Tolman Oppenheimer Volkoff Research Articles

Do we need dense matter equation of state in curved spacetime for neutron stars?

Neutron stars are regarded as natural laboratories for the study of dense strong interaction matter. The equation of state (EoS) of dense matter computed in flat spacetime is used to predict the structure of neutron stars by solving the Tolman-Oppenheimer-Volkoff (TOV) equation. Recently, it has been reported that the curved spacetime effect or specifically gravitational time dilation effect on the EoS of dense matter leads to a significant increase of the maximum mass limit of neutron stars [Phys. Rev. D \textbf{104}, 123005 (2021) and J. Cosmol. Astropart. Phys. 02 (2021) 026]. However, in this work, we show that to study the hydrostatic equilibrium of dense matter within the framework of general relativity and relativistic fluid dynamics, the grand canonical EoS of dense matter, $p(T,\mu)$, should be the same as that computed in flat spacetime, otherwise it is not consistent with local thermodynamic relations and energy-momentum conservation of the fluid. The gravitation influences the pressure $p$ only through enhancing the temperature $T$ and the chemical potential $\mu$, known as Tolman's law and Klein's law. We rewrite the TOV equation as an alternative version so that the grand canonical EoS computed by using field theoretical methods can be used as a direct input. This may provide a tool to study the grand canonical EoS of dense matter via deep learning.

Traversable wormholes solutions in f(ℛ,φ,χ) gravity under conformal symmetry

The present analysis deals with the wormhole (WH) solutions in [Formula: see text] gravity, where [Formula: see text], [Formula: see text] and [Formula: see text] represent the Ricci scalar, kinetic expression and potential field, respectively. To complete this analysis, we use the WH geometry via spherical spacetime with the anisotropic matter distribution. Further, we consider the Gaussian distribution as non-commutative geometry to complete the analysis under conformal symmetry. We calculate the exact WH shape function by plugging the possible conformal Killing vectors. Further, we have discussed the embedded surface to understand the WH geometry. Furthermore, the Tolman–Oppenheimer–Volkoff equation is considered to discuss the stability of WH configuration with the Gaussian energy density source.

Existence of photon sphere at or outside the throat of stable wormholes

In this paper, the effects of strong gravitational lensing are explored in the context of traversable wormholes by determining the existence of photon spheres. The redshift function is defined as [Formula: see text], where [Formula: see text] and [Formula: see text] are constants. Using this redshift function, the points of maximum potentials are determined which consequently gives the radius of photon spheres. It is obtained that either the throat itself can act as an effective photon sphere or the photon sphere exists outside the throat of the wormhole. Further, the nature of matter supporting the wormhole solutions is examined by analyzing the energy conditions, and the stability of solutions is tested with the help of the TOV (Tolman–Oppenheimer–Volkoff) equation.

Buchdahl quark stars within f(Q) theory

In the present paper, authors study the strange stars with the MIT Bag EoS admitting Buchdahl symmetry (non-singular and physically viable metric potential) in the both linear $$f(Q)=aQ+b$$ and nonlinear $$f(Q)=Q+aQ^b$$ forms of modified symmetric teleparallel gravitation. In order to obtain the correct form of Buchdahl metric coefficients, they matched interior strange star space-time with the exterior Schwarzschild vacuum space-time. As a strange star candidate, PSRJ1416-2230 has been used with mass $$M=1.69M_\odot$$ and radius $$R=9.69R_\odot$$ . For either linear and nonlinear f(Q) gravities, they probed Null, Dominant and Strong Energy Conditions as well as the radial, tangential Equation of State (EoS), gradients of the perfect fluid energy-momentum tensor elements, Tolman–Oppenheimer–Volkoff equilibrium condition, relativistic adiabatic index and causality conditions, surface redshift. It was found that strange stars in the linear and nonlinear f(Q) gravity show physically viable behavior, respect energy and causality conditions, has EoS in the bounds $$0\le \omega \le 1$$ and surface redshift does not exceed 2, as expected.

Bardeen compact stars in modified f(G) gravity

The goal of this work was to investigate the behavior of charge compact stars in the context of [Formula: see text] theory of gravity, which is one of the most powerful candidates responsible for the accelerated expansion of the universe. The salient feature of the current research is the consideration of Bardeen’s model, which describes an exterior space–time and interprets the magnetic monopole arising from gravity collapse caused by some specific conditions of nonlinear electrodynamics. Moreover, we analyzed the structure of the star by using the solution provided by a Finch–Skea-type metric potential. All the physically necessary parameters and characteristics of relativistic spheres are displayed graphically. We further studied the energy density, pressure curves, equation-of-state parameters, anisotropy factor, energy conditions, Tolman–Oppenheimer–Volkoff equation, redshift functions, compactness parameters, adiabatic index, and stability analysis in detail.

Realistic compact stars in conformal teleparallel gravity

Abstract We explore an interior solution of a physically symmetric vierbein with two unknown functions in conformal teleparallel gravity. The field equations can be described in a closed system for a particular form of the metric potentials and an appropriate anisotropic function. As a result, we find a new set of configurations consistent with observed pulsars. In particular, the boundary conditions for the interior spacetime are used for the Schwarzschild spacetime to constrain the conformal field with a unit value through the surface of a compact object. Furthermore, we apply the present model to the pulsar 4U 1608−52 with an approximate radius R = 9.52 ± 0.15 km and mass $M= 1.74 \pm 0.14\, \mathrm{M}_{\odot }$. To analyze the stability, we also study the causality conditions and the adiabatic index by assuming the Tolman–Oppenheimer–Volkoff equation, an adiabatic index, and the static state. Moreover, the consistency of the model under consideration with other pulsars is investigated.

Integrability of the Tolman–Oppenheimer–Volkoff equation

In this work we study the global analytic integrability, Louville integrability and Puiseux integrability of the Tolman–Oppenheimer–Volkoff equation.

Stability Analysis of Isotropic Spheres in Einstein Gauss–Bonnet Gravity

AbstractThis work investigates the effect of electromagnetic field on relativistic compact stellar structures coupled with anisotropic collapsing fluid under the framework of string‐motivated Gauss–Bonnet‐powered gravity. Using the power‐law form of Maxwell‐GB corrections, the stellar structure equations dubbed as Tolman–Oppenheimer–Volkoff (TOV) equations are developed. In the presence of a power‐law form of ‐corrections, an evolution equation for the Weyl scalar is obtained, which plays a central role in the investigation of the examined fluid configuration. It is observed that the existence of shear in the fluid flow, irregularities in the distribution of energy density, dissipative fluxes, and modified Gauss–Bonnet corrections are the certain factors that are accountable for generating anisotropies in an originally isotropic fluid distribution. Some of the interesting consequences of formulated results are examined.

Solving Tolman–Oppenheimer–Volkoff equations in f(T) gravity: A novel approach applied to some realistic equations of state

There are many ways to probe alternative theories of gravity, namely, via experimental tests at solar system scale, cosmological data and models, gravitational waves and compact objects. In this paper, we consider a model of gravity with torsion [Formula: see text] applied to compact objects such as neutron stars (NSs) for a couple of realistic equations of state (EOS). To do so, we follow our previous articles, in which we show how to model compact stars in [Formula: see text] gravity by obtaining its corresponding Tolman–Oppenheimer–Volkof equations. In this modeling of NS in [Formula: see text] gravity presented here, we calculate, among other things, the maximum mass allowed for a given realistic EOS, which would also allow us to evaluate which models are in accordance with the observations. The results already known to General Relativity must be reproduced to some extent and, eventually, we can find models that allow higher maximum masses for NSs than Relativity itself, which could explain, for example, the secondary component of the event GW190814, if this star is a massive NS.

Traversable wormhole solutions in f(R,T) gravity with noncommutative geometry

In this paper, the wormholes have been constructed in the framework of the linear [Formula: see text] gravity model with noncommutative geometry. The wormhole solutions are obtained in the context of Gaussian and Lorentzian distributions of matter using [Formula: see text] gravity. The energy conditions such as null, weak, strong, and dominant energy conditions are explored and the regions satisfying these conditions are examined for both forms of matter distributions. Further, the stability of wormhole solutions is studied with the help of TOV (Tolman–Oppenheimer–Volkoff) equations. It is found that the wormhole solutions are stable and free from exotic matter for the suitable choice of parameters.

A study of charged stellar structure in modified f (R,ϕ,χ) gravity

The aim of this paper is to investigate and analyze the behavior of charged compact stars in the modified [Formula: see text] theory of gravity. When solving the field equations, we assume that Krori– Barua space-time describes the geometry of the inner space [K. Krori and J. Barua, A singularity-free solution for a charged fluid sphere in general relativity, J. Phys. A Math. Gen. 8 (1975) 508]. We further analyzed various physical characteristics for our model, including energy density, pressure components, anisotropy parameter, mass function, compactness element, and redshift through their graphical representations. Additionally, we have checked the equilibrium position by taking Tolman–Oppenheimer–Volkoff equation and stability by using Abreu’s criterion [H. Abreu, H. Hernandez, and L. Nunez, Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects, Class. Quantum Grav. 24 (2007) 4631] and relativistic adiabatic index. For our study, we choose Hercules XI, Centaurus XIII, EXO 1785-248, LMC XIV stars for analysis.

Dark matter admixed neutron star properties in light of gravitational wave observations: A two fluid approach

We consider the effect of density dependent dark matter on the neutron star mass, radius, and tidal deformability. Nuclear matter (normal matter) as well as the fermionic dark matter sector is considered in a mean field model. We adopt the two fluid formalism to investigate the effect of dark matter on the neutron star properties. In the two fluid picture, there is no direct interaction between the dark matter and the nuclear matter. Rather these two sectors interact only through gravitational interaction. The nuclear matter sector is described by the $\ensuremath{\sigma}\ensuremath{-}\ensuremath{\omega}\ensuremath{-}\ensuremath{\rho}$ meson interaction in the ``FSU2R'' parametrization. In the dark matter sector, we use the Bayesian parameter optimization technique to fix the unknown parameters in the dark matter equation of state. In the two fluid picture, we solve the coupled Tolman-Oppenheimer-Volkoff (TOV) equations to obtain the mass and radius of dark matter admixed neutron stars (DANSs). We also estimate the effect of the density dependent dark matter sector on the tidal deformability of dark matter admixed neutron stars (DANSs).

Radial oscillations and gravitational wave echoes of strange stars with nonvanishing lambda

We study the effect of the cosmological constant on radial oscillations and gravitational wave echoes (GWEs) of non-rotating strange stars. To depict strange star configurations we used two forms of equations of state (EoSs), viz., the MIT Bag model EoS and the linear EoS. By taking a range of positive and negative values of cosmological constant, the corresponding mass–radius relationships for these stars have been calculated. For this purpose, first we solved the Tolman–Oppenheimer–Volkoff (TOV) equations with a non-zero cosmological constant and then we solved the pressure and radial perturbation equations arising due to radial oscillations. The eigenfrequencies of the fundamental f-mode and first 22 pressure p-modes are calculated for each of these EoSs. Again considering the remnant of the GW170817 event as a strange star, the echo frequencies emitted by such stars in presence of the cosmological constant are computed. From these numerical calculations, we have inferred relations between cosmological constant and mode frequency, structural parameters, GWE frequencies of strange stars. Our results show that for strange stars, the effective range of cosmological constant is 10−15cm−2≤Λ≤3×10−13cm−2.

Charged strange stars with dust and phantom regimes in Rastall gravity

In this paper, we are focused on studying the possibility of providing a new well-behaved class of exact solutions for viable anisotropic stellar systems with dust and phantom regimes in the framework of Rastall gravity theory. This gravity theory modifies the matter sector only, incorporating new ingredients to the physical parameters that describe the model like charge density, electric field, density, and pressure components. Furthermore, other significant amounts are influenced, such as subliminal speeds of the pressure waves in radial and transversal directions, observational parameters such as the surface redshift associated with the total mass M and the radius R of the compact stellar configurations. Likewise, a transcendent mechanism such as equilibrium via generalized Tolman–Oppenheimer–Volkoff equation and stability of the stellar system is upset. The unidentified constraints are evaluated via the boundary conditions along with the dust and phantom models to describe as exterior space–times considering experimental statistics of five different stars i.e., EXO 1785 - 248, SMC X - 1, SAX J 1808.4 - 3658, 4U 1538 - 52, and HER X - 1. Various physical aspects have been analyzed with the help of modified dynamical equations. Exclusively, all the stellar configurations under observations are realistic, stable, and are free from all singularities. After witnessing the minor differences between our proposed models in both cases, Andréasson’s limit M≤R/3+R/9+Q2/3R has been fulfilled as required by the charged stellar structures. In such an astrophysical scenario, our new results provide circumstantial evidence in favor of super-massive pulsars.

Anisotropic quintessence charged strange stars in Rastall–Maxwell gravity

In this work, we investigate the Rastall–Maxwell theory around the strange quark matter (SQM) in the presence of a quintessence field and a quintessence dark energy having a characteristic parameter [Formula: see text] such that [Formula: see text]. The SQM is governed by the simplified MIT bag model equation of state: [Formula: see text], with [Formula: see text] the bag constant, in the presence of a load distribution given by [Formula: see text]. We find some solutions by using the modified Tolman–Oppenheimer–Volkoff (TOV) equation in the framework of Rastall gravity. We investigate the energy condition, the mass–radius relation, modified TOV equation, redshift and the stability of the system is checked by exploring the adiabatic index, the compactification factor and the causality condition for verifying the physical consistency of our model. We notify that for physical values of Rastall parameter, the stellar system is more massive compared to its size. Hence, it is revealed that the alternative Rastall theory is appropriate to explain the behavior of massive stellar objects. The presence of dark energy motivates us to consider that the existing strange stars are a mixture of both ordinary matter and quintessence matter in different proportions. The incorporation of quintessence matter with the real one describes the well-known SQM.

Neutron stars in scalar–tensor gravity with quartic order scalar potential

In this work we investigate the effects of a non-minimally coupled quartic order scalar model on static neutron stars, with the non-minimal coupling in the Jordan frame being of the form f(ϕ)=1+ξϕ2. Particularly we derive the Einstein frame Tolman–Oppenheimer–Volkoff equations, and by numerically integrating them for both the interior and the exterior of the neutron star, using a double shooting python 3 based numerical code, we extract the masses and radii of the neutron stars evaluated finally in the Jordan frame, along with several other related physical quantities of interest. With regard to the equation of state for the neutron star, we use a piecewise polytropic equation of state with the central part being Skyrme-Lyon (SLy), Akmal–Pandharipande–Ravenhall (APR) or the Wiringa–Fiks–Fabrocini (WFF1) equations of state. The resulting M–R graphs are compatible with the observational bounds imposed by the GW170817 event which require the radius of a static M∼1.6M⊙ neutron star to be larger than R=10.68−0.04+15km and the radius of a static neutron star corresponding to the maximum mass of the star to be larger than R=9.6−0.03+0.14km. Moreover, the WFF1 EoS, which was excluded for static neutron stars in the context of general relativity, for the quartic order scalar model neutron star model provides realistic results compatible with the GW170817 event.

Anisotropic Compact Stars in D → 4 Limit of Gauss–Bonnet Gravity

In the frame of Gauss–Bonnet gravity and in the limit of D→4, based on the fact that spherically symmetric solution derived using any of regularization schemes will be the same form as the original theory, we derive a new interior spherically symmetric solution assuming specific forms of the metric potentials that have two constants. Using the junction condition we determine these two constants. By using the data of the star EXO 1785-248, whose mass is M=1.3±0.2M⊙ and radius l=8.849±0.4 km, we calculate the numerical values of these constants, in terms of the dimensionful coupling parameter of the Gauss–Bonnet term, and eventually, we get real values for these constants. In this regard, we show that the components of the energy–momentum tensor have a finite value at the center of the star as well as a smaller value to the surface of the star. Moreover, we show that the equations of the state behave in a non-linear way due to the impact of the Gauss–Bonnet term. Using the Tolman–Oppenheimer–Volkoff equation, the adiabatic index, and stability in the static state we show that the model under consideration is always stable. Finally, the solution of this study is matched with observational data of other pulsars showing satisfactory results.

An isotropic compact stellar model in curvature coordinate system consistent with observational data

This paper investigates a spherically symmetric compact relativistic body with isotropic pressure profiles within the framework of general relativity. In order to solve the Einstein’s field equations, we have considered the Vaidya–Tikekar type metric potential, which depends upon parameter K. We have presented a charged perfect fluid model, considering $$K\notin [0,1]$$ , which represent compact stars like Her X-1, 4U 1538-52, SAX J1808.4-3658, LMC X-4, SMC X-4, EXO 1785-248, Cen X-3 and Cyg X-2, to an excellent degree of accuracy. We have investigated the physical features such as the energy conditions, velocity of sound, surface redshift, adiabatic index of the model in detail and shown that our model obeys all the physical requirements for a realistic stellar model. Using the Tolman–Oppenheimer–Volkoff equations, we have explored the hydrostatic equilibrium and the stability of the compact objects. This model also fulfils the Harrison–Zeldovich–Novikov stability criterion. We have checked the behaviour of the system in the presence of a very high charge (around $$10^{20}$$ Coulomb at surface), which causes an electric field intensity above the Schwinger limit. This amount of charge is mainly caused due to very high density of the system, and a dense system like a compact star can contain such a huge charge. The results obtained in this paper can also be used in analysing other isotropic compact objects.

Isoentropic equations of state of beta -stable hadronic matter with a quark phase transition

We construct isoentropic equations of state (EOSs) of beta -stable dense hadronic matter considering the possibility that a quark deconfinement phase transition can take place. These conditions can be actually realized in different astrophysical contexts like core-collapse supernovae (CCSNe), during the early stages of the evolution of a newly formed neutron star (protoneutron star, PNS) or in the postmerger compact object formed in binary neutron star (BNS) mergers. We consider four different EOSs to describe the hadronic phase: three EOSs from relativistic mean field theory and one EOS recently derived from microscopic calculations in the framework of the Brueckner–Hartree–Fock approach. We combine these hadronic EOSs with a quark matter EOS obtained from a modified MIT-Bag model which takes into account some perturbative corrections in the grand canonical potential due to the quark–quark interaction. The two phases are then joined up through a Gibbs construction. For each model we study thermal and neutrino trapping effects on the matter composition and consequently on the EOS. We finally determine the PNS static structure integrating the Tolman–Oppenheimer–Volkoff equations. We find that the thermal contribution and particularly the effect of neutrino trapping play an important role on the full EOS. The latter can get softer or stiffer according to the strangeness content in the hadronic phase. These effects are thus crucial to provide a proper description of the dynamical evolution of both the postmerger compact object formed in a BNS merger or the PNS formed in a CCSN.

Anisotropic spheres via embedding approach in f(R) gravity

This study explores the anisotropic stellar structures in the background of f(R) modified gravity, where R is a Ricci scalar. To complete this analysis, we use the spherically symmetric space-time. Further, an anisotropic source of matter is used to investigate the stability of stellar structures. The embedded class-I approach is used to demonstrate the behavior of stellar structures. Schwarzschild space-time is taken as exterior space-time to calculate the values of involved parameters. The observational data of three different stars, like LMC X-4, Cen X-3, and EXO 1785-248, are taken for the current analysis. For this study, we used Starobinsky-like model f(R) = R + βR2 for f(R) modified gravity. The stability analysis is discussed via the equation of state (EoS) parameters, Tolman–Oppenheimer–Volkoff (TOV) equation, anisotropy, etc. Graphical and analytical results are provided as viable results in f(R) gravity.