Self-gravitating Stars Research Articles

Dynamical instability of charged self-gravitating stars in modified gravity

This paper explores the instability limits for the stellar objects in the background of a particular modified gravity theory. In order to accomplish the instability conditions, a spherically symmetric anisotropic charged fluid influenced by the modified gravity is taken under consideration. The modified field equations and the equations of motion are accomplished in background of the Gauss–Bonnet gravity. These equations are perturbed to constitute the collapse equation. The Newtonian and post-Newtonian limits are imposed and found that the dynamical instability of the fluid is explained by the adiabatic index which consists on analytical value depending on static profile of material variables.

Polytropic stars in bootstrapped Newtonian gravity

We study self-gravitating stars in the bootstrapped Newtonian picture for polytropic equations of state. We consider stars that span a wide range of compactness values. Both matter density and pressure are sources of the gravitational potential. Numerical solutions show that the density profiles can be well approximated by Gaussian functions. Later we assume Gaussian density profiles to investigate the interplay between the compactness of the source, the width of the Gaussian density profile and the polytropic index. We also dedicate a section to comparing the pressure and density profiles of the bootstrapped Newtonian stars to the corresponding General Relativistic solutions. We also point out that no Buchdahl limit is found, which means that the pressure can in principle support a star of arbitrarily large compactness. In fact, we find solutions representing polytropic stars with compactness above the Buchdhal limit.

Dynamical analysis of self-gravitating stars in modified Gauss-Bonnet gravity

In this paper, we have continued the work of Herrera \emph{et al.} \cite{herrera2012dynamical} in $f(G)$ gravitational theory. For this purpose, a spherically symmetric fluid exhibiting locally anisotropic pressure along with the energy density, is taken under consideration. The perturbation scheme is imposed on modified field equations and the dynamical equations. The collapse equation is devised from these perturbed equations which stimulates to disclose the instability zone under both Newtonian and post-Newtonian constraints. It is wrapped up by concluding that dynamical instability is interpreted by the adiabatic index $\Gamma$ which relies on the anisotropic pressure, energy density and the dark source terms due to $f(G)$ gravity.

Structure of polytropic stars in General Relativity

The inner structure of a star or a primordial interstellar cloud is a major topic in classical and relativistic physics. The impact that General Relativistic principles have on this structure has been the subject of many research papers. In this paper we consider within the context of General Relativity a prototype model for this problem by assuming that a star consists of polytropic gas. To justify this assumption we observe that stars undergo thermodynamically irreversible processes and emit heat and radiation to their surroundings. Due to the emission of this energy it is worthwhile to consider an idealized model in which the gas is polytropic. To find interior solutions to the Einstein equations of General Relativity in this setting we derive a single equation for the cumulative mass distribution of the star and use Tolman-Oppenheimer-Volkoff equation to derive formulas for the isentropic index and coefficient. Using these formulas we present analytic and numerical solutions for the polytropic structure of self-gravitating stars and examine their stability. We prove also that when the thermodynamics of a star as represented by the isentropic index and coefficient is known, the corresponding matter density within the star is uniquely determined.

Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein–Gordon wave equation for a linearized scalar field of mass mu and proper frequency omega in the curved background of a spherically symmetric compact reflecting star of mass M and radius R_{text {s}}. It is proved that the regime of existence of these stationary composed star–field configurations is characterized by the simple inequalities 1-2M/R_{text {s}}<(omega /mu )^2<1. Interestingly, in the regime M/R_{text {s}}ll 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {omega (M,R_{text {s}},mu )}^{n=infty }_{n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star–linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star–field configurations with direct numerical computations.

Dynamical analysis of self-gravitating stars in f(R,T) gravity

We study the factors affecting the stability of a locally isotropic spherical self-gravitating systems in f(R,T) gravity, where R is the Ricci curvature invariant and T is the trace of stress-energy tensor. Specifically, the collapse equation is obtained from conservation laws with non-null expansion scalar at Newtonian and post-Newtonian approximations. Initially, we consider the hydrostatic phase of the system which upon radial perturbation provides linearized field equations. This approach gives rise to specific instability constraints to ensure the collapsing behavior of the spherical isotropic fluid distribution. Finally, we discuss the role played by matter variables in this perspective.

On the stability of a class of radiating viscous self-gravitating stars with axial symmetry

This study investigates the stability of a class of radiating viscous self-gravitating stars with axial symmetry having anisotropic pressure. We use perturbation technique to establish the perturbed form of the Einstein field equations and dynamical equations. The instability range in the Newtonian and post-Newtonian eras has been analyzed by constructing the collapse equation. It is found that the adiabatic index has a key role in the discussion of instability ranges which depends upon the physical parameters, i.e., energy density, anisotropic pressure and shear viscosity of the fluid and heat flux. We conclude that the shear viscosity decreases the instability range and makes the system more stable.

Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit

We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.

Critical Dimension for Stable Self-Gravitating Stars in AdS

We study the self-gravitating stars with a linear equation of state, P = aρ, in AdS space, where a is a constant parameter. There exists a critical dimension, beyond which the stars are always stable with any central energy density; below which there exists a maximal mass configuration for a certain central energy density and when the central energy density continues to increase, the configuration becomes unstable. We find that the critical dimension depends on the parameter a, it runs from d = 11.1429 to 10.1291 as a varies from a = 0 to 1. The lowest integer dimension for a dynamically stable self-gravitating configuration should be d = 12 for any a ∊ [0, 1] rather than d = 11, the latter is the case of self-gravitating radiation configurations in AdS space.

Statistical mechanics of systems with long range interactions

Many physical systems are governed by long range interactions, the main example being self-gravitating stars. Long range interaction implies a lack of additivity for the energy. As a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with many claims, the statistical mechanics of such systems is a well understood subject. In this proceeding, we explain briefly the classical way to equilibrium and non equilibrium statistical mechanics, starting from first principles and emphasizing some new results.At equilibrium, we explain how the Boltzmann-Gibbs entropy can be proved to be the appropriate one, using large deviations tools. We explain the thermodynamics consequences of the lack of additivity, like the generic occurence of statistical ensemble inequivalence and negative specific heat. This well known behavior is not the only way inequivalence may occur, as emphasized by a recent new classification of phase transitions and ensemble inequivalence in systems with long range interaction. We note a number of generic situations that have not yet been observed in any physical systems.Out of equilibrium, we show that algebraic temporal correlations or anomalous diffusion may occur in these systems, and can be explained using usual statistical mechanics and kinetic theory.

On the Thermal Instability in a Contracting Cloud and Formation of a Bound Cluster

We perform linear analysis of thermal instability in a contracting large cloud filled with warm H I gas and investigate the effect of metallicity and radiation flux. When the cloud reaches critical density nf, the cloud fragments into cool, dense condensations because of thermal instability. For a lower metallicity gas cloud, the value of nf is high. Collision between condensations will produce self-gravitating clumps and stars thereafter. From the result of the calculations, we suggest that high star formation efficiency and bound cluster formation are realized in low-metallicity and/or strong-radiation environments.

HYDRODYNAMICAL MODELS OF GASEOUS STARS

We revisit the main results concerning the local and global existence and the stability of solutions for some simplified models of self-gravitating stars used in astrophysical hydrodynamics, with an emphasis on the spherical situation.

Two newly discovered millisecond pulsars

Two millisecond pulsars have been discovered in the course of systematic surveys being made with the Arecibo radio telescope. PSR J2019 + 2425 has a 3.935 ms period and moves in a nearly circular, 76.5 day orbit around a about 0.3 solar mass companion. PSR J2322 + 2057, with a period of 4.808 ms, is an isolated object. The two pulsars have unusually small period derivatives, corresponding to spin-down time scales of 7.5 +/- 0.5 and 11 +/- 5 Gyr, respectively. Both objects show pulse time-of-arrival residuals no larger than a few microseconds over many months, lending further support to the observation that 'recycled' pulsars have extremely stable rotational behavior. The timing results also confirm that physics related to the rotational dynamics of these strongly self-gravitating stars - in particular, the value of the gravitational coupling constant G - remains essentially constant over time scales comparable to the Hubble time. Dispersion measures of the two pulsars indicate distances of 0.8-0.9 kpc.

Spherical shock wave propagation in self-gravitating stars

The problem of shock wave propagation in a heat-conducting and self-gravitating medium has been studied. The shock is strong enough so that the ambient gas pressure can be neglected. The variation of velocity, density, temperature, and mass distributions behind the shock have been obtained from a numerical solution of similarity equations involved.

Fission sequence and equilibrium models of rigidity rotating polytropes

Equilibrium sequences of self-gravitating and polytropic stars including binary stars are computed for various polytropic indexes. We find a fission sequence from an ellipsoidal configuration to a binary by way of dumb-bell equilibrium.