General Relativistic Stellar Models Research Articles

Charged radiating stars with Lie symmetries

We consider the general model of an accelerating, expanding and shearing radiating star in the presence of charge. Using a new set of variables arising from the Lie symmetries of differential equations we transform the boundary equation into ordinary differential equations. We present several new exact models for a charged gravitating sphere. A particular family of solution may be interpreted as a generalised Euclidean star in the presence of the electromagnetic field. This family admits a linear barotropic equation of state. In the uncharged limit, we regain general relativistic stellar models where proper and areal radii are equal, and its generalisations. Our group theoretical approach selects the physically important cases of Euclidean stars and equations of state.

Analytical Solutions of the Riccati Equation with Coefficients Satisfying Integral or Differential Conditions with Arbitrary Functions

Ten new exact solutions of the Riccati equation dy/dx = a(x) + b(x)y + c(x)y² are presented. The solutions are obtained by assuming certain relations among the coefficients a(x), b(x) and c(x) of the Riccati equation, in the form of some integral or differential expressions, also involving some arbitrary functions. By appropriately choosing the form of the coefficients of the Riccati equation, with the help of the conditions imposed on the coefficients, we obtain ten new integrability cases for the Riccati equation. For each case the general solution of the Riccati equation is also presented. The possibility of the application of the obtained mathematical results for the study of anisotropic general relativistic stellar models is also briefly considered.

Proof that static stellar models are spherical

We give a proof that static general-relativistic stellar models, in other words static perfect fluid stars in asymptotically-flat spacetimes, are spherically symmetric for physically reasonable equations of state. The analysis may also be of independent interest for differential geometric rigidity theorems.

On the spherical symmetry of static stellar models

This paper completes the proof of the necessity of spherical symmetry in the static general-relativistic stellar models that have equations of state satisfying certain inequalities. The technical assumption — that there exists a “reference spherical stellar model” — that was essential in the previous discussions of this problem is removed. This paper also extends beyond previous discussions the class of equations of state included in the proof. The analysis of the equations for spherical stellar models, used here to demonstrate the existence of a “reference spherical model,” may also be of independent interest.

The effects of thermal radiation on some general relativistic stellar models

We study the effects of heat flow on the evolution of two different families of self-gravitating, radiating spheres. The sensitivity of the system of differential equations, governing the evolution of the boundary surface, to the emission of radiation is brought out

Relation of gauge formalisms for pulsations of general-relativistic stellar models.

There have been two recent reformulations of the equations for even-parity perturbations of general-relativistic stellar models, in both of which fluid perturbation variables are absent in the final set of equations. The recent reformulation by Chandrasekhar and Ferrari uses the diagonal coordinate gauge and leads to a fifth-order system of differential equations; we have recently presented a reformulation, based on the Regge-Wheeler coordinate gauge, which leads to a fourth-order system. The difference in the orders is similar to that for perturbations of Schwarzschild and of Reissner-Nordstroem black holes; in both cases the diagonal-gauge formulation led to a system one degree higher than that for equations based on the Regge-Wheeler gauge. For perturbations of holes, however, the equations could be reduced by one degree. We show that this is the case also for the Chandrasekhar-Ferrari equations for stellar perturbations. More important, we show that the extra degree of freedom, in all descriptions based on the diagonal gauge, is due to the fact that the diagonal gauge is an incomplete constraint on coordinates; a one degree of freedom set of gauge transformations can be made within the diagonal gauge. This previously unnoticed degree of freedom is responsible for the extra degree ofmore » freedom in the Chandrasekhar-Ferrari equations, and the related black-hole equations. It also provides an {ital a} {ital priori} solution with which those equations can be reduced.« less

Shear as a source of inhomogeneity in general relativistic stellar models

We investigate the class of spherically symmetric, anisotropic (principal stresses unequal) fluids admitting the existence of a vector field, assumed to be orthogonal to the four velocity of the fluid, and with respect to which the Lie derivative of the metric tensor is proportional to the shear tensor. The physical variables, as well as the evolution equation of the bounday surface, are found for different models.

On the chaotic behaviour induced by surface phenomena in some general relativistic stellar models

The effects of surface phenomena on the evolution of the boundary of some general relativistic compact objects are analyzed. In particular it is shown that for a subfamily of these objects which expand permanently in the absence of surface phenomena, the presence of arbitrarily small surface tension leads to bounded configurations.

The accuracy of the relativistic Cowling approximation

view Abstract Citations (39) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Accuracy of the Relativistic Cowling Approximation Lindblom, Lee ; Splinter, Randall J. Abstract The accuracy of two versions of the relativistic Cowling approximation for the oscillations of general relativistic stellar models are investigated: one by McDermott et al. (1983) and a refinement by Finn (1988). The oscillation frequencies and the viscous damping time scales of several of the lowest frequency dipole p-modes in these approximations are compared to the exact values for these quantities. The accuracy of the Cowling approximation improves as the number of nodes in the eigenfunctions of the mode increases. Furthermore, the McDermott version of the Cowling approximation is more accurate than Finn's refined version for the low-order p-modes studied here. Publication: The Astrophysical Journal Pub Date: January 1990 DOI: 10.1086/168227 Bibcode: 1990ApJ...348..198L Keywords: Gravitational Fields; Relativistic Theory; Stellar Gravitation; Stellar Models; Stellar Oscillations; Computational Astrophysics; Energy Dissipation; Perturbation Theory; Astrophysics; RELATIVITY; STARS: PULSATION full text sources ADS |

Surface phenomena in general relativistic stellar models: critical mass and stability

The influence of surface phenomena on general relativistic stellar models is investigated, with particular emphasis on the critical mass value and the adiabatic stability. It will be shown, in a particular model, that for a given radius, the maximum value of the total mass (compatible with a static, singularity-free configuration) is a decreasing function of the surface tension coefficient. It will also be shown that the inclusion of surface phenomena enhances the adiabatic instability of the model in the high density regime.

Effects of nuclear equation of state on general relativistic stellar core collapse models

The consequences of the equation of state above nuclear density, parameterized by a compressibility and an adiabatic index, for the strength of the reflected shock wave following core bounce in stellar collapse are studied using a hydrodynamic model. Particular attention is paid to the amplification of the shock strength when bounce occurs near those critical parameters which would result in continued collapse to the black hole. Comparisons are made to models where Newtonian hydrodynamics is assumed, and the relativistic effects are contrasted with the dependence on the homologous core mass. The dependence of the collapsed core mass (and the Newtonian shock strength) on the (constant) electron fraction Y(e) is shown. 22 references.

On the nonradial pulsations of general relativistic stellar models

view Abstract Citations (128) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the nonradial pulsations of general relativistic stellar models Detweiler, S. ; Lindblom, L. Abstract The present nonsingular fourth-order system of equations for the nonradial pulsations of general relativistic stellar models represents an improvement over previous discussions which employed fifth-order systems, or regular fourth-order ones, to describe the pulsations. Attention is given to the nonsingular power series solutions to these equations near r = zero. In order to further investigate the reliability of previously published results, a novel computer code is developed which evaluates the eigenfrequencies of the quasi-normal modes of general relativistic stellar models by integrating the nonsingular equations. Publication: The Astrophysical Journal Pub Date: May 1985 DOI: 10.1086/163127 Bibcode: 1985ApJ...292...12D Keywords: Nonlinear Equations; Pulsars; Relativistic Effects; Singularity (Mathematics); Stellar Models; Stellar Oscillations; Equations Of State; Error Analysis; Perturbation Theory; Power Series; Astrophysics full text sources ADS |

Some properties of static general relativistic stellar models. II

We expand here the study of the type of identity which has been successfully used to prove the necessity of spherical symmetry in static black holes and uniform density stellar models. We show how the system of partial differential equations, whose solutions correspond to these identities, can be decoupled and partially integrated for fluids with an arbitrary equation of state. The problem of finding such identities is reduced thereby to the problem of finding the solutions to a single ordinary differential equation, plus quadratures.

Some properties of static general relativistic stellar models

A number of properties of static general relativistic stellar models are presented which appear to be relevant to the ongoing search for a proof that all such models must have spherical symmetry. It is shown that any such model, having conformally flat spatial sections, must have spherical symmetry. A general procedure is described which allows one to construct the type of ’’divergence equals positive quantity’’ identities for static stellar models, which were used to prove that static black holes must have spherical symmetry. This procedure is used to produce a large new class of identities for the exterior vacuum regions of static stellar models and identities are constructed for the interior regions of uniform density models. These identities are used to prove that static uniform density stellar models must have spherical symmetry.

Stars with degenerate neutron cores. I - Structure of equilibrium models

view Abstract Citations (286) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Stars with degenerate neutron cores. I. Structure of equilibrium models. Thorne, K. S. ; Zytkow, A. N. Abstract Possible equilibrium states are investigated for a star consisting of a massive nondegenerate envelope surrounding a degenerate neutron core. General-relativistic stellar models are constructed that are spherically symmetric, nonrotating, devoid of magnetic fields, and in slowly evolving equilibrium states. Three interior regions are delineated, and the structure of each region is analyzed. Numerical models corresponding to red giants and supergiants are presented in which the large diffuse envelope is separated from the compact core by a thin (about 40 meters thick) nearly isothermal layer, or 'halo', where all the gravitational energy release occurs. Observable features of the models are considered along with their stability and evolution. Publication: The Astrophysical Journal Pub Date: March 1977 DOI: 10.1086/155109 Bibcode: 1977ApJ...212..832T Keywords: Late Stars; M Stars; Neutron Stars; Stellar Models; Stellar Structure; Supergiant Stars; Helium; Hydrogen; Relativity; Stellar Envelopes; Stellar Luminosity; Astrophysics full text sources ADS |

Nonradial Pulsation of General-Relativistic Stellar Models.VI. Corrections

view Abstract Citations (41) References (6) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonradial Pulsation of General-Relativistic Stellar Models.VI. Corrections Ipser, James R. ; Thorne, Kip S. Abstract The equations governing the nonradial pulsations of general-relativistic stellar models are shown to form a fourth-order system, rather than a fifth-order system as was believed previously. Incorrect statements about the application of boundary conditions at the stellar surface are also rectified. The errors corrected here do not invalidate any of the final results obtained in previous papers of this series. Subject headings: neutron stars - pulsation - relativity Publication: The Astrophysical Journal Pub Date: April 1973 DOI: 10.1086/152040 Bibcode: 1973ApJ...181..181I full text sources ADS | Related Materials (5) Part 1: 1967ApJ...149..591T Part 2: 1969ApJ...155..163P Part 3: 1969ApJ...158....1T Part 4: 1969ApJ...158..997T Part 5: 1970ApJ...159..847C

Nonradial Pulsation of General-Relativistic Stellar Models. V. Analytic Analysis for L = 1

view Abstract Citations (82) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Nonradial Pulsation of General-Relativistic Stellar Models. V. Analytic Analysis for L = 1 Campolattaro, Alfonso ; Thorne, Kip S. Abstract The theory of small, adiabatic, dipole perturbations of a star away from hydrostatic equilibrium is developed within the framework of general relativity. The analysis is linearized in the perturbation amplitudes. The "odd-parity" perturbations describe differential rotation, while the "even-parity" perturbations describe pulsation. In the pulsational case there are two degrees of freedom associated with the fluid motion and no degrees of freedom in the gravitational field (no dipole gravitational waves). During the pulsation the star's external gravitational field is completely unperturbed, to first order in the amplitude, despite the fact that its surface performs a finite, back-and-forth motion. In both the pulsational and rotational cases, the Einstein field equations are put into simple forms suitable for numerical integration. Publication: The Astrophysical Journal Pub Date: March 1970 DOI: 10.1086/150362 Bibcode: 1970ApJ...159..847C full text sources ADS | Related Materials (5) Part 1: 1967ApJ...149..591T Part 2: 1969ApJ...155..163P Part 3: 1969ApJ...158....1T Part 4: 1969ApJ...158..997T Part 6: 1973ApJ...181..181I

Nonradial Pulsation of General-Relativistic Stellar Models. III. Analytic and Numerical Results for Neutron Stars

Nonradial Pulsation of General-Relativistic Stellar Models. III. Analytic and Numerical Results for Neutron Stars

Non-Radial Pulsation of General-Relativistic Stellar Models. II. Properties of the Gravitational Waves

view Abstract Citations (105) References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Non-Radial Pulsation of General-Relativistic Stellar Models. II. Properties of the Gravitational Waves Price, Richard ; Thorne, Kip S. Abstract An analysis is presented of the properties of the gravitational waves emitted by a fully relativistic, non-rotating stellar model, which is pulsating in a non-radial manner. Attention is focused on quasi- normal-mode pulsations in which the star is excited at some initial moment of time, it radiates gravita- tional waves thereafter, and these waves gradually damp its nearly periodic pulsations. For such quasi- normal modes a discussion is presented of the polarization of the gravitational waves and of the energy, momentum, and angular momentum which the waves transport Publication: The Astrophysical Journal Pub Date: January 1969 DOI: 10.1086/149857 Bibcode: 1969ApJ...155..163P full text sources ADS | Related Materials (5) Part 1: 1967ApJ...149..591T Part 3: 1969ApJ...158....1T Part 4: 1969ApJ...158..997T Part 5: 1970ApJ...159..847C Part 6: 1973ApJ...181..181I

A Catalogue of Methods for Studying the Normal Modes of Radial Pulsation of General-Relativistic Stellar Models

A Catalogue of Methods for Studying the Normal Modes of Radial Pulsation of General-Relativistic Stellar Models