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It has been recently shown in[\href{https://link.aps.org/doi/10.1103/PhysRevLett.125.041302}{Phys. Rev.Lett. 125 (2020) 041302}] that microstate counting carried out for quantumstates residing on the horizon of a black hole leads to a correction of theform $\exp(-A/4l_p^2)$ in the Bekenstein-Hawking form of the black holeentropy. In this letter we develop a novel approach to obtain the possible formof the spacetime geometry from the entropy of the black hole for a givenhorizon radius. The uniqueness of this solution for a given energy-momentumtensor has also been discussed. Remarkably, the black hole geometryreconstructed has striking similarities to that of noncommutative inspiredSchwarzschild black holes[\href{https://www.sciencedirect.com/science/article/pii/S0370269305016126}{Phys.Lett. B 632 (2006) 547}]. We also obtain the matter density functions using theEinstein's field equations for the geometries we reconstruct fromthermodynamics of black holes. These also have similarities to that of thematter density function of a noncommutative inspired Schwarzschild black hole.We finally compute the Komar energy and the Smarr formula for the effectiveblack hole geometry and compare it with that of the noncommutative inspiredSchwarzschild black hole. We also discuss some astrophysical implications ofthe solutions.

Signatures of noncommutative inspired black holes from exponential corrections to the black hole entropy and the Smarr formula