Saša Ilijić

Gravastar solutions with continuous pressures and equation of state

We study the gravitational vacuum star (gravastar) configuration as proposed by Cattoen et al (2005 Class. Quantum Grav. 22 4189) in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure of Mazur and Mottola (2001 Preprint gr-qc/0109035, 2003 Proc. 6th Workshop on Quantum Field Theory Under the Influence of External Conditions (Oklahoma) (Princeton, NJ: Rinton), Preprint gr-qc/0405111 (2004 Proc. Natl Acad. Sci. 111 9545) is replaced by a continuous stress–energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial pr and tangential pt pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar (Cattoen et al 2005 Class. Quantum Grav. 22 4189). Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.

Radial pulsations and stability of anisotropic stars with a quasi-local equation of state

Quasi-local variables, i.e. quantities whose values can be derived from physics accessible within an arbitrarily small neighborhood of a spacetime point, are used to construct the equation of state (EoS) for the anisotropic fluid in the spherical symmetry. One parameter families of equilibrium solutions are obtained making it possible to assess stability properties by means of the standard M(R) method. Normal modes of radial pulsation are computed as well and are found to confirm the onset of instability as predicted by the M(R) method. As an example, a stable configuration with outwardly increasing energy density in the core is obtained with a simple quasi-local extension of the polytropic EoS. It is also found that the loss of stability occurs at higher surface compactness when the anisotropy of pressures is present.

Electrically charged gravastar configurations

The notion of a compact object immune to the horizon problem and comprising an anisotropic inhomogeneous fluid with a specific radial pressure behavior, i.e. the gravastar, is extended by introducing an electrically charged component. Einstein–Maxwell field equations are solved in the asymptotically de Sitter interior where a source of electric field is coupled to the fluid energy density. Two different solutions which satisfy the dominant energy condition are given: one is the δ-shell model for which the analysis is carried out within Israels thin shell formalism, the other approach—the continuous profile model—is solved numerically and the interior solutions have been (smoothly) joined with the Reissner–Nordstrom exterior. The effect of electric charge is considered, and the equation of state, the speed of sound and the surface redshift are calculated for both models.

Gravastar energy conditions revisited

We consider the gravastar model where the vacuum phase transition between the de Sitter interior and the Schwarzschild or Schwarzschild–de Sitter exterior geometries takes place at a single spherical δ-shell. We derive sharp analytic bounds on the surface compactness (2m/r) that follow from the requirement that the dominant energy condition (DEC) holds at the shell. In the case of Schwarzschild exterior, the highest surface compactness is achieved with the stiff shell in the limit of vanishing (dark) energy density in the interior. In the case of Schwarzschild–de Sitter exterior, in addition to the gravastar configurations with the shell under surface pressure, gravastar configurations with vanishing shell pressure (dust shells), as well as configurations with the shell under surface tension, are allowed by the DEC. Respective bounds on the surface compactness are derived for all cases. We also consider the speed of sound on the shell as derived from the requirement that the shell is stable against the radial perturbations. The causality requirement (sound speed not exceeding that of light) further restricts the space of allowed gravastar configurations.

Radial stability analysis of the continuous pressure gravastar

Radial stability of the continuous pressure gravastar is studied using the conventional Chandrasekhar method. The equation of state for the static gravastar solutions is derived and Einstein equations for small perturbations around the equilibrium are solved as an eigenvalue problem for radial pulsations. Within the model there exists a set of parameters leading to a stable fundamental mode, thus proving the radial stability of the continuous pressure gravastar. It is also shown that the central energy density possesses an extremum in ρc(R) curve which represents a splitting point between stable and unstable gravastar configurations. As such the ρc(R) curve for the gravastar mimics the famous M(R) curve for a polytrope. Together with the former axial stability calculations this work completes the stability problem of the continuous pressure gravastar.

The envelope of projectile trajectories

The paper presents yet another elegant solution to the classical problem of maximizing the range of a projectile fired from above or from below the horizontal target plane. The method makes use of the envelope of the family of the projectile trajectories and it not only solves the original problem, but can be applied to maximize the projectile range on a target surface of arbitrary shape. Three different ways of deriving the equation of the envelope are shown. As an example the range of a projectile is maximized on a parabolic target surface. The envelope can also be used to minimize the kinetic energy of a projectile given the target point.

Fourier Disentangling of Composite Spectra

The Fourier disentangling algorithm can be applied on a time series of observed composite spectra to obtain orbital parameters and component spectra, in the assumption that the intrinsic spectra do not vary with time. Applications are shortly reviewed with the purpose to emphasize the power of the method. Thereafter, the progression of noise from the input data into the disentangled spectra and the orbital parameters is discussed. It is concluded that no bias is introduced by purely random noise when the necessary precautions are taken. Systematic noise is presently discussed from an empirical viewpoint.

Formation of photon spheres in boson stars with a nonminimally coupled field

A static, spherically symmetric, asymptotically flat spacetime may allow for circular, closed null-geodesics which are said to belong to a photon sphere. In the context of gravitational lensing in the strong deflection regime, the presence of a photon sphere leads to an unbounded angle of deflection of light (multiple turns) and formation of relativistic images. In this paper, we show that photon spheres may form in some configurations of boson stars constructed with a free massive complex scalar field nonminimally coupled to gravity. Assuming that the boson star is transparent to light, photon spheres would give rise not only to phenomena in the realm of strong gravitational lensing, but also to considerably increased photon flux in the central region of the star, relative to the flux in its surroundings.

Maximizing the range of a projectile

The problem of maximizing the horizontal range of a projectile fired from a height above or a depth below the assumed horizontal target plane has been discussed and solved in several different ways. However, it seems to be a neverending story. This paper offers a remarkably simple solution to the problem that does not require the use of calculus. It is based on the fact that the equation θ = f(R), where θ is the firing angle and R is the range, must have a unique solution for R = Rmax .

Nonminimally coupled scalar field in teleparallel gravity: boson stars

We study the nonminimally coupled complex scalar field within the framework of teleparallel gravity. Coupling of the field nonminimally to the torsion scalar destroys the Lorentz invariance of the theory in the sense that the resulting equations of motion depend on the choice of a tetrad. For the assumed static spherically symmetric spacetime, we find a tetrad which leads to a self-consistent set of equations, and we construct the self-gravitating configurations of the scalar field—boson stars. The resulting configurations develop anisotropic principal pressures and satisfy the dominant energy condition. An interesting property of the configurations obtained with sufficiently large field-to-torsion coupling constant is the outwardly increasing energy density, followed by an abrupt drop towards the usual asymptotic tail. This feature is not present in the boson stars with the field minimally or nonminimally coupled to the curvature scalar, and therefore appears to be a torsion-only effect.