Gravitation, Astrophysics, And Cosmology - Proceedings Of The Twelfth Asia-pacific International Conference

Proceedings of the Twelfth Asia-Pacific International Conference

Vitaly Melnikov, Jong-Ping Hsu

• Publisher: WSPC
• Year: 2016
• eBook ISBN:
  9789814759823
• Topic: Physical Sciences
• Subtopic: Astronomy & Astrophysics

The ICGAC-12 aimed to serve as a common platform around the Asia-Pacific region for the exchange and communication among all researchers in the fields of gravitation, astrophysics and cosmology. The scope covered in the conference includes dark matter, dark energy, experimental study of gravity, black holes, quantum Yang-Mills gravity, GR extension, variation of constants, fundamental physics space projects, relativistic astrophysics, white dwarfs, neutron stars, and gamma ray bursts.

The ICGAC-12 aimed to serve as a common platform around the Asia-Pacific region for the exchange and communication among all researchers in the fields of gravitation, astrophysics and cosmology. The scope covered in the conference includes dark matter, dark energy, experimental study of gravity, black holes, quantum Yang-Mills gravity, GR extension, variation of constants, fundamental physics space projects, relativistic astrophysics, white dwarfs, neutron stars, and gamma ray bursts.

Readership: Students and Professionals in the areas of Gravitation, Astrophysics, and Cosmology.
Key Features:

• New approach to accelerated cosmic expansion based on extremely weak gauge fields associated with conserved baryon number
• Quantum gravity based on Yang-Mills type gauge symmetry of space-time and translational gauge symmetry
• Prominent contributors: A Beesham, R Maartence (South Africa); Shapiro, C Romero, D Ditman (Brazil); V Frolov (Canada); V Man'ko (Mexico); A Dolgov (Italy); and well-known scientists from Russia

Section 1

Classical Gravity and GR Extensions

Accretion disks around a mass with quadrupole

M. Abishev, K. Boshkayev, H. Quevedo and S. Toktarbay*

Physical-Technical Faculty, Al-Farabi Kazakh National Universityr,
Al Farabi av. 71, 050040 Almaty, Kazakhstan
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
AP 70543, México, DF 04510, Mexico
*E-mail: [email protected]

We consider the stability properties of circular orbits of test particles moving around a mass with quadrupole. We show that the quadrupole modifies drastically the properties of an accretion disk made of such test particles.

Keywords: Quadrupole; compact objects; geodesics.

The simplest generalization of the Schwarzschild metric which contains a quadrupole parameter q is given by

This solution is known as the δ−metric or as the γ−metric and was first obtained by Zipoy and Voorhees.¹ We propose to use the term quadrupole metric (q−metric) to emphasize the role of the parameter q. The q−metric is an axially symmetric exact vacuum solution, and reduces to the Schwarzschild metric for q → 0. It is asymptotically flat with a central curvature singularity at r = 0 and an outer singularity at r = 2m which is naked. According to the Geroch definition, the independent multipole moments are the monopole M₀ = m(1 + q) and the quadrupole

. For more details, see Ref. 2.

As a first approximation, an accretion disk can be considered as a set of test particles moving along circular orbits around the central mass. In this case, the geodesic equations on the equatorial plane are equivalent to the equations for the motion in the effective potential³

where E and l are constants of motion. The radius and stability properties of circular orbits are completely determined by the behavior of the effective potential which, in turn, depends on the behavior of the first and second radial derivatives. We performed a detailed analysis of the behavior of the effective potential. The result of this study is summarized in Fig. 1. The region of stability determines the spatial region where an accretion disk can exist, and the radius of the last stable circular orbit is interpreted as the minimum inner radius of the disk.

Fig. 1. (a) Radius of the last stable circular orbit as a function of the quadrupole. Below the critical radius r_c = m(3 + 2q), no motion is allowed. The outer singularity r_sing = 2m is also plotted. Accretion disks are illustrated for positive q in (b), for − 0.5 > q > 0 in (c) and for q = −0.52 in (d).

We see that for positive values of q the accretion disk is always located outside the Schwarzschild radius of the last stable circular orbit

. For negative values of q, the disk can be completely inside the radius

. Finally, for values of q close to −0.5, a second inner disk appears in a region very closed to the outer singularity r_sing = 2m.

We conclude that the quadrupole parameter can modify drastically the geometric structure of accretion disks. Therefore, it should be possible to determine the value of q from the geometric properties of the disk.

We acknowledge the support through a Grant of the Target Program of the MES of the RK, Grant No. 3101/GF4 IPC-11/2015, DGAPA-UNAM, Grant No. 113514, and Conacyt, Grant No. 166391.

References

1.D. M. Zipoy, J. Math. Phys. 7 (1966) 1137; B. Voorhees, Phys. Rev. D 2 (1970) 2119.

2.H. Quevedo, Int. J. Mod. Phys. D 20, 1779 (2011).

3.K. Boshkayev, E. Gasperin, A.C. Gutierrez-Pineres, H. Quevedo and S. Toktarbay, Motion of test particles in the field of a naked singularity, arXiv: gr-qc/1509.03827.

Orbital stability of the restricted three-body problem in General Relativity

M. Abishev¹, H. Quevedo², S. Toktarbay¹* and B. Zhami¹

Physical-Technical Faculty, Al-Farabi Kazakh National University,
Al Farabi av. 71, 050040 Almaty, Kazakhstan
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México,
AP 70543, México, DF 04510, Mexico
*E-mail: [email protected]

We consider the problem of orbital stability of the motion of a test particle in the restricted three-body problem, by ...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Dedication
• Preface
• Einstein, Grossmann, Hilbert
• Contents
• Plenary Sessions
• Section 1. Classical Gravity and GR Extensions
• Section 2. Classical and Quantum Cosmology, Dark Matter and Dark Energy
• Section 3. Black Holes and Wormholes
• Section 4. Strings, Branes, Higher Spin Fields, Quantum Gravity
• Section 5. Extra Dimensions and Variation of Constants
• Section 6. Gravitational Experiments
• Section 7. Relativistic Astrophysics
• Epilogue
• International Organizing Committee, International Advisory Committee,
• Sections and moderators
• List of participants
• Photos: Delightful Moments at The 2015 ICGAC-12