https://doi.org/10.1140/epjp/s13360-024-05487-3
Regular Article
Well-behaved class of Heintzmann’s solution within 
framework
1
Department of Mathematics, Sarat Centenary College, 712 302, Dhaniakhali, Hooghly, West Bengal, India
2
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711 103, Howrah, West Bengal, India
a pramitrej@gmail.com, pramitr@sccollegednk.ac.in, pramit.rej@associates.iucaa.in
Received:
22
April
2024
Accepted:
22
July
2024
Published online:
5
August
2024
The primary objective of this paper is to develop a well-behaved class of Heintzmann IIa [H. Heintzmann, Z. Physik 228, 489-493 (1969)] solution in the context of 
gravity. In the f(R, T) framework, the gravitational action includes both the Ricci scalar (R) and the trace of the energy–momentum tensor (T). We chose a particular model s.t. 
, where 
is known as the coupling parameter. This solution describes a novel isotropic compact fluid sphere with positively finite central pressure and density in this extended theory of gravity. The results obtained analytically are better described by graphical representations of the physical parameters for various values of the coupling parameter . The solution for a specific compact object, Vela X-1, with radius 
km and mass 
[M. L. Rawls et al. ApJ, 730, 25 (2011)], is shown here. We analyze the fundamental physical attributes of the star, which reveals the influence of the coupling parameter on the values of substance parameters. This helps us to make a fruitful comparison of this modified gravity with the standard GR and notice that it holds good for stable compact objects. In this framework, the star under our consideration exhibits a stable structure consistent with the Heintzmann IIa ansatz. From all of our obtained graphical and numerical results, we can ultimately conclude that our reported model is physically admissible and satisfies all the physical criteria for an acceptable model.
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