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We propose a unique stellar model under the $f(R,\mathcal{T})$ gravity byusing the conjecture of Mazur-Mottola [P. Mazur and E. Mottola, Report number:LA-UR-01-5067., P. Mazur and E. Mottola, Proc. Natl. Acad. Sci. USA 101, 9545(2004)] which is known as gravastar and a viable alternative to the black holeas available in literature. This gravastar is described by the three differentregions, viz., (I) Interior core region, (II) Intermediate thin shell, and(III) Exterior spherical region. The pressure within the interior region isequal to the constant negative matter density which provides a repulsive forceover the thin spherical shell. This thin shell is assumed to be formed by afluid of ultra relativistic plasma and the pressure, which is directlyproportional to the matter-energy density according to Zel'dovich's conjectureof stiff fluid [Y.B. Zel'dovich, Mon. Not. R. Astron. Soc. 160, 1 (1972)], doescounter balance the repulsive force exerted by the interior core region. Theexterior spherical region is completely vacuum and assumed to be de Sitterspacetime which can be described by the Schwarzschild solution. Under thisspecification we find out a set of exact and singularity-free solution of thecollapsing star which presents several other physically valid features withinthe framework of alternative gravity.

Gravastars in $f(R,\mathcal{T})$ gravity