Gravastar model in the structure of $f(R,L_{m}, T)$ modified theory of gravity

Abstract: The Gravastar ( or the Gravitational Vacuum Star ) is a very serious alternatives proposed to the principle of the Black Hole, the model of which was originally developed by Mazur and Mottola. A Gravastar is an astronomically hypothetically condensed object which is a gravitationally dark vacuum star or a gravitational vacuum condensate star, which is singularity free, spherically symmetric and also super compact. The current study concerns about the model of the Gravastar in the modified $f(R,L_{m}, T)$ gravity considering the form $f(R,L_{m},T) = R + {\alpha}TL_{m} $. From Mazur-Mottola \cite{Mazur}-\cite{Mottola}, we get to know that a Gravastar model has three distinct regions having various Equations of State (EoS). We have inquired into the interior portion with the space-time considering $ \rho = - p $, for the dark sector of the interior region, here the negative matter-energy density exerting a repulsive force on the immediate thin shell with the EoS $ \rho = p $ where it is considered as an ultra-relativistic fluid. We have studied the properties such as energy density, proper length, total energy and entropy. Next comes the vacuum exterior region of the Gravastar which is being described by the Schwarzschild-de-Sitter solution. And also from Darmois-Israel formalism, we have probed the junction connecting the inner and the outer surfaces of the Gravastar.