Neutron stars in Scalar-Tensor-Vector Gravity

Scalar-Tensor-Vector Gravity (STVG), also referred as Modified Gravity (MOG), is an alternative theory of the gravitational interaction. Its weak field approximation has been successfully used to describe Solar System observations, galaxy rotation curves, dynamics of clusters of galaxies, and cosmological data, without the imposition of dark components. The theory was formulated by John Moffat in 2006. In this work, we derive matter-sourced solutions of STVG and construct neutron star models. We aim at exploring STVG predictions about stellar structure in the strong gravity regime. Specifically, we represent spacetime with a static, spherically symmetric manifold, and model the stellar matter content with a perfect fluid energy-momentum tensor. We then derive the modified Tolman–Oppenheimer–Volkoff equation in STVG and integrate it for different equations of state. We find that STVG allows heavier neutron stars than General Relativity (GR). Maximum masses depend on a normalized parameter that quantifies the deviation from GR. The theory exhibits unusual predictions for extreme values of this parameter. We conclude that STVG admits suitable spherically symmetric solutions with matter sources, relevant for stellar structure. Since recent determinations of neutron stars masses violate some GR predictions, STVG appears as a viable candidate for a new gravity theory.     

Anisotropic quark stars in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) gravity

The aim of this paper is to analyze the nature of anisotropic spherically symmetric relativistic star models in the framework of f(R, T) gravity. To discuss the features of compact stars, we consider that in the interior of the stellar system, the fluid distribution is influenced by MIT bag model equation of state. We construct the field equations by employing Krori–Barua solutions and obtain the values of unknown constants with the help of observational data of Her X-1, SAX J 1808.4-3658, RXJ 1856-37 and 4U1820-30 star models. For a viable f(R, T) model, we study the behavior of energy density, transverse as well as radial pressure and anisotropic factor in the interior of these stars for a specific value of the bag constant. We check the physical viability of our proposed model and stability of stellar structure through energy conditions, causality condition and adiabatic index. It is concluded that our model satisfies the stability criteria as well as other physical requirements, and the value of bag constant is in well agreement with the experimental value which highlights the viability of our considered model.     

Spherical conformal models for compact stars

We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass–radius limit and the surface red shift are consistent with observational constraints.     

Anisotropic relativistic stellar models

We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.     

Quark matter imprint on gravitational waves from oscillating stars

We discuss the possibility that the detection of gravitational waves emitted by compact stars may allow to constrain the MIT bag model of quark matter equation of state. Our results show that the combined knowledge of the frequency of the emitted gravitational wave and of the mass, or the radiation radius, of the source allows one to discriminate between strange stars and neutron stars and set stringent bounds on the bag constants.     

Gravitational loss-cone instability

We study physical corollaries of the existing analogy between the simplest plasma traps (mirror traps) and star clusters surrounding massive black holes or dense galactic nuclei. There is a loss cone in the system through which plasma particles with low velocities transverse to the trap axis or, similarly, stars with low angular momenta (destroyed or absorbed by the central body) escape. The consequences of the “beam-like” deformation of the plasma distribution function in a trap are well known: a peculiar loss-cone instability producing a plasma flow into the loss cone develops as a result. We show that a similar gravitational loss-cone instability can also arise under certain conditions in the galactic case of interest to us. This instability is related to the slow precessional motions of highly elongated (nearly radial) stellar orbits and the main condition for its growth is that the precession of such orbits be retrograde (in the direction opposite to the orbital rotation of stars). Only under this condition do oscillations that can become unstable in the presence of a loss cone arise instead of the radial orbit instability (a variety of the Jeans instability in systems with highly elongated orbits) that takes place in the case of prograde precession. The instability produces a stream of stars onto the galactic center, i.e., serves as a mechanism of fueling the nuclear activity of galaxies. For a mathematical analysis, we have obtained relatively simple characteristic equations that describe small perturbations in a sphere of radially highly elongated stellar orbits. These characteristic equations are derived through a number of successive simplifications from a general linearized system of equations, including the collisionless Boltzmann kinetic equation and the Poisson equation (in action-angle variables). The central point of our analysis of the characteristic equations is preliminary detection of neutral modes (or proof of their absence in the case of stability).     

Dynamical Evolution and Leading Order Gravitational Wave Emission of Riemann-S Binaries

An approximate strategy for studying the evolution of binary systems of extended objects is introduced. The stars are assumed to be polytropic ellipsoids. The surfaces of constant density maintain their ellipsoidal shape during the time evolution. The equations of hydrodynamics then reduce to a system of ordinary differential equations for the internal velocities, the principal axes of the stars and the orbital parameters. The equations of motion are given within Lagrangian and Hamiltonian formalism. The special case when both stars are axially symmetric fluid configurations is considered. Leading order gravitational radiation reaction is incorporated, where the quasi-static approximation is applied to the internal degrees of freedom of the stars. The influence of the stellar parameters, in particular the influence of the polytropic index n, on the leading order gravitational waveforms is studied.     

Strong energy condition and the repulsive character of <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The Raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of Einstein’s equations, playing a central role for the understanding of the gravitational interaction in cosmology. In General Relativity, without considering a cosmological constant, a non-positive contribution in the Raychaudhuri equation is usually interpreted as the manifestation of the attractive character of gravity. In this case, particular energy conditions—indeed the strong energy condition—must be assumed in order to guarantee the attractive character. In the context of f(R) gravity, however, even assuming the standard energy conditions one may have a positive contribution to the Raychaudhuri equation. Besides providing a simple way to explain the observed cosmic acceleration, this fact opens the possibility of a repulsive character of this kind of gravity. In order to discuss physical bounds on f(R) models, we address the attractive/non-attractive character of f(R) gravity considering the Raychaudhuri equation and assuming the strong energy condition along with recent estimates of the cosmographic parameters.     

Relativistic stellar models

We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.     

The reflection of gravitational waves from compact stars

It is shown that gravitational waves reflect from sufficiently dense stellar objects. The condition of reflection is found and the reflection index, which reaches a value of 25% for neutron stars, is estimated.     

Generating Interior Sources for the Reissner-Nordström Metric

We study the Einstein-Maxwell equations for isotropic pressure distributions. We postulate a relationship between the electric field intensity and one of the gravitational potentials. An algorithm is developed that allows us to systematically generate new classes of exact solutions for charged relativistic stars. The solutions are expressed in terms of simple elementary functions; it is possible to parametrize the solutions so that different values of a constant allows us to tabulate the models. For a particular class it is possible to generate models without any integration. We study the qualitative features of a particular solution, and show that it is physically reasonable in the region of a spherical shell surrounding the centre.     

热中子星r-mode 不稳定性的研究

理论上,不稳定的中子星r-mode 能辐射可探测的引力波。采用具有超软对称能的非对称核物质物态方程,并考虑非牛顿引力效应影响,数值计算了由于CFS(Chandrasekhar-Friedmann-Schutz) 不稳定性引起的年轻热中子星的r-mode 不稳定窗口,给出了引力辐射时标和耗散时标随温度的变化关系。利用中子星观测对非牛顿引力参数的约束,给出了热中子星在高温区不稳定窗口边界的约束,并发现较大的非牛顿引力参数对应着较宽的r-mode 不稳定窗口。研究结果可为地面引力辐射探测提供有意义的参考。Theoritically, instable r-mode in neutron star may radiate detectable gravitational waves. In this work,considering the non-Newtonian gravity proposed in the grand unification theories, we numerically calculate the CFS instabilities of r-mode s in the hot neutron stars by using an equation of state with super-soft symmetry energies. The changes of the gravitational radiation time scales and the viscous time scales versus the stellar temperatures are obtained.And according to the constraint of the neutron star observation on the parameter of non-Newtonian gravity, the constraint on the boundary of the instability window is also given. It is found that a stronger non-Newtonian gravity corresponds with a wider r-mode instability window. These results may provide interesting reference for the gravitational wave detection.     

Classes of exact Einstein–Maxwell solutions

We find new classes of exact solutions to the Einstein–Maxwell system of equations for a charged sphere with a particular choice of the electric field intensity and one of the gravitational potentials. The condition of pressure isotropy is reduced to a linear, second order differential equation which can be solved in general. Consequently we can find exact solutions to the Einstein–Maxwell field equations corresponding to a static spherically symmetric gravitational potential in terms of hypergeometric functions. It is possible to find exact solutions which can be written explicitly in terms of elementary functions, namely polynomials and product of polynomials and algebraic functions. Uncharged solutions are regainable with our choice of electric field intensity; in particular we generate the Einstein universe for particular parameter values.     

The gravitational field of spherically symmetric matter distributions in the Yang-Mills gauge theory of gravity

In the new SO(1,3)-gauge theory of gravity, the exterior gravitational field of any spherically symmetric equilibrium distribution of matter and non-gravitational force fields is determined by two parameters, the gravitational mass M and the structure parameter γ. We discuss the physical interpretation of the parametrized post-Newtonian parameter γ in this theory of gravity. The boundary conditions fix uniquely the values of M and γ; it turns out that γ ? 1 is a measure for the gravitational binding of the source. In the Newtonian limit, stars with negligible radiation pressure are characterized by $\text{γ=1?}\text{2}\text{3}\text{M}\text{R}$, while radiation-dominated stellar structures may even have γ > 1; the value of γ for tightly bound neutron stars of one solar mass is about 0.9.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Hypergeometric Equation in Modeling Relativistic Isotropic Sphere

We study the Einstein system of equations in static spherically symmetric spacetimes. We obtained classes of exact solutions to the Einstein system by transforming the condition for pressure isotropy to a hypergeometric equation choosing a rational form for one of the gravitational potentials. The solutions are given in simple form that is a desirable requisite to study the behavior of relativistic compact objects in detail. A physical analysis indicate that our models satisfy all the fundamental requirements of realistic star and match smoothly with the exterior Schwarzschild metric. The derived masses and densities are consistent with the previously reported experimental and theoretical studies describing strange stars. The models satisfy the standard energy conditions required by normal matter.     

Brownian motion in gravitationally interacting systems

We derive a model that describes the dynamics of a Brownian particle, such as a massive black hole, in a stellar system dominated by gravitational forces, and examine whether it achieves a state of equipartition of kinetic energy with the stars. This problem has been considered before only for stellar systems with an isothermal Maxwellian distribution of velocities; here we study other examples and confirm our calculations with N-body simulations. We show that in certain cases the black hole's steady state kinetic energy can be very far from equipartition.     

Separable metrics and radiating stars

We study the junction condition relating the pressure to heat flux at the boundary of an accelerating and expanding spherically symmetric radiating star. We transform the junction condition to an ordinary differential equation by making a separability assumption on the metric functions in the space–time variables. The condition of separability on the metric functions yields several new exact solutions. A class of shear-free models is found which contains a linear equation of state and generalizes a previously obtained model. Four new shearing models are obtained; all the gravitational potentials can be written explicitly. A brief physical analysis indicates that the matter variables are well behaved.     

Neutrino wave packet propagation in gravitational fields

We discuss the propagation of neutrino wave packets in a Lense–Thirring metric using a gravitational phase approach. We show that the neutrino oscillation length is altered by gravitational corrections and that neutrinos are subject to helicity flip induced by stellar rotation. For the case of a rapidly rotating neutron star, we show that absolute neutrino masses can be derived, in principle, from rotational contributions to the mass-induced energy shift, without recourse to mass generation models presently discussed in the literature.     

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.