# Exact anisotropic polytropic cylindrical solutions

Exact anisotropic polytropic cylindrical solutions In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential z ( x ) = ( 1 + b x ) η ( η = 1 , 2 , 3 ) $z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)$ and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for η = 1 , 2 $\eta =1,~2$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Astrophysics and Space Science Springer Journals

# Exact anisotropic polytropic cylindrical solutions

, Volume 363 (3) – Feb 21, 2018
10 pages

/lp/springer_journal/exact-anisotropic-polytropic-cylindrical-solutions-xHa7do2m06
Publisher
Springer Netherlands
Subject
Physics; Astrophysics and Astroparticles; Astronomy, Observations and Techniques; Cosmology; Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics) ; Astrobiology
ISSN
0004-640X
eISSN
1572-946X
D.O.I.
10.1007/s10509-018-3273-6
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we study anisotropic compact stars with static cylindrically symmetric anisotropic matter distribution satisfying polytropic equation of state. We formulate the field equations as well as the corresponding mass function for the particular form of gravitational potential z ( x ) = ( 1 + b x ) η ( η = 1 , 2 , 3 ) $z(x)=(1+bx)^{\eta }~(\eta =1,~2,~3)$ and explore exact solutions of the field equations for different values of the polytropic index. The values of arbitrary constants are determined by taking mass and radius of compact star (Her X-1). We find that resulting solutions show viable behavior of physical parameters (density, radial as well as tangential pressure, anisotropy) and satisfy the stability condition. It is concluded that physically acceptable solutions exist only for η = 1 , 2 $\eta =1,~2$ .

### Journal

Astrophysics and Space ScienceSpringer Journals

Published: Feb 21, 2018

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