemness

Several physico-chemical properties of the tumour microenvironment (TME) are dysregulated during tumour progression, such as tissue stiffness, extracellular pH and interstitial fluid flow. Traditional preclinical models, although useful to study biological processes, do not provide sufficient control over these physico-chemical properties, hence limiting the understanding of cause-effect relationships between the TME and cancer cells. Breast cancer stem cells (B-CSCs), a dynamic population within the tumour, are known to affect tumour progression, metastasis and therapeutic resistance. With their emerging importance in disease physiology, it is essential to study the interplay between above-mentioned TME physico-chemical variables and B-CSC marker expression. In this work, 3D in vitro models with controlled physico-chemical properties (hydrogel stiffness and composition, perfusion, pH) were used to mimic normal and tumour breast tissue to study changes in proliferation, morphology and B-CSC population in two separate breast cancer cell lines (MCF-7 and MDA-MB 231). Cells encapsulated in alginate-gelatin hydrogels varying in stiffness (2-10 kPa), density and adhesion ligand (gelatin) were perfused (500 µL/min) for up to 14 days. Physiological (pH 7.4) and tumorigenic (pH 6.5) media were used to mimic changes in extracellular pH within the TME. We found that both cell lines have distinct responses to changes in physico-chemical factors in terms of proliferation, cell aggregates size and morphology. Most importantly, stiff and dense hydrogels (10 kPa) and acidic pH (6.5) play a key role in B-CSCs dynamics, increasing both epithelial (E-CSCs) and mesenchymal cancer stem cell (M-CSCs) marker expression, supporting direct impact of the physico-chemical microenvironment on disease onset and progression. Statement of significanceCurrently no studies evaluate the impact of physico-chemical properties of the tumour microenvironment on breast cancer stem cell (B-CSC) marker expression in a single in vitro model and at the same time. In this study, 3D in vitro models with varying stiffness, extracellular pH and fluid flow are used to recapitulate the breast tumour microenvironment to evaluate for the first time their direct effect on multiple breast cancer phenotypes: cell proliferation, cell aggregate size and shape, and B-CSC markers. Results suggest these models could open new ways of monitoring disease phenotypes, from the early-onset to progression, as well as being used as testing platforms for effective identification of specific phenotypes in the presence of relevant tumour physico-chemical microenvironment.

Kinetic axion F(R) gravity inflation

In this work we investigate the quantitative effects of the misalignment kinetic axion on ${R}^{2}$ inflation. Due to the fact that the kinetic axion possesses a large kinetic energy that dominates its potential energy, during inflation its energy density redshifts as stiff matter fluid and evolves in a constant-roll way, making the second slow-roll index to be nontrivial. At the equations of motion level, the ${R}^{2}$ term dominates the evolution; thus the next possible effect of the axion could be found at the cosmological perturbations level, via the second slow-roll index which is nontrivial. As we show, the latter elegantly cancels from the observational indices; however, the kinetic axion extends the duration of the inflationary era to an extent that it may cause a 15% decrease in the tensor-to-scalar ratio of the vacuum ${R}^{2}$ model. This occurs because as the ${R}^{2}$ model approaches its unstable quasi--de Sitter attractor in the phase space of $F(R)$ gravity due to the $⟨{R}^{2}⟩$ fluctuations, the kinetic axion dominates over the ${R}^{2}$ inflation and in effect the background equation of state is described by a stiff era, or equivalently a kination era, different from the ordinary radiation domination era. This in turn affects the duration of the inflationary era, increasing the $e$-foldings number up to $5e$-foldings in some cases, depending on the reheating temperature, which in turn has a significant quantitative effect on the observational indices of inflation and especially on the tensor-to-scalar ratio.

Tilted congruence with big rip singularity in f(T) theory of gravity

In this paper, tilted congruence with big rip singularity in f(T) theory of gravity is presented. f(T) theory of gravity is the generalization of the Teleparallel theory of gravity, where [Formula: see text] is the torsion scalar. In this work, tilted model is studied in which the three-velocity represents additional degree of freedom and tilted model detected the presence of dissipative processes including gravitational radiation. The solution of the field equations is explored by using the stiff fluid, power law of velocity field and a linear relationship between [Formula: see text] and [Formula: see text]. In this paper, the big bang and big rip singularity are observed. The cosmological evolution in f(T) model is examined. The physical and geometrical phases of the models are also investigated.

Kuchowicz gravastars in the braneworld formalism

In the current letter, we study isotropic static spherically symmetric gravastars without charge under the framework of braneworld gravity (dimensionally reduced RS-II braneworld with positive brane tension) using the metric potential of Kuchowicz type (which is physically acceptable, non-singular and stable) in the Mazur-Motolla conjuncture. We derived the Kuchowicz free parameters from the junction conditions assuming Schwarzschild vacuum without cosmological constant. As well, we assume that the interior is filled with Dark Energy (DE-like) fluid, shell with ultrarelativistic stiff fluid. Adopting this conditions, we probed several physical aspects of the gravastars, such as proper length, shell energy and entropy, surface redshift and adiabatic index, interior region mass.

Gravastar configuration in non-conservative rastall gravity

In the present article, we have presented the exact solutions of gravastar with Kuchowicz metric potential in the background of non-conservative Rastall gravity. Within the context of Mazur-Mottola’s [1, 2] concept of Bose–Einstein condensation to gravitational systems, the grvastar structure consists of three layers: interior part, intermediate part (i.e., thin shell) and exterior part. All the gravastar’s exact solutions have been derived with the aid of Kuchowicz metric potential by considering isotropic matter distribution. For the thin shell (filled with ultra-relativistic stiff fluid) with different parameters like length, energy, entropy and surface redshift have been calculated, which show the stability of our proposed model. Interestingly, all the thin shell results are obtained without taking shell approximation i.e., 0 < e −ν ≡ h ≪ 1. The exterior part, which is absolutely a vacuum is characterized by the Schwarzschild geometry and the interior part give output in the form of non-singular results. Generally, the main purpose of this work is to obtain the exact, non-singular, horizon free, stable model and we have achieved these goals in the presence of Rastall parameter.

Future dynamics of FLRW for the massless-scalar field system with positive cosmological constant

We consider solutions to the Einstein-massless-scalar field system with a positive cosmological constant, arising from sufficiently regular, near-FLRW (Friedmann-Lemaître-Robertson-Walker), initial data. We establish global existence in the future direction and derive their precise asymptotic behavior toward infinity. As a corollary, we infer that, unlike the FLRW background, the perturbed solutions do not describe a regular irrotational stiff fluid with a linear equation of state p = ρ for general asymptotic data at infinity. The reason for the breakdown of this interpretation is that the gradient of the scalar field stops being timelike at large times, eventually becoming null and then spacelike near infinity. Our results hold for open sets of initial data in Sobolev spaces without symmetries.

The dark side of the torsion: dark energy from propagating torsion

An extension to the Einstein–Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector S^mu . The dynamics of torsion is invoked by a novel kinetic term. Here we show that this kinetic term gives rise to dark energy, while the quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing cosmology solution. A constraint on the bouncing solution is calculated using cosmological data from different epochs.

Spatially Hyperbolic Gravitating Sources in Λ-Dominated Era

This study focuses on the impact of the cosmological constant on hyperbolically symmetric matter configurations in a static background. I extend the work of Herrera et al. 2021. and describe the influences of such a repulsive character on a few realistic features of hyperbolical anisotropic fluids. After describing the Einstein-Λ equations of motion, I elaborate the corresponding mass function along with its conservation laws. In our study, besides observing negative energy density, I notice the formation of a Minkowskian core as matter content is compelled not to follow inward motion near the axis of symmetry. Three families of solutions are found in the Λ-dominated epoch. The first is calculated by keeping the Weyl scalar to a zero value, while the second solution maintains zero complexity in the subsequent changes of the hyperbolical compact object. However, the last model encompasses stiff fluid within the self-gravitating system. Such a type of theoretical setup suggests its direct link to study a few particular quantum scenarios where negative behavior of energy density is noticed at the Λ-dominated regime.

Isotropization of N-component orthogonal fluid within the framework of Einstein field equations

In this study, we build up a general formalism for tilted N-component fluid form to investigate the isotropization features of the Bianchi-type models excluding Bianchi-IX. We applied this formalism to Bianchi type I and V models analytically and numerically using the metric approach of Einstein field equations. It is found that only the stiff fluid for Bianchi I model does not isotropize, in the absence of cosmological constant. Other Bianchi type I and V models become isotropic regardless of the type of the fluid or how much component it has. The result does not change with the existence of a cosmological constant.

Reheating in Runaway Inflation Models via the Evaporation of Mini Primordial Black Holes

We investigate the cosmology of mini Primordial Black Holes (PBHs) produced by large density perturbations that collapse during a stiff fluid domination phase. Such a phase can be realized by a runaway-inflaton model that crosses an inflection point or a sharp feature at the last stage of inflation. Mini PBHs evaporate promptly and reheat the early universe. In addition, we examine two notable implications of this scenario: the possible presence of PBH evaporation remnants in galaxies and a non-zero residual potential energy density for the runaway inflaton that might play the role of the dark energy. We specify the parameter space that this scenario can be realized and we find that a transit PBH domination phase is necessary due to gravitational wave (GW) constraints. A distinct prediction of the scenario is a compound GW signal that might be probed by current and future experiments. We also demonstrate our results employing an explicit inflation model.

Stiff matrices enhance myoblast proliferation, reduce differentiation, and alter the response to fluid shear stress in vitro.

During myofiber regeneration, myoblasts are continuously subjected to shear stress. It is currently not known whether shear stress affects the regenerative capacity of myoblasts when extracellular matrix (ECM) stiffness increases (e.g. upon aging). Therefore, we aimed to assess (1) whether matrix stiffness and pulsating fluid shear stress affect myoblast proliferation and/or expression of differentiation-associated genes in myoblasts, and (2) whether matrix stiffness modulates the mechanoresponse of myoblasts to pulsating fluid shear stress. Myoblasts were seeded on matrigel-coated polyacrylamide gel matrices of varying stiffness, mimicking young ("soft", 0.5 kPa) and old ECM ("stiff", 20 kPa), as well as on matrigel-coated glass matrices with very high stiffness (40 ϺPa), and subjected to 1 h pulsating fluid shear stress (3 Pa/s or 4 Pa/s, 1 Hz). We found enhanced proliferation of myoblasts on stiff matrices, but reduced differentiation compared to myoblasts on soft matrices. Pulsating fluid shear stress significantly upregulated gene expression of proliferation-associated genes C-fos and Il-6, as well as expression of cytoskeletal α-actin in myoblasts seeded on glass. In contrast, pulsating fluid shear stress significantly downregulated gene expression of α-actin and Myogenin in myoblasts seeded on soft matrices. In conclusion, these results suggest that age and disease-associated increased ECM stiffness may contribute to declined regenerative capacity of myoblasts, by reducing their capacity to differentiate into new muscular tissue, at least in the absence of mechanical stimulation.

Curious case of the Buchdahl-Land-Sultana-Wyman-Ibañez-Sanz spacetime

We revisit Wyman's "other" scalar field solution of the Einstein equations and its Sultana generalization to positive cosmological constant, which has a finite 3-space and corresponds to a special case of a stiff fluid solution proposed by Buchdahl and Land and, later, by Iba\~nez and Sanz to model relativistic stars. However, there is a hidden cosmological constant and the peculiar geometry prevents the use of this spacetime to model relativistic stars.

A Hybrid Model for Fast and Efficient Simulation of Fluid Power Circuits With Small Volumes Utilizing a Recurrent Neural Network

The modeling and simulation of fluid power systems are essential parts of the real-time simulation of virtual prototypes of mobile working machines. In several cases in the dynamic simulation of such fluid power systems, a longer simulation time is required. This makes the traditional mathematical models inefficient for real-time simulations, particularly when simulating fluid power systems because of the small volumes in stiff differential equations of pressure. The main reason for such an issue in the simulation of fluid power systems is the existence of small oil volumes in stiff differential equations of pressure. To overcome this issue, a novel hybrid model is proposed for stiff fluid power systems simulation. The main feature of the model is the utilization of a recurrent neural network instead of stiff differential equations of pressure with small volume. At the same time, the dynamics of the rest system are traditionally presented with algebraic and differential equations. The testing results of the introduced hybrid model showed that the novel method can reduce the simulation time, which makes the model suitable for real-time applications. Moreover, the accuracy of the model remains at a fairly high level compared to traditional mathematical models.