M. K. Mak

Dark matter density profile and galactic metric in Eddington-inspired Born–Infeld gravity

We consider the density profile of pressureless dark matter in Eddington-inspired Born–Infeld (EiBI) gravity. The gravitational field equations are investigated for a spherically symmetric dark matter galactic halo, by adopting a phenomenological tangential velocity profile for test particles moving in stable circular orbits around the galactic center. The density profile and the mass distribution, as well as the general form of the metric tensor is obtained by numerically integrating the gravitational field equations, and in an approximate analytical form by using the Newtonian limit of the theory. In the weak field limit, the dark matter density distribution is described by the Lane–Emden equation with polytropic index n = 1, and is nonsingular at the galactic center. The parameter κ of the theory is determined so that the theory could provide a realistic description of the dark matter halos. The gravitational properties of the dark matter halos are also briefly discussed in the Newtonian approximation.

Exact models for anisotropic relativistic stars

We present a class of exact solutions of the Einstein gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solution is represented in a closed integral form. The energy density and both radial and tangential pressure are finite and positive inside the anisotropic star. The energy density, radial pressure, pressure-density ratio and the adiabatic speed of sound are monotonically decreasing functions. Several stellar models with the anisotropy coefficient proportional to r2 are discussed, the values of the basic physical parameters of the star (radius, mass and red shift) and bound on anisotropy parameter is obtained.

Wormhole geometries in Eddington-Inspired Born–Infeld gravity

Eddington-inspired Born-Infeld gravity (EiBI) gravity is a recently proposed modified theory of gravity, based on the classic work of Eddington and on Born-Infeld nonlinear electrodynamics. In this paper, we consider the possibility that wormhole geometries are sustained in EiBI gravity. We present the gravitational field equations for an anisotropic stress-energy tensor and consider the generic conditions, for the auxiliary metric, at the wormhole throat. In addition to this, we obtain an exact solution for an asymptotically flat wormhole.

Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: an Abel equation based approach.

We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth through travelling waves can be reduced to a first order Abel type equation. By using the integrability conditions for the Abel equation several classes of exact travelling wave solutions of the general reaction-diffusion equation that describes glioblastoma growth are obtained, corresponding to different forms of the product of the diffusion and reaction functions. The solutions are obtained by using the Chiellini lemma and the Lemke transformation, respectively, and the corresponding equations represent generalizations of the classical Fisher-Kolmogorov equation. The biological implications of two classes of solutions are also investigated by using both numerical and semi-analytical methods for realistic values of the biological parameters.

Bianchi type I cosmologies in arbitrary dimensional dilaton gravities

We study the low energy string effective action with an exponential type dilaton potential and vanishing torsion in a Bianchi type I space-time geometry. In the Einstein and string frames the general solution of the gravitational field equations can be expressed in an exact parametric form. Depending on the values of the dilaton coupling constant and of the coefficient in the exponential, the obtained cosmological models can be generically divided into three classes, leading to both singular and non-singular behaviors. The effect of the potential on the time evolution of the mean anisotropy parameter is also considered in detail, and it is shown that a Bianchi type I universe isotropizes only in the presence of a dilaton field potential or a central deficit charge.

A Chiellini type integrability condition for the generalized first kind Abel differential equation

The Chiellini integrability condition of the first order first kind Abel equation

Bianchi Type I Cosmological Models in Eddington-inspired Born-Infeld Gravity

dy/dx=f(x)y^2+g(x)y^3

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

is extended to the case of the general Abel equation of the form

Rotational Perturbations in Neveu-Schwarz-Neveu-Schwarz String Cosmology

dy/dx=a(x)+b(x)y+f(x)y^{\alpha -1}+g(x)y^{\alpha}

Jacobi stability analysis of scalar field models with minimal coupling to gravity in a cosmological background

, where