Conformal Killing Geometry Classifies Black Hole Thermodynamics and Stability Regimes.

Research demonstrates a universal thermodynamic topological classification for static black holes utilising Conformal Killing geometry. This significantly modifies thermodynamic properties and stability across temperature ranges, categorising charged Reissner-Nordström and Schwarzschild black holes into distinct classes based on parameter settings.

Black holes, conventionally understood as regions of spacetime exhibiting such strong gravitational effects that nothing, not even light, can escape, continue to yield nuanced behaviours when examined through modified theories of gravity. Recent research focuses on the thermodynamic properties of static black holes within the framework of Conformal Killing Gravity (CKG), a theory extending general relativity by incorporating conformal symmetry. This approach reveals alterations to black hole stability and classifications across varying temperature scales, impacting our understanding of these cosmic entities. Hao Chen (Zunyi Normal University), Di Wu (China West Normal University), Meng-Yao Zhang (Guizhou University of Commerce), Soroush Zare (Universidad de Valladolid), Hassan Hassanabadi and Bekir Can Lütfüoğlu (University of Hradec Králové), alongside Zheng-Wen Long (Guizhou University), detail these findings in their paper, “Universal thermodynamic topological classes of static black holes in Conformal Killing Gravity”.

Black Hole Thermodynamics Reimagined Through Conformal Symmetry

Black holes continue to challenge our comprehension of fundamental physics, and recent research offers a refined thermodynamic classification of these objects, utilising the mathematical concept of Conformal Killing (CK) vectors. This approach reveals how these vectors actively modify black hole behaviour and stability, offering a new perspective on their properties.

CK vectors represent infinitesimal symmetries of a spacetime, meaning they describe transformations that leave the spacetime’s geometry unchanged at a given point. The investigation demonstrates that CK vectors influence thermodynamic properties at both the inner and outer event horizons – the boundaries defining the region from which nothing, not even light, can escape. This alteration impacts the stability of black holes across a range of temperatures, revealing a complex relationship between temperature, stability, and conformal symmetry – a type of symmetry where angles are preserved during transformations.

Researchers classified charged Anti-de Sitter (AdS) black holes and Reissner-Nordström black holes – a type of electrically charged, non-rotating black hole – within this CK framework. They assigned these black holes to distinct topological classes based on the specific parameters defining the CK vector. This sensitivity to symmetry highlights the power of CK geometry in differentiating black hole characteristics and providing a more detailed understanding of their behaviour.

The study identifies two primary topological classes. Crucially, different parameter settings for the CK vector can yield different classifications for the same black hole, demonstrating the importance of carefully selecting the appropriate mathematical tools for analysis. When applied to the simpler case of uncharged black holes, the Schwarzschild black hole – a non-rotating, uncharged black hole – also conforms to these established classes.

This consistency suggests a unifying principle governing black hole classification across varying charge states and spacetime geometries. The findings indicate that CK vectors are not merely a mathematical convenience, but actively reshape black hole behaviour, offering a new framework for understanding their properties and evolution. The research builds upon established thermodynamics, where stability is often assessed through heat capacity – a measure of how much energy is required to raise an object’s temperature. However, this new approach incorporates geometric considerations via the CK vectors, providing a more nuanced understanding of black hole stability.

This refined classification scheme offers a novel approach to characterising and differentiating black hole solutions, potentially informing future research into their properties and behaviour, and contributing to a deeper understanding of the fundamental nature of gravity and spacetime.