Thermodynamic GUP correction for black hole within quintessence matter

Abstract We examine the black hole geometry in general relativity using Einstein's equations to modify the geometry in quintessence matter. In quintessence matter, we incorporate black hole geometry into the standard formula to assess the Hawking temperature. We implement the Hamilton-Jacobi semi-classical technique to examine the Hawking temperature of a four-dimensional black hole spacetime. The boson particles are tunnelled into the horizon under the action of the generalized uncertainty principle (GUP) by implementing the relativistic field equation and WKB strategy. The Hawking temperature is investigated under the influence of the GUP parameter, particle properties, and black hole geometry parameters. Entropy and emission energy corrections are also examined using the Hawking temperature.