Van der Waals Black Holes Maintain Universal Extremality with Uncertainty Principle Corrections

Van der Waals black holes, theoretical objects exhibiting behaviour similar to everyday fluids, present a unique opportunity to explore the fundamental connection between gravity and thermodynamics, and Ankit Anand from the Indian Institute of Technology Kanpur, alongside Saeed Noori Gashti from Damghan University, and colleagues, have investigated their properties in detail. This research delves into the universal relationships governing these black holes, even when quantum effects are considered, revealing how their behaviour changes at extremely small scales. The team demonstrates that a fundamental connection between a black hole’s entropy and its properties persists despite incorporating corrections from three different quantum gravity frameworks, offering insights into the underlying structure of spacetime. Furthermore, the study maps the ‘topological charges’ of these black holes, revealing how these charges classify different black hole configurations and how stable these classifications are under varying conditions, potentially offering a new way to understand black hole stability and evolution.

The work investigates connections between black hole thermodynamics, the Weak Gravity Conjecture, and the Weak Cosmic Censorship Conjecture, aiming to understand the underlying microscopic structure of gravity. Researchers are particularly interested in how quantum corrections influence the behavior of extremal black holes, those with zero temperature and maximal entropy, as these represent crucial tests of theoretical predictions. The study also examines the role of photon spheres, regions around black holes where light orbits, as potential tools for constraining black hole parameters and validating the Weak Gravity Conjecture.

The research incorporates concepts like the Generalized Uncertainty Principle, which introduces a minimal length scale at extremely small distances, and modified dispersion relations, which alter the relationship between energy and momentum. By exploring these concepts, the team seeks to understand how quantum gravity might affect the stability and behavior of black holes. This ongoing investigation aims to push the boundaries of our understanding of black hole physics and the fundamental nature of spacetime.

Black Hole Thermodynamics Mimic Van der Waals Fluids

Researchers have developed a novel approach to studying black holes by drawing parallels with the behavior of Van der Waals fluids, systems exhibiting properties similar to everyday liquids and gases. This allows them to investigate how quantum gravity effects might influence the stability and properties of these black holes. The team constructed a mathematical model of a black hole spacetime, carefully choosing a description of its geometry to accurately reflect the thermodynamic characteristics of a fluid. The resulting model provides a “dual” representation, allowing researchers to translate properties between the gravitational system and the more familiar fluid.

A key innovation lies in the application of a topological framework, utilizing a mathematical tool called a vector field to analyze the stability and phase transitions of the black holes. By examining the behavior of this vector field, researchers can determine the topological charge of the black hole, a measure of its overall “twistedness” and a crucial indicator of its stability. To account for quantum gravity effects, the researchers incorporated corrections based on the Generalized Uncertainty Principle, effectively introducing quantum corrections to the classical solution. This detailed analysis offers insights into how quantum gravity might influence the behavior of black holes and their potential to undergo phase transitions.

Quantum Corrections Preserve Black Hole Extremality

Researchers investigated the thermodynamic properties of Van der Waals black holes, incorporating corrections from three distinct theories of quantum gravity: the Generalized Uncertainty Principle, the Extended Uncertainty Principle, and Rainbow Gravity. These corrections aim to refine our understanding of black hole behavior at extremely small scales and high energies. The team discovered that despite these quantum corrections altering the relationship between a black hole’s entropy and its size, a key principle known as the universal extremality relation continues to hold true, suggesting a surprising robustness in black hole thermodynamics. The analysis reveals that each quantum gravity framework impacts the topological classification of black holes and their stability.

Notably, black holes subject to the Generalized Uncertainty Principle exhibit a consistent topological classification, indicating a stable structure. In contrast, black holes corrected by the Extended Uncertainty Principle display more varied behavior, sometimes possessing multiple topological charges. Interestingly, the team found that the impact on entropy differs significantly between these frameworks, with Rainbow Gravity predicting an increase in entropy, a unique thermodynamic implication. These findings offer insights into the fundamental nature of quantum gravity and its influence on black hole physics, highlighting the persistence of the universal extremality relation and the differing predictions of various quantum gravity theories.

Black Hole Topology and Quantum Gravity Corrections

This research investigates the thermodynamic properties of Van der Waals black holes, exploring how quantum gravity corrections impact their behavior. The study demonstrates that despite modifications to the standard entropy law introduced by the Generalized Uncertainty Principle, the Extended Uncertainty Principle, and Rainbow Gravity, a generalized form of the universal extremality relation continues to hold true. Furthermore, the analysis of thermodynamic topology reveals that variations in black hole parameters and model corrections significantly alter topological classifications and stability. Notably, the Generalized Uncertainty Principle-corrected scenario exhibits robust topological classifications, while the Extended Uncertainty Principle framework identifies distinct topological classes with varying charge configurations. The findings contribute to a deeper understanding of black hole thermodynamics and the role of quantum gravity corrections, offering a topological framework for interpreting black hole stability.