Tolman-Oppenheimer-Volkoff Equations Research Articles

The universal thermodynamic properties of extremely compact objects

Abstract An extremely compact object (ECO) is defined as a quantum object without horizon, whose radius is just a small distance s outside its Schwarzschild radius. We show that any ECO of mass M in d + 1 dimensions with s ≪ ( M / m p ) 2 / ( d − 2 ) ( d + 1 ) l p must have (at leading order) the same thermodynamic properties—temperature, entropy and radiation rates—as the corresponding semiclassical black hole of mass M. An essential aspect of the argument involves showing that the Tolman–Oppenheimer–Volkoff equation has no consistent solution in the region just outside the ECO surface, unless this region is filled with radiation at the (appropriately blueshifted) Hawking temperature. In string theory it has been found that black hole microstates are fuzzballs—objects with no horizon—which are expected to have a radius that is only a little larger than the horizon radius. Thus the arguments of this paper provide a nice closure to the fuzzball paradigm: the absence of a horizon removes the information paradox, and the thermodynamic properties of the semiclassical hole are nonetheless recovered to an excellent approximation.

Influence of GUP corrected Casimir energy on zero tidal force wormholes in modified teleparallel gravity with matter coupling

In recent times, the study of the Casimir effect in quantum field theory has garnered increasing attention because of its potential to be an ideal source of exotic matter needed for stabilizing traversable wormholes. It has been confirmed through experimental evidence that this phenomenon involves fluctuations in the vacuum field, leading to a negative energy density. Motivated by the above, we have investigated Casimir wormholes with corrections from the Generalized Uncertainty Principle (GUP) within the framework of matter-coupled teleparallel gravity. Our analysis includes three well-known GUP models: the Kempf, Mangano, and Mann (KMM) model, the Detournay, Gabriel, and Spindel (DGS) model, and a third model called Model II. For a broader analysis, we have considered two well-known model functions for the teleparallel theory: a linear f(T,T)=αT+βT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\alpha T+\\beta \\mathcal {T}$$\\end{document} and a quadratic model f(T,T)=ηT2+χT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})=\\eta T^2+\\chi \\mathcal {T}$$\\end{document}. The shape function solutions corresponding to both models are examined in the absence of tidal forces in spacetime. We also demonstrate the crucial role played by the parameters of the f(T,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T,\\mathcal {T})$$\\end{document} models in the violation of the energy conditions. With the increasing interest in detecting gravitational waves from astrophysical objects, we have thoroughly discussed the perturbation of the wormhole solutions in the scalar, electromagnetic, axial gravitational, and Dirac field backgrounds. We employ the 3rd order WKB expansion to find the complex frequencies associated with the quasinormal modes of energy dissipation. Additionally, we also calculate the active mass and total gravitational energy for the wormhole geometry. The amount of exotic matter involved in sustaining these wormholes is also found in this paper. Furthermore, the physical stability of such Casimir wormholes is examined using the Tolman–Oppenheimer–Volkoff equation.

Casimir wormholes inspired by electric charge in Einstein–Gauss–Bonnet gravity

This investigation assesses the feasibility of a traversable wormhole by examining the energy densities associated with charged Casimir phenomena. We focus on the influence of the electromagnetic field created by an electric charge as well as the negative energy density arising from the Casimir source. We have developed different shape functions by defining energy densities from this combination. This paper explores various configurations of Casimir energy densities, specifically those occurring between parallel plates, cylinders and spheres positioned at specified distances from each other. Furthermore, the impact of the generalized uncertainty principle correction is also examined. The behavior of wormhole conditions is evaluated based on the Gauss–Bonnet coupled parameter (μ) and electric charge (Q) through the electromagnetic energy density constraint. This is attributed to the fact that the electromagnetic field satisfies the characteristic ρ = −p r . Subsequently, we examine the active gravitational mass of the generated wormhole geometries and explore the behavior of μ and Q concerning active mass. The embedding representations for all formulated shape functions are examined. Investigations of the complexity factor of the charged Casimir wormhole have demonstrated that the values of the complexity factor consistently fall within a particular range in all scenarios. Finally, using the generalized Tolman–Oppenheimer–Volkoff equation, we examine the stability of the resulting charged Casimir wormhole solutions.

Impact of charge on the stability of pulsar SAX J1748.9-2021 in modified symmetric teleparallel gravity

In this paper, we explore the effect of charge on the stability of pulsar star SAX J1748.9-2021 in f(Q) gravity, where Q represents non-metricity. For this purpose, we apply the Krori-Barua metric ansatz with anisotropic fluid and use a linear f(Q) model f(Q)=ζQ, where ζ is a non-zero constant. We derive exact relativistic solutions of the corresponding field equations. Furthermore, we study its geometric and physical properties through astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. We examine features like anisotropic pressure, the mass–radius relationship, redshift, the Zeldovich condition, energy and causality conditions, the adiabatic index, the Tolman–Oppenheimer–Volkoff equation, the equation of state parameter and compactness. Our findings align with the observational data which indicate that the pulsar SAX J1748.9-2021 is viable and stable under this modified theory of gravity.

Toward Accelerated Nuclear-physics Parameter Estimation from Binary Neutron Star Mergers: Emulators for the Tolman–Oppenheimer–Volkoff Equations

Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman–Oppenheimer–Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: multilayer perceptrons (MLPs), Gaussian processes, and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms, whereas the RBM results in the largest speedup with respect to the full high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver.

Physical characteristics of anisotropic solutions in f(Q,T) gravity under the vanishing complexity, embedding class one, conformally flat and conformally Killing conditions

The foundation of this paper is to present a comparative study of the properties of anisotropic solutions for compact stars in the framework of modified f(Q,T) gravity for the first time under the schemes of vanishing complexity, embedding class one, conformally flat and conformally Killing, where Q is the nonmetricity scalar and T is the trace of the energy-momentum tensor. The model f(Q,T)=ϕQ+αQn+1−γ(1−e−Q/γ)+βT is chosen in order to compare the results of the various forms f(Q,T) and f(Q) gravity theories. The f(Q,T) and f(Q) gravities in this model are then further simplified to depend on parameters ϕ,α,γ&β. Then, we discussed several approaches to determining the spherically symmetric spacetime components. Schwarzschild geometry represents the exterior spacetime, while a Tolman-Kuchowiz spacetime is used to examine the spherically symmetric spacetime inside the interior geometry. Many properties of compact stars are investigated, like energy density, energy conditions, pressure profiles, sound speeds, gradients, adiabatic index, TOV equation, mass function, compactness, and redshift function are all carefully examined in order to complete the analysis. We have compiled results for both stable and unstable scenarios, derived from gravity theories categorized into various cases, with solutions considered under different frameworks such as Tolman-Kuchowiz spacetime, embedding class 1 spacetime, the vanishing complexity condition, the conformally flat condition, and the conformal Killing vector condition.

Stability and viability of charged anisotropic pulsar SAX J1748.9-2021 in extended symmetric teleparallel gravity

This manuscript aims to study the viability and stability of a pulsar SAX J1748.9-2021, containing a charged anisotropic matter configuration within the framework of f(Q,T) theory (Q and T are the non-metricity scalar and energy–momentum tensor, respectively). We employ a non-singular solution and a specific model of this gravitational theory and use junction conditions to determine the unknown constants in the metric coefficients. We explore different geometric and physical properties using astrophysical observations from the pulsar SAX J1748.9-2021, which is found in X-ray binary systems within globular clusters. This framework establishes relationships between various physical quantities, including fluid parameters, anisotropy, mass–radius relation, redshift, the Zeldovich condition, energy conditions, causality conditions, adiabatic index, Tolman–Oppenheimer–Volkoff equation, equation of state parameter and compactness. Our findings affirm the feasibility and stability of the proposed charged pulsar within this theoretical framework.

A comprehensive analysis of charged pulsars and cracking condition

The main aim of this manuscript is to analyze the viability and stability of pulsars filled with charged anisotropic matter configuration in extended symmetric teleparallel theory. A particular model of this gravitational theory is considered to reduce the complexity of the system and formulate the explicit field equations which govern the interaction between matter and geometry. The configuration of static spherical symmetric structures is examined through the non-singular viable solutions. The undetermined constants in the metric coefficients are determined by the Darmois junction conditions. Further, we explore different physical characteristics in the interior of charged pulsars to check their viability. The equilibrium state of the charged stellar objects is discussed using the Tolman–Oppenheimer–Volkoff equation and the stability is examined by the causality condition, Herrera cracking approach and adiabatic index, respectively. Our findings indicate that the proposed charged stars in this modified gravity are physically viable and stable.

Relativistic model for anisotropic compact stars in embedding class-I spacetime

Abstract In the present article, we introduce a completely new regular model for static, spherically symmetric celestial fluid spheres in embedding class I spacetime. In this regard, needfully, we propose a new suitable metric potential e^λ(r) to generate the present model. The various analyses on energy density, pressure, anisotropic factor, mass, compactness parameter, redshift, and energy condition make sure the model is physically viable on the ground of model stars Vela X-1, Cen X-3, SMC X-4, and LMC X-4. The reported solutions also respect the equilibrium state by satisfying the Tolman–Oppenheimer–Volkoff equation and ensure stability by satisfying the causality condition, condition on the adiabatic index, and Harrison-Zeldovich-Novikov condition. The generated M − R graph matches the ranges of masses and radii for the model compact stars. Additionally, this study provides estimates of
the moment of inertia based on the I − M graph.

Anisotropic compact stellar model: a vanishing complexity approach

In this article, we develop a new class of solutions that describe stellar structures of recently observed pulsars. We adopt the condition of the vanishing complexity proposed by Herrera (Phys Rev D 97:044010, 2018) and an appropriate metric potential for generating the solutions. The solutions which are obtained from the complexity-free conditions, are physically well-behaved and satisfy all the rigorous conditions to describe static and spherically symmetric realistic compact objects. The features of observed anisotropic compact stars including Vela X-1, LMC X-4, Cen X-3, and EXO 1785-248 are validated with our model. It is further shown that the solutions supporting matter configurations are physically plausible, stable with positive anisotropy, and in an equilibrium state as verified by investigating the generalized TOV equation in the case of our model.

Stability analysis of charged neutron stars and Darmois junction conditions

This research article examines the impact of f(Q,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {Q}},{\\mathcal {T}})$$\\end{document} theory on the geometry of charged neutron stars filled with anisotropic matter configuration. Here, 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} represents non-metricity and T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {T}}$$\\end{document} denotes the trace of energy-momentum tensor. We use a particular functional form of this modified theory to reduce the system’s complexity and derive explicit relations of the energy density and pressure components. Further, we consider viable non-singular solutions to analyze the internal structure of the charged neutron stars. The unspecified parameters in the metric coefficients are evaluated through Darmois junction conditions, which ensures consistency between interior and exterior solutions of the stellar objects. These parameters are then used to explore different physical characteristics such as the behavior of energy density, pressure components, anisotropy, energy bounds, equation of state parameter, compactness and redshift function in the interior of charged neutron stars. The stability and equilibrium states of the charged stellar objects are discussed using the Tolman–Oppenheimer–Volkoff equation and the speed of sound, respectively. Our results suggest that the charged neutron stars are viable and stable in the presence of dark source terms.

Interacting quark star with pressure anisotropy and recent astrophysical observations

This paper investigates the internal structure and equation of state (EoS) of quark stars (QS) with pressure anisotropy, incorporating recent astrophysical observations. Utilizing perturbative QCD corrections and color superconductivity, the EoS is expressed as a dimensionless function dependent on a single parameter, providing a comprehensive exploration of strong interaction effects. By rescaling the EoS and introducing dimensionless variables, the study encompasses scenarios ranging from noninteracting quark matter to extreme stiffness characterized by a parameter, λ̄. Anisotropic QS configurations are constructed using a spherically symmetric metric, with locally anisotropic matter described by a generalized EoS for tangential pressure. The Tolman–Oppenheimer–Volkoff equations governing star structure are presented in dimensionless form, and numerical solutions explore the parameter space defined by effective bag constants and λ̄. Mass–radius relations and the compactness of anisotropic QSs are analyzed under various model parameter variations, considering constraints from pulsar masses and gravitational wave phenomena. The study highlights the influence of pressure anisotropy on the maximum mass of QSs and discusses the impact of model parameters on internal properties. Additionally, the paper considers static stability, adiabatic index, and sound velocity profiles, providing a comprehensive understanding of QS behavior. Overall, this investigation contributes valuable insights into the properties of QSs and their compatibility with observational constraints, offering a detailed exploration of their EoS and internal structure.

The role of pressure anisotropy on quark stars in gravity’s rainbow

This work is seeking for the existence of stable quark stars (QSs) in the framework of a modified theory of gravity known as gravity’s rainbow. This modification comes from the fact that the geometry of spacetime depends on the energy of the test particle. We solve numerically the modified TOV equations and present the mass–radius (M–R) diagram for quark matter equations of state. To constrain the allowed values of the model parameters, we use current astrophysical measurements of the masses and radii of neutron stars. Finally, we investigate the dynamical stability of the hydrostatic equilibrium equations in gravity’s rainbow by analyzing the static stability, adiabatic index, and sound velocity profiles.

Anisotropic pressure effect on central EOS of PSR J0740+6620 in the light of dimensionless TOV equation

Abstract It is generally agreed upon that the pressure inside a neutron star is isotropic. However, a strong magnetic field or superfluidity suggests that the pressure anisotropy may be a more realistic model. We derived the dimensionless TOV equation for anisotropic neutron stars based on two popular models, namely the BL model and the H model, to investigate the effect of anisotropy. Similar to the isotropic case, the maximum mass $M_{max}$ and its corresponding radius $R_{Mmax}$ can also be expressed linearly by a combination of radial central pressure $p_{rc}$ and central energy density $\varepsilon_{c}$, which is insensitive to the equation of state (EOS). We also found that the obtained central EOS would change with different values of $\lambda_{BL}$ ($\lambda_{H}$), which controls the magnitude of the difference between the transverse pressure and the radial pressure. Combining with observational data of PSR J0740+6620 and comparing to the extracted EOS based on isotropic neutron star, it is shown that in the BL model, for $\lambda_{BL}$ = 0.4, the extracted central energy density $\varepsilon_{c}$ changed from 546 -- 1056 MeV/fm$^{3}$ to 510 -- 1005 MeV/fm$^{3}$, and the extracted radial central pressure $p_{rc}$ changed from 87 -- 310 MeV/fm$^{3}$ to 76 -- 271 MeV/fm$^{3}$. For $\lambda_{BL}$ = 2, the extracted $\varepsilon_{c}$ and $p_{rc}$ changed to 412 -- 822 MeV/fm$^{3}$ and 50 -- 165 MeV/fm$^{3}$, respectively. In the H model, for $\lambda_{H}$ = 0.4, the extracted $\varepsilon_{c}$ changed to 626 -- 1164 MeV/fm$^{3}$, and the extracted $p_{rc}$ changed to 104 -- 409 MeV/fm$^{3}$. For $\lambda_{H}$ = 2, the extracted $\varepsilon_{c}$ decreased to 894 -- 995 MeV/fm$^{3}$, and the extracted $p_{rc}$ changed to 220 -- 301 MeV/fm$^{3}$.

Compact stars with non-uniform relativistic polytrope

This paper presents new relativistic composite polytropic models for compact stars by simultaneously solving Einstein field equations with the polytropic state equation to simulate the spherically symmetric, static matter distribution. Using a non-uniform polytropic index, we get the Tolman–Oppenheimer–Volkoff equation for the relativistic composite polytrope (CTOV). To analyze the star's structure, we numerically solve the CTOV equation and compute the Emden and mass functions for various relativistic parameters and polytropic indices appropriate for neutron stars. The calculation results show that, as the relativistic parameter approaches zero, we recover the well-known Lane-Emden equation from the Newtonian theory of polytropic stars; thus, testing the computational code by comparing composite Newtonian models to those in the literature yields good agreement. We compute composite relativistic models for the neutron star candidates Cen X-3, SAXJ1808.4-3658, and PSR J1614-22304. We compare the findings with various existing models in the literature. Based on the accepted models for PSR J1614-22304 and Cen X-3, the star's core radius is predicted to be between 50 and 60% percent of its total radius, while we found that the radius of the core of star SAXJ1808.4-3658 is around 30% of the total radius. Our findings show that the neutron star structure may be approximated by a composite relativistic polytrope, resulting in masses and radii that are quite consistent with observation.

Noncommutative wormhole in de Rham-Gabadadze-Tolley like massive gravity

The wormhole solution in dRGT massive gravity is examined in this paper in the background of non-commutative geometry. In order to derive the wormhole model, along with the zero tidal force, we assume that the matter distribution is given by the Gaussian and Lorentzian distributions. The shape function in both models involves the massive gravity parameters m2c1 and m2c2. But the spacetime loses its asymptotic flatness due to the action of the massive gravity parameter. It is noticed that the asymptotic flatness is affected by the repulsive effect induced in the massive gravitons that push the spacetime geometry very strongly. We observed that each model violates the null energy criteria, indicating the presence of exotic matter which is necessary to sustain the wormholes. The exotic matter is measured using the volume integral quantifier. Moreover, it is discovered that the model is stable under the hydrostatic equilibrium condition by utilizing the TOV equation. Finally, our research encompassed an exploration of the repulsive influence exerted by gravity. Our findings demonstrated that the presence of repulsive gravity results in a negative deflection angle for photons following null geodesics. Remarkably, we consistently observed negative values for the deflection angle across all values of r0 in the two scenarios examined. This consistent negativity unequivocally signifies the manifestation of the repulsive gravity effect.

Neutron stars in f(R,Lm,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,L_m,T)$$\\end{document} gravity

This study explores the behavior of compact stars within the framework of f(R,Lm,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,L_m,T)$$\\end{document} gravity, focusing on the functional form f(R,Lm,T)=R+αTLm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,L_m,T) = R + \\alpha TL_m$$\\end{document}. The modified Tolman–Oppenheimer–Volkoff (TOV) equations are derived and numerically solved for several values of the free parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} by considering both quark and hadronic matter—described by realistic equations of state (EoSs). Furthermore, the stellar structure equations are adapted for two different choices of the matter Lagrangian density (namely, Lm=p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_m= p$$\\end{document} and Lm=-ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_m= -\\rho $$\\end{document}), laying the groundwork for our numerical analysis. As expected, we recover the traditional TOV equations in General Relativity (GR) when α→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 0$$\\end{document}. Remarkably, we found that the two choices for Lm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_m$$\\end{document} have appreciably different effects on the mass-radius diagrams. Results showcase the impact of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} on compact star properties, while final remarks summarize key findings and discuss implications, including compatibility with observational data from NGC 6397’s neutron star. Overall, this research enhances comprehension of f(R,Lm,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,L_m,T)$$\\end{document} gravity’s effects on compact star internal structures, offering insights for future investigations.

Comparative analysis of dark energy compact stars in f(T,T) and f(T) gravity theories via conformally flat condition

This manuscript is the first investigation of dark energy celestial phenomena in the modified gravity theory by examining dark energy compact stars within the context of modified f(T,T) gravity. In order to compare the outcomes of the f(T,T) and f(T) gravity theories, the model f(T,T)=αT(r)+βT(r)+ϕ is selected. This model is then simplified to f(T) gravity by setting β = 0. The f(T) gravity is torsion-based gravity, while in f(T,T ) gravity trace of energy-momentum tensor is coupled with torsion. Moreover, we note that we have more dense object formation in f(T,T) gravity as compared to f(T )-gravity. The spherically symmetric space-time inside the internal geometry is analyzed using a conformally flat condition, while the Schwarzschild geometry represents the outer space-time. Numerous characteristics of dark energy stars are examined, including equation of state components, energy conditions, and dark energy pressure components. Empirical evidence for the existence of dark energy in stellar configurations is presented by the results for pressure components in dark energy, which show a significant negative tendency in these stellar parameters. A complete analysis is performed by thoroughly investigating energy conditions, pressure profiles, sound speeds, gradients, adiabatic index, Tolman–Oppenheimer–Volkoff equation, mass function, compactness, and redshift function. The mass-radius relation is also discussed via M − R curves. This confirms that the studied star configuration is realistic and acceptable.

Moment of inertia and compactness of quark stars within the context of f(R, T, L m ) gravity

Within the metric formalism of f(R, T, L m ) gravity theories, we investigate the hydrostatic equilibrium structure of compact stars taking into account both isotropic and anisotropic pressure. For this purpose, we focus on the f(R, T, L m ) = R + α TL m model, where α is a free parameter. We derive the modified TOV equations and the relativistic moment of inertia in the slowly rotating approximation. Using an equation of state (EoS) for color-superconducting quark stars, we examine the effects of the α TL m term on the different macroscopic properties of these stars. Our results reveal that the decrease of the parameter α leads to a noticeable increase in the maximum-mass values. For negative α with sufficiently small ∣α∣, we obtain a qualitative behavior similar to the general relativistic (GR) context, namely, it is possible to obtain a critical stellar configuration such that the mass reaches its maximum. However, for sufficiently large values of ∣α∣ keeping negative α, the critical point cannot be found on the mass-radius diagram. We also find that the inclusion of anisotropic pressure can provide masses and radii quite consistent with the current observational measurements, which opens an outstanding window onto the physics of anisotropic quark stars. By comparing the I − C relations of isotropic quark stars in modified gravity, we show that such a correlation remains almost unchanged as the parameter α varies from GR counterpart. On the other hand, given a fixed α, the I − C relation is insensitive to variations of the anisotropy parameter β to O(4%) .

Casimir wormholes in Brans–Dicke theory

In recent years there has been a growing interest in the field of wormhole physics in the presence of Casimir effect. As this effect provides negative energy density, it can be utilized as an ideal candidate for the exotic matter required for creating a traversable wormhole. In the context of modified theories of gravity such as Brans–Dicke (BD) theory (Brans and Dicke 1961 Phys. Rev. 124 925), wormhole geometries have been vastly investigated. However, the scientific literature is silent on the issue of BD wormholes in the presence of Casimir energy. Our aim in the present study is to seek for static spherically symmetric solutions representing wormhole configurations in BD theory with Casimir energy as the supporting matter. The Casimir setup we assume comprises two electrically neutral, infinitely large parallel planes placed in a vacuum. We then consider the Casimir vacuum energy density of a scalar field in such a configuration with Dirichlet and mixed boundary conditions. In the former case the corresponding Casimir force is attractive and in the latter this force is repulsive. We present exact zero tidal force wormhole solutions as well as those with non vanishing redshift function for both types of Casimir energies. The conditions on wormhole solutions along with the weak (WEC) and null (NEC) energy conditions put constraints on the values of BD coupling parameter. These constraints are also subject to the value of BD scalar field at the throat and the throat radius. We therefore find that BD wormholes in the presence of Casimir energy can exist without violating NEC and WEC (for the repulsive Casimir force). Finally, we examine the equilibrium condition for stability of the obtained solutions using Tolman–Oppenheimer–Volkoff equation.