Abstract:
The non-commutative (NC) geometry is an intriguing result of the well-known string the-
ory, provides a way to combine gravitational forces as well as weak and strong forces in a
single framework. Space-time quantization is the fundamental development of string theory
where the coordinates of space-time become NC operators in the D-brane. A simple and
precise way to define a global monopole (GM) parameter in the presence of a triplet scalar
fields with a global O(3) symmetry. If such a GM parameter is induced by an ordinary
black hole (BH), a new version of a modified BH can be derived, which gives the inter-
esting aspects about the space-time geometry. By getting motivation from these we have
obtained the exact static spherically symmetric for NC BHs coupled with GM in anti-di
sitter (Ads) space-time. We have calculated the thermodynamic quantities for NC BHs and
introduced cosmological constant P = − Λ
8π . We observed that for the graphs of the metric
function h(r) and r, there exist BHs with single horizon, double horizon, and no horizon
depending on the value of parameters η and θ . From the perspective of the stability of BHs,
we observed that for small values of r the BH Gibbs free energy (GFE) increased initially
with respect to horizon r+ and after reaching a certain value of event horizon enters the
negative region, with the increasing values of η and θ . Finally, we also analyze the phase
transition, critically exponents and the infalling matter of spherically symmetric distribu-
tion graphically. These findings helps us to further explore the heuristics configurations of
BHs space-time geometry and its associated deeper phenomenological consequences
