We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Ho... more We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability analysis of the geodesic equations is performed by considering the important geometric invariants that can be used for the description of this system (the nonlinear and the Berwald connections), as well as the deviation curvature tensor, respectively. The characteristic values of the deviation curvature tensor are specifically calculated, as given by the second derivative of effective potentia...
In the framework of the inverse problem of Dynamics we investigate the compatibility between a tw... more In the framework of the inverse problem of Dynamics we investigate the compatibility between a two-parametric family of precessing orbits and autonomous force fields. In a previous work, for a specific choice of the two parameters in the precessing family of orbits, we obtained that if the family is compatible with a central force, than this is derived from a Manev's type potential. In this work we consider another choice of the parameters in the two-parametric family of precessing orbits, for which we know that there is no central force compatible and study its compatibility with an autonomous force field.
In this note we take a dynamical systems approach to the equations of motion of a free test parti... more In this note we take a dynamical systems approach to the equations of motion of a free test particle moving around a spherically symmetric static dilaton black hole, written in the Einstein frame. The equations of motion are obtained using the Euler-Lagrange formalism. Using the first integrals of motion, we reach the conclusion that the free test particles are moving in a plane, named plane of motion. In it we analyze the existence and nature of the equilibrium points and compare the behavior of free test particles near the equilibrium points using the dynamics systems approach. The study revealed that in the exact phase-plane exist distinct regions of motion, separated through a curve named separatrix. In the end we obtained a relation between the parameters describing the black hole and the free test particle that holds on a parabolic separatrix.
In this note we examine the circular time-like geodesics near a spherically symmetric dilaton bla... more In this note we examine the circular time-like geodesics near a spherically symmetric dilaton black hole, described using the exact solution for a static charged black hole found by Gibbons and Maeda and, independently, by Garfinkle, Horowitz and Strominger. The existence and stability of the circular orbits are analysed using the effective potential of a free material test particle moving on time-like geodesic near this black hole. We determine the radius of the innermost stable circular orbit, the radius of the shortest circular orbit and compare our results with those obtained by other authors for specific values of the parameters involved in our analysis.
arXiv: General Relativity and Quantum Cosmology, 2019
The purpose of this article is to obtain the periastron precession of a free particle moving arou... more The purpose of this article is to obtain the periastron precession of a free particle moving around an extremal spherically symmetric dilaton black hole. To get the formulae for the periastron precession we use the phase-plane analysis of the general relativistic equations of motion.
We describe here a package, tableau.sty, created by N. Kisselhoff, very useful especially for the... more We describe here a package, tableau.sty, created by N. Kisselhoff, very useful especially for the courses of Calculus, designed for the construc- tion of variation and sign tables for the study of function. The package provides a new environment, based on PSTricks.
arXiv: General Relativity and Quantum Cosmology, 2016
In this article we study the stability in the sense of Lyapunov of the circular orbits in the gen... more In this article we study the stability in the sense of Lyapunov of the circular orbits in the generalized Manev two bodies problem. First, we explore the existence of the circular orbits and determine their radius. Then, using the first integrals of motion we build a positive definite function, known as a Lyapunov function. It's existence proves that the circular orbit is stable in the sense of Lyapunov. In the end, we consider several real systems of two bodies and compare the characteristics of the circular orbits in Newtonian and modified Manev gravitational field, arguing about our possibilities to observe the differences between the motion in these two fields.
Using the homological Milne variables and the phase portrait of the Lane-Emden equation in these ... more Using the homological Milne variables and the phase portrait of the Lane-Emden equation in these variables we determine the boundary between layers of different polytropic indices. We argue about the homological properties of the equilibrium equation of a polytrope in the presence of a weak poloidal magnetic field and obtain the field distribution in a sequence of composite polytropic stars
In this paper we study the timelike geodesics around a spherically symmetric charged dilaton blac... more In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
The aim of this paper is to show that the geodesic Hamilton-Jacobi equation for a new spherical s... more The aim of this paper is to show that the geodesic Hamilton-Jacobi equation for a new spherical symmetric exact solution of the Einstein-dilation equation is separable and to construct its complete integral.
The authors study the equilibrium of polytropes in a poloidal magnetic field. The magnetic field ... more The authors study the equilibrium of polytropes in a poloidal magnetic field. The magnetic field is the solution of a nonhomogeneous Euler equation for which the authors are able to give the general solution. It depends on the Lane-Emden function. The authors use the approximate analytic solution of the Lane-Emden equation proposed by Liu, to write it explicitly. For the
Revista Mexicana De Astronomia Y Astrofisica, 1992
RESUMEN Usando la ley de distribuci6n de densidad propuesta por Sehnal and Pospisilova (1988), se... more RESUMEN Usando la ley de distribuci6n de densidad propuesta por Sehnal and Pospisilova (1988), se estudia el movimiento inicial circular de una 6rbita en la atmosfera de Marte (considerada oblicua y en rotaci6n). Se estiman analiticamente la diferencia entre el perfodo nodal y Kepleriano correspondiente, asf como los cambios independientes en cinco elementos orbitales, sobre un perfodo nodal. ABSTRACT Using
Publications of the Astronomy Department of the …, 2005
The paper is devoted to a qualitative analysis of the nonlinear, radial oscillations of magnetic ... more The paper is devoted to a qualitative analysis of the nonlinear, radial oscillations of magnetic polytropes. The magnetic field is assumed to be purely toroidal. The small adiabatic perturbations are investigated using the normal forms method. The nonadiabatic ...
The two-body problem corresponding to a gravitational force with anisotropic G is treated by mean... more The two-body problem corresponding to a gravitational force with anisotropic G is treated by means of perturbation theory. The integration of Newton-Euler equations shows that the perturbed orbit is of elliptic type, lies in a fixed plane, and its semimajor axis, ...
We discuss the two-body problem within the framework of the photogravitational model proposed by ... more We discuss the two-body problem within the framework of the photogravitational model proposed by the Romanian astronomer Constantin Popovici. The motion equations in polar coordinates and the angular momentum integral are established, then transposed in ...
The archive of photometric plates obtained at the Astronomical Observatory of Cluj in the period ... more The archive of photometric plates obtained at the Astronomical Observatory of Cluj in the period 1952-1974 is presented. The plate inventory is made within the framework of the Wide-Field Plate Database project. The plates were taken in the regions around 110 ...
The paper includes a qualitative study of the N-dimensional (N= 1, 2, 3) Lane-Emden equation, wri... more The paper includes a qualitative study of the N-dimensional (N= 1, 2, 3) Lane-Emden equation, written as a two-dimensional autonomous nonlinear system of ordinary differential equations by using Milne's homological invariant variables. The discussion is ...
We examine the question of finding al potentials V (x, y) which can produce a specific isolated p... more We examine the question of finding al potentials V (x, y) which can produce a specific isolated planar orbit f (x, y)= 0, given in advance and traced by a material point for adequate initial conditions. We study in some detail an example to clarify the difference of ...
Given any two-dimensional potential V (x, y), we find (if there exists, of course) without integr... more Given any two-dimensional potential V (x, y), we find (if there exists, of course) without integration of the pertinent equation of motion a monoparametric family of orbits of the form f (x, y)= y+ h (x)= c (whose members are shifted parallely to the y-axis) traced by a ...
We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Ho... more We analyze the stability of the geodesic curves in the geometry of the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole, describing the space time of a charged black hole in the low energy limit of the string theory. The stability analysis is performed by using both the linear (Lyapunov) stability method, as well as the notion of Jacobi stability, based on the Kosambi–Cartan–Chern theory. Brief reviews of the two stability methods are also presented. After obtaining the geodesic equations in spherical symmetry, we reformulate them as a two-dimensional dynamic system. The Jacobi stability analysis of the geodesic equations is performed by considering the important geometric invariants that can be used for the description of this system (the nonlinear and the Berwald connections), as well as the deviation curvature tensor, respectively. The characteristic values of the deviation curvature tensor are specifically calculated, as given by the second derivative of effective potentia...
In the framework of the inverse problem of Dynamics we investigate the compatibility between a tw... more In the framework of the inverse problem of Dynamics we investigate the compatibility between a two-parametric family of precessing orbits and autonomous force fields. In a previous work, for a specific choice of the two parameters in the precessing family of orbits, we obtained that if the family is compatible with a central force, than this is derived from a Manev's type potential. In this work we consider another choice of the parameters in the two-parametric family of precessing orbits, for which we know that there is no central force compatible and study its compatibility with an autonomous force field.
In this note we take a dynamical systems approach to the equations of motion of a free test parti... more In this note we take a dynamical systems approach to the equations of motion of a free test particle moving around a spherically symmetric static dilaton black hole, written in the Einstein frame. The equations of motion are obtained using the Euler-Lagrange formalism. Using the first integrals of motion, we reach the conclusion that the free test particles are moving in a plane, named plane of motion. In it we analyze the existence and nature of the equilibrium points and compare the behavior of free test particles near the equilibrium points using the dynamics systems approach. The study revealed that in the exact phase-plane exist distinct regions of motion, separated through a curve named separatrix. In the end we obtained a relation between the parameters describing the black hole and the free test particle that holds on a parabolic separatrix.
In this note we examine the circular time-like geodesics near a spherically symmetric dilaton bla... more In this note we examine the circular time-like geodesics near a spherically symmetric dilaton black hole, described using the exact solution for a static charged black hole found by Gibbons and Maeda and, independently, by Garfinkle, Horowitz and Strominger. The existence and stability of the circular orbits are analysed using the effective potential of a free material test particle moving on time-like geodesic near this black hole. We determine the radius of the innermost stable circular orbit, the radius of the shortest circular orbit and compare our results with those obtained by other authors for specific values of the parameters involved in our analysis.
arXiv: General Relativity and Quantum Cosmology, 2019
The purpose of this article is to obtain the periastron precession of a free particle moving arou... more The purpose of this article is to obtain the periastron precession of a free particle moving around an extremal spherically symmetric dilaton black hole. To get the formulae for the periastron precession we use the phase-plane analysis of the general relativistic equations of motion.
We describe here a package, tableau.sty, created by N. Kisselhoff, very useful especially for the... more We describe here a package, tableau.sty, created by N. Kisselhoff, very useful especially for the courses of Calculus, designed for the construc- tion of variation and sign tables for the study of function. The package provides a new environment, based on PSTricks.
arXiv: General Relativity and Quantum Cosmology, 2016
In this article we study the stability in the sense of Lyapunov of the circular orbits in the gen... more In this article we study the stability in the sense of Lyapunov of the circular orbits in the generalized Manev two bodies problem. First, we explore the existence of the circular orbits and determine their radius. Then, using the first integrals of motion we build a positive definite function, known as a Lyapunov function. It's existence proves that the circular orbit is stable in the sense of Lyapunov. In the end, we consider several real systems of two bodies and compare the characteristics of the circular orbits in Newtonian and modified Manev gravitational field, arguing about our possibilities to observe the differences between the motion in these two fields.
Using the homological Milne variables and the phase portrait of the Lane-Emden equation in these ... more Using the homological Milne variables and the phase portrait of the Lane-Emden equation in these variables we determine the boundary between layers of different polytropic indices. We argue about the homological properties of the equilibrium equation of a polytrope in the presence of a weak poloidal magnetic field and obtain the field distribution in a sequence of composite polytropic stars
In this paper we study the timelike geodesics around a spherically symmetric charged dilaton blac... more In this paper we study the timelike geodesics around a spherically symmetric charged dilaton black hole. The trajectories around the black hole are classified using the effective potential of a free test particle. This qualitative approach enables us to determine the type of orbit described by test particle without solving the equations of motion, if the parameters of the black hole and the particle are known. The connections between these parameters and the type of orbit described by the particle are obtained. To visualize the orbits we solve numerically the equation of motion for different values of parameters envolved in our analysis. The effective potential of a free test particle looks different for a non-extremal and an extremal black hole, therefore we have examined separately these two types of black holes.
The aim of this paper is to show that the geodesic Hamilton-Jacobi equation for a new spherical s... more The aim of this paper is to show that the geodesic Hamilton-Jacobi equation for a new spherical symmetric exact solution of the Einstein-dilation equation is separable and to construct its complete integral.
The authors study the equilibrium of polytropes in a poloidal magnetic field. The magnetic field ... more The authors study the equilibrium of polytropes in a poloidal magnetic field. The magnetic field is the solution of a nonhomogeneous Euler equation for which the authors are able to give the general solution. It depends on the Lane-Emden function. The authors use the approximate analytic solution of the Lane-Emden equation proposed by Liu, to write it explicitly. For the
Revista Mexicana De Astronomia Y Astrofisica, 1992
RESUMEN Usando la ley de distribuci6n de densidad propuesta por Sehnal and Pospisilova (1988), se... more RESUMEN Usando la ley de distribuci6n de densidad propuesta por Sehnal and Pospisilova (1988), se estudia el movimiento inicial circular de una 6rbita en la atmosfera de Marte (considerada oblicua y en rotaci6n). Se estiman analiticamente la diferencia entre el perfodo nodal y Kepleriano correspondiente, asf como los cambios independientes en cinco elementos orbitales, sobre un perfodo nodal. ABSTRACT Using
Publications of the Astronomy Department of the …, 2005
The paper is devoted to a qualitative analysis of the nonlinear, radial oscillations of magnetic ... more The paper is devoted to a qualitative analysis of the nonlinear, radial oscillations of magnetic polytropes. The magnetic field is assumed to be purely toroidal. The small adiabatic perturbations are investigated using the normal forms method. The nonadiabatic ...
The two-body problem corresponding to a gravitational force with anisotropic G is treated by mean... more The two-body problem corresponding to a gravitational force with anisotropic G is treated by means of perturbation theory. The integration of Newton-Euler equations shows that the perturbed orbit is of elliptic type, lies in a fixed plane, and its semimajor axis, ...
We discuss the two-body problem within the framework of the photogravitational model proposed by ... more We discuss the two-body problem within the framework of the photogravitational model proposed by the Romanian astronomer Constantin Popovici. The motion equations in polar coordinates and the angular momentum integral are established, then transposed in ...
The archive of photometric plates obtained at the Astronomical Observatory of Cluj in the period ... more The archive of photometric plates obtained at the Astronomical Observatory of Cluj in the period 1952-1974 is presented. The plate inventory is made within the framework of the Wide-Field Plate Database project. The plates were taken in the regions around 110 ...
The paper includes a qualitative study of the N-dimensional (N= 1, 2, 3) Lane-Emden equation, wri... more The paper includes a qualitative study of the N-dimensional (N= 1, 2, 3) Lane-Emden equation, written as a two-dimensional autonomous nonlinear system of ordinary differential equations by using Milne's homological invariant variables. The discussion is ...
We examine the question of finding al potentials V (x, y) which can produce a specific isolated p... more We examine the question of finding al potentials V (x, y) which can produce a specific isolated planar orbit f (x, y)= 0, given in advance and traced by a material point for adequate initial conditions. We study in some detail an example to clarify the difference of ...
Given any two-dimensional potential V (x, y), we find (if there exists, of course) without integr... more Given any two-dimensional potential V (x, y), we find (if there exists, of course) without integration of the pertinent equation of motion a monoparametric family of orbits of the form f (x, y)= y+ h (x)= c (whose members are shifted parallely to the y-axis) traced by a ...
Uploads
Papers by Cristina Blaga