Keywords
Shadow thermodynamics
Non-commutative geometry
Quantum gravity
Critical phenomenon
Submitted : 2026-03-25
Accepted : 2026-04-09
Published : 2026-04-24
Abstract
In this paper, we innovatively adopt the shadow radius to investigate the thermodynamics of an AdS black hole with non-commutative geometry terms. First, via geodesic analysis, we establish a quantitative relationship between the shadow radius and the event horizon radius, and derive the shadow radius of the black hole as a function of the event horizon radius, which exhibits a positive correlation between the two quantities. Furthermore, within the shadow framework, we find that the stability and heat capacity of the black hole can be effectively represented through the shadow radius. Further analysis reveals that the results obtained using the shadow radius in revealing the black hole phase transition process are essentially consistent with those obtained using the event horizon. Based on this, we constructed the thermal profile for an AdS black hole incorporating non-commutative parameters. Within the framework of non-commutative geometry, for P < Pc , the temperature derived from the shadow radius exhibits a distinct N-shaped trend, which is in perfect agreement with that obtained from the event horizon radius. This result reveals that even in non-commutative spacetime, the phase transition process of AdS black holes can be effectively and intuitively characterized by the thermal profiles of their shadows.
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