Anisotropic generalization of Buchdahl bound for specific stellar models
Ranjan Sharma, Arpita Ghosh, Soumik Bhattacharya, Shyam Das
Abstract
Abstract Anisotropy is one factor that appears to be significantly important in the studies of relativistic compact stars. In this paper, we make a generalization of the Buchdahl limit by incorporating an anisotropic effect for a selected class of exact solutions describing anisotropic stellar objects. In the isotropic case of a homogeneous distribution, we regain the Buchdahl limit $$2M/R \le 8/9$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>M</mml:mi> <mml:mo>/</mml:mo> <mml:mi>R</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>8</mml:mn> <mml:mo>/</mml:mo> <mml:mn>9</mml:mn> </mml:mrow> </mml:math> . Our investigation shows a direct link between the maximum allowed compactness and pressure anisotropy vi-a-vis geometry of the associated 3-space.