Relativistic Stars Research Articles

Shock-avoiding slicing conditions: Tests and calibrations

While the $1+\mathrm{log}$ slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop ``gauge shocks'' in some examples. Alternative ``shock-avoiding'' slicing conditions suggested by Alcubierre prevent these pathologies in those examples, but have not yet been explored and tested very broadly. In this paper we compare the performance of shock-avoiding slicing conditions with those of 1+log slicing for a number of ``text-book'' problems, including black holes and relativistic stars. While, in some simulations, the shock-avoiding slicing conditions feature some unusual properties and lead to more ``gauge dynamics'' than the $1+\mathrm{log}$ slicing condition, we find that they perform quite similarly in terms of stability and accuracy, and hence provide a very viable alternative to $1+\mathrm{log}$ slicing.

Construction of a pseudo-Newtonian potential for a spinning black hole embedded in quintessence background: Brief accretion studies

It is found difficult to construct a complete general relativistic theory for an accretion disc around a relativistic compact star. There exists a trend to reproduce the effects of general relativistic attraction by using a pseudo-Newtonian approach. One such pseudo-Newtonian force for a spinning black hole sitting in quintessence background is constructed in this paper. Comparison with general relativity at different parametric values is picturised thoroughly. Next, an accretion model using this newly constructed pseudo-Newtonian force is built. The radial inward speed gradient is found to be expressed as a ratio of two functions. It can be realized easily that among these two functions, the denominator might vanish for a particular value of radial speed in the interval zero to speed of light. To make the flow physical, the numerator should vanish at the same radial distance. This will ultimately generate two speed profiles starting from the particular radial distance. This is the cause of generation for accretion and wind branches. It has been followed that the disc is truncated at a finite distance due to the fact that the specific angular momentum becomes larger than the Keplerian angular momentum beyond that. Effects of the spin of the central gravitating object are followed along with the intense effect of the quintessence parameters concerned. Accretion and wind density profiles are also studied to find the density variations near the central engine. Ratio of shear viscosity to entropy density is analyzed in the presence of quintessence for viscous accretion flows.

Erratum: Relativistic hybrid stars in light of the NICER PSR J0740+6620 radius measurement [Phys. Rev. D 104 , 121302 (2021)

In this erratum, we correct a subset of our numerical results for $s\ensuremath{\ne}1$, where $s$ is the sound speed squared, presented in ``Relativistic hybrid stars in the light of NICER PSR $\mathrm{J}0740+6620$ radius measurement'' [Phys. Rev. D 104, L121302 (2021)]. The results for hybrid stars with $s=1$ remain unchanged.

Model of hybrid star with baryonic and strange quark matter in Tolman–Kuchowicz spacetime

The purpose of our work is to investigate some new features of a static anisotropic relativistic hybrid compact star composed of strange quark matter (SQM) in the inner core and normal baryonic matter distribution in the crust. Here we apply the simplest form of the phenomenological MIT bag model equation of state [Formula: see text] to correlate the density and pressure of strange quark matter within the stellar interior, whereas radial pressure and matter density due to baryonic matter are connected by the simple linear equation of state [Formula: see text]. In order to obtain the solution of the Einstein field equations, we have used the Tolman–Kuchowicz ansatz [R. C. Tolman, Static solutions of Einstein’s field equations for spheres of fluid, Phys. Rev. 55 (1939) 364–373; B. Kuchowicz, Acta Phys. Pol. 33 (1968) 541] and further derivation of the arbitrary constants from some physical conditions. Here, we examine our proposed model graphically and analytically in detail for physically plausible conditions. In particular, for this investigation, we have reported on the compact object Her [Formula: see text] [[Formula: see text]; [Formula: see text] km] in our paper as a strange quark star candidate. In order to check the physical validity and stability of our suggested model, we have performed various physical tests both analytically and graphically, namely, dynamical equilibrium of applied forces, energy conditions, compactness factor and surface redshift. Finally, we have found that our present model meets all the necessary physical requirements for a realistic model and can be studied for strange quark stars (SQS).

Embedding in Anisotropic Spheres

Exact solutions to the Einstein field equations for class I spacetime symmetry in relativistic stars are generated. The symmetry provides a relation between the gravitational potentials that lead to generalized solutions of the Einstein field equations. We choose one of the gravitational potentials on a physical basis, which allows us to obtain the other gravitational potential via an embedding approach. It is therefore possible to generate a model with astrophysical significance. The model generated satisfies physical properties like stability, causality, regularity, equilibrium and energy conditions.

Numerical Equilibrium Configurations and Quadrupole Moments of Post-Merger Differentially Rotating Relativistic Stars

Numerical simulations of binary neutron star mergers invariably show that, when a long-lived remnant forms, its rotation profile is never a simple decaying function of the radius but rather exhibits a maximum rotation rate shifted away from the center. This is in contrast to the usual differential rotation profile employed for the numerical modeling of axisymmetric equilibria of relativistic stars. Two families of rotation rate functions that mimic post-merger profiles were proposed by Uryū et al. (2017). In this work we implement Uryū’s profiles into the XNS code by Bucciantini and Del Zanna (2011) and we present novel equilibrium sequences of differentially rotating neutron stars. These are constructed by using three different equations of state, in order to study the dependence of mass, radius, angular momentum, and other important physical quantities, especially the quadrupole deformation and metric quadrupole moment, from the rotation properties.

Exploring physical features of anisotropic quark stars in Brans-Dicke theory with a massive scalar field via embedding approach * *Supported by the Postdoctoral Fellowship at Zhejiang Normal University (ZC304022919)

The main aim of this study is to explore the existence and salient features of spherically symmetric relativistic quark stars in the background of massive Brans-Dicke gravity. The exact solutions to the modified Einstein field equations are derived for specific forms of coupling and scalar field functions using the equation of state relating to the strange quark matter that stimulates the phenomenological MIT-Bag model as a free Fermi gas of quarks. We use a well-behaved function along with the Karmarkar condition for class-one embedding as well as junction conditions to determine the unknown metric tensors. The radii of strange compact stars viz., PSR J1416-2230, PSR J1903+327, 4U 1820-30, CenX-3, and EXO1785-248, are predicted via their observed mass for different values of the massive Brans-Dicke parameters. We explore the influences of the mass of scalar field , coupling parameter , and bag constant on state determinants and perform several tests on the viability and stability of the constructed stellar model. Conclusively, we find that our stellar system is physically viable and stable as it satisfies all the energy conditions and necessary stability criteria under the influence of a gravitational scalar field.

Non-singular T–K axion stars with/without the dynamical bosonic field in the presence of negative Λ term

In the present work authors derive exact solutions for the relativistic compact stars in the presence of two fields axion (Dante’s Inferno model) and with/without the complex scalar field (with the quartic self-interaction) coupled to gravity. The matter source is assumed as the perfect fluid one, and we also use barotropic/MIT bag EoS to derive energy density and anisotropic/isotropic pressures from Einstein Field Equations (EFE’s). For simplicity, as the metric potentials we use Tolman–Kuchowicz metric potentials, which are non-singular and physically acceptable. Unknown variables for the T–K metric potentials were derived from the junction conditions. To examine the redshift function, adiabatic index and energy, causality conditions we used such compact stars as PSR J1416-223, PSR J1903+32, 4U 1820-30, Cen X-3, EXO 1785-248, SAX J1808.4365.

Relativistic star perturbations in Horndeski theories with a gauge-ready formulation

We present a general framework for studying the relativistic star perturbations on a static and spherically symmetric background in full Horndeski theories. We take a perfect fluid into account as a form of the Schutz-Sorkin action. Our formulation is sufficiently versatile in that the second-order actions of perturbations in odd- and even-parity sectors are derived without choosing particular gauge conditions, so they can be used for any convenient gauges at hand. The odd-parity sector contains one dynamical gravitational degree of freedom coupled to a time-independent four velocity of the fluid. In the even-parity sector there are three dynamical perturbations associated with gravity, scalar field, and matter sectors, whose equations of motion are decoupled from other nondynamical perturbations. For high radial and angular momentum modes, we obtain the propagation speeds of all dynamical perturbations and show that the perfect fluid in the even-parity sector has a standard sound speed affected by neither gravity nor the scalar field. Our general stability conditions and perturbation equations of motion can be directly applied to the stabilities of neutron stars and black holes as well as the calculations of their quasinormal frequencies.

Classical Love number for quantum black holes

We present a method for comparing the classical and quantum calculations of the electric quadrupolar Love number $k_2$ and show that our previous derivation of the quantum Love number of a quantum blackhole matches exactly the classical calculation of $k_2$ when quantum expectation values are replaced by the corresponding classical quantities, as dictated by the Bohr correspondence principle. The standard derivation of $k_2$ for classical relativistic stars relies on fixing boundary conditions on the surface of the star for the Einstein equations in the presence of an external perturbing field. An alternative method for calculating $k_2$ uses properties of the spectrum of the non-relativistic fluid modes of the star. We adopt this alternative method and use it to derive an effective description of the interior modes in terms of a collection of driven harmonic oscillators characterized by different frequencies and amplitudes. We compare these two classical methods and find that most of the interior information can be integrated out, reducing the problem of calculating $k_2$ to fixing a single boundary condition for the perturbed Einstein equations on the surface of the deformed star. We then determine this single boundary condition in terms of the spectrum of the object and proceed to identify the relationship between classical quantities and quantum expectation values and to verify the agreement between the results of the effective classical calculation and the quantum calculation.

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.

Progress in Understanding the Nature of SS433

SS433 is the first example of a microquasar discovered in the Galaxy. It is a natural laboratory for studies of extraordinarily interesting physical processes that are very important for the relativistic astrophysics, cosmic gas dynamics and theory of evolution of stars. The object has been studied for over 40 years in the optical, X-ray and radio bands. By now, it is generally accepted that SS433 is a massive eclipsing X-ray binary in an advanced stage of evolution in the supercritical regime of accretion on the relativistic object. Intensive spectral and photometric observations of SS433 at the Caucasian Mountain Observatory of the P. K. Sternberg Astronomical Institute of M. V. Lomonosov Moscow State University made it possible to find the ellipticity of the SS433 orbit and to discover an increase in the system’s orbital period. These results shed light on a number of unresolved issues related to SS433. In particular, a refined estimate of the mass ratio MxMv>0.8 was obtained (Mx and Mv are the masses of the relativistic object and optical star). Based on these estimates, the relativistic object in the SS433 system is the black hole; its mass is >8M⊙. The ellipticity of the orbit is consistent with the “slaved” accretion disc model. The results obtained made it possible to understand why SS433 evolves as the semi-detached binary instead of the common envelope system.

Radio loudness and spindown of pulsars in Einstein-aether gravity

The exact analytic solutions of Maxwell equations for magnetic field exterior to a slowly rotating magnetized relativistic star in Einstein-aether gravity have been obtained. The obtained analytical expressions were used to derive Goldreich–Julian charge density in plasma magnetosphere and solutions of Poisson equation for the unscreened electric field being parallel to the magnetic field lines in the presence of the aether theory parameters were obtained. As astrophysical applications, we have explored the effects of Einstein-aether gravity on total energy losses of rotating magnetized relativistic star due to magnetodipolar and magnetospheric electromagnetic radiations. The performed study of deathline of radio pulsars through inverse Compton and curvature radiation shows that the position of deathline shifts up (down) in period and its derivative space, so-called P − P ̇ diagram in the presence of larger values of the Einstein-aether gravity parameter c 13 ( c 14 ). Finally, we have provided upper limits for Einstein-aether gravity parameters using observational data on precise measurements of periods of rotation from the different types of isolated neutron stars. In particular, we have shown that some combinations and range of the Einstein-aether are excluded from pulsar observations.

Separable Hamiltonian PDEs and Turning Point Principle for Stability of Gaseous Stars

AbstractWe consider stability of nonrotating gaseous stars modeled by the Euler‐Poisson system. Under general assumptions on the equation of states, we proved a turning point principle (TPP) that the stability of the stars is entirely determined by the mass–radius curve parametrized by the center density. In particular, the stability can only change at extrema (i.e., local maximum or minimum points) of the total mass. For a very general equations of state, TPP implies that for increasing center density the stars are stable up to the first mass maximum and unstable beyond this point until the next mass extremum (a minimum). Moreover, we get a precise counting of unstable modes and exponential trichotomy estimates for the linearized Euler‐Poisson system. To prove these results, we develop a general framework of separable Hamiltonian PDEs. The general approach is flexible and can be used for many other problems, including stability of rotating and magnetic stars, relativistic stars, and galaxies. © 2021 Wiley Periodicals LLC.

Effects of modified dispersion relations on free Fermi gas: Equations of state and applications in astrophysics

Deformed dispersion relations are considered in the study of equations of state of Fermi gas with applications to compact objects. Different choices of deformed energy relations are used in the formulation of our model. As a first test, we consider a relativistic star with a simple internal structure. The mass-radius diagrams obtained suggest a positive influence of deformed Fermi gas, depending of the functions employed. In addition, we comment on how realistic equations of state, in which interactions between nucleons are taken into account, can be addressed.

Ricci-Determinant gravity: Dynamical aspects and astrophysical implications

The Palatini gravitational action is enlarged by an arbitrary function $f(\mathbit{X})$ of the determinants of the Ricci tensor and the metric, $\mathbit{X}=|\mathbf{det}.R|/|\mathbf{det}.g|$. The resulting Ricci-determinant theory exhibits novel deviations from general relativity. We study a particular realization where the extension is characterized by the square-root of the Ricci determinant, $f(\mathbit{X})={\ensuremath{\lambda}}_{\mathrm{Edd}}\sqrt{\mathbit{X}}$, which corresponds to the famous Eddington action. We analyze the obtained equations for perfect fluid source and show that the affine connection can be solved in terms of the energy density and pressure of the fluid through an obtained disformal metric. As an application, we derive the hydrostatic equilibrium equations for relativistic stars and inspect the significant effects induced by the square-root of the Ricci tensor. We find that an upper bound on ${\ensuremath{\lambda}}_{\text{Edd}}$, at which deviations from the predictions of general relativity on neutron stars become prominent, corresponds to the hierarchy between the Planck and the vacuum mass scales. The Ricci-determinant gravity that we propose here is expected to have interesting implications in other cosmological domains.

Polar Quasinormal Modes of Neutron Stars in Massive Scalar-Tensor Theories

We study polar quasinormal modes of relativistic stars in scalar-tensor theories, where we include a massive gravitational scalar field and employ the standard Brans-Dicke coupling function. For the potential of the scalar field we consider a simple mass term as well as a potential associated withR2gravity. The presence of the scalar field makes the spectrum of quasinormal modes much richer than the spectrum in General Relativity. We here investigate radial modes (l= 0) and quadrupole modes (l= 2). The general relativisticl= 0 normal modes turn into quasinormal modes in scalar-tensor theories, that are able to propagate outside of the stars. In addition to the pressure-led modes new scalar-ledϕ-modes arise. We analyze the dependence of the quasinormal mode frequencies and decay times on the scalar field mass.

Compact stars in f(ℛ,𝒢,𝒯 ) gravity

This work is to introduce a new kind of modified gravitational theory, named as [Formula: see text] (also [Formula: see text]) gravity, where [Formula: see text] is the Ricci scalar, [Formula: see text] is Gauss–Bonnet invariant and [Formula: see text] is the trace of the energy–momentum tensor. With the help of different models in this gravity, we investigate some physical features of different relativistic compact stars. For this purpose, we develop the effectively modified field equations, conservation equation, and the equation of motion for test particle. Then, we check the impact of additional force (massive test particle followed by a nongeodesic line of geometry) on compact objects. Furthermore, we took three notable stars named as [Formula: see text], [Formula: see text] and [Formula: see text]. The physical behavior of the energy density, anisotropic pressures, different energy conditions, stability, anisotropy, and the equilibrium scenario of these strange compact stars are analyzed through various plots. Finally, we conclude that the energy conditions hold, and the core of these stars is so dense.

Neutron stars in f(R,T) gravity with conserved energy-momentum tensor: Hydrostatic equilibrium and asteroseismology

We investigate the equilibrium and radial stability of spherically symmetric relativistic stars, considering a polytropic equation of state (EoS), within the framework of f(R,T) gravity with a conservative energy-momentum tensor. Both modified stellar structure equations and Chandrasekhar's pulsation equations are derived for the f(R,T)= R+ h(T) gravity model, where the function h(T) assumes a specific form in order to safeguard the conservation equation for the energy-momentum tensor. The neutron star properties, such as radius, mass, binding energy and oscillation spectrum are studied in detail. Our results show that a cusp — which signals the appearance of instability — is formed when the binding energy is plotted as a function of the compact star proper mass. We find that the squared frequency of the fundamental vibration mode passes through zero at the central-density value corresponding to such a cusp where the binding energy is a minimum.

Mass correction and deformation of slowly rotating anisotropic neutron stars based on Hartle\u2013Thorne formalism

Due to their compactness, neutron stars are the best study matter in high density and strong-field gravity. Hartle and Thorne have proposed a good approximation or perturbation procedure within general relativity for slowly rotating relativistic stars by assuming the matter inside the stars is an ideal isotropic fluid. This study extends the analytical Hartle–Thorne formalism for slowly rotating neutron stars, including the possibility that the neutron star pressure can be anisotropic. We study the impact of neutron stars’ anisotropy pressure on mass correction and deformation numerically. For the anisotropic model, we use the Bowers-Liang model. For the equation of state of neutron stars, we use a relativistic mean-field BSP parameter set with the hyperons, and for the crust equation of state, we use the one of Miyatsu et al. We have found that the mass of neutron stars increases but the radius decreases by increasing lambda _{BL} value. Therefore, the NS compactness increases when lambda _{BL} becomes larger. This fact leads to a condition in which NS is getting harder to deformed when the lambda _{BL} increased.