Modified Black Hole Solution Eliminates Ultraviolet Divergences at Planck Scale

The extreme conditions near black holes provide a unique testing ground for theories attempting to reconcile gravity with quantum mechanics, and recent research explores how these conditions might resolve problematic infinities arising in standard calculations. Athanasios G. Tzikas from the University of Bergamo, along with colleagues, investigates electrically charged black holes modified by principles from quantum theory, specifically incorporating a minimal length scale at the Planck level. This work demonstrates that such modifications successfully eliminate ultraviolet divergences, effectively preventing calculations from breaking down, while still aligning with established physics at larger scales. The resulting black hole solution exhibits behaviour analogous to a Van der Waals fluid, and the team further examines its potential role in the early universe, calculating the rate at which these black holes could have formed from quantum fluctuations, offering new insights into the origins of cosmic structure.

Black Hole Thermodynamics and Early Universe Connections

This extensive collection of references explores the intersection of black hole physics, cosmology, and quantum gravity, encompassing topics from fundamental black hole properties to their potential roles as dark matter and their formation in the early universe. The material is organized around core black hole physics, their connection to cosmology, explorations of quantum gravity, and advanced theoretical models. The foundational work covers classical black hole mechanics, Hawking radiation, and black hole thermodynamics, including concepts like enthalpy and pressure, with researchers applying these principles to explore extended phase space and potential phase transitions within black holes. Investigations into Euclidean quantum gravity and the no-boundary proposal attempt to describe the universe’s initial conditions.

A major theme is the study of primordial black holes, formed in the early universe, and their potential contribution to dark matter, with researchers investigating their formation during inflation and exploring constraints on their abundance. The list also covers cosmological pair production, the creation of black holes in expanding universes, and the implications of Nariai black holes for cosmology. Beyond standard general relativity, the collection includes work on modified theories of gravity and quantum gravity effects, exploring noncommutative geometry, regular black holes that avoid singularities, and the application of extended phase space to understand critical phenomena in black hole thermodynamics. Advanced topics include the duality between electric and magnetic black holes, black holes in higher dimensions, and the connection between black holes and quintessence models of dark energy. This collection highlights the interdisciplinary nature of modern black hole research, drawing from diverse fields like general relativity, quantum field theory, and cosmology, with a strong emphasis on primordial black holes suggesting their importance as potential dark matter candidates and probes of the early universe.

Primordial Black Hole Nucleation in Expanding Spacetime

Researchers investigated the potential creation of primordial black holes in expanding spacetime, considering lukewarm, cold, and de Sitter backgrounds to assess the likelihood of black hole formation and survival. Their methodology focuses on calculating the rate at which black holes nucleate, a process influenced by gravity, electromagnetism, and the expansion of the universe. A key innovation is the application of a “no-boundary proposal” combined with a detailed analysis of spacetime geometry and thermodynamics, allowing researchers to model the creation of black holes from quantum fluctuations in the early universe. The team meticulously calculated the “action” associated with each scenario, comparing it to empty de Sitter space to determine the likelihood of black hole nucleation, and modified standard black hole descriptions to account for a minimal length scale. Researchers explored the relationships between black hole properties, such as mass, charge, and the radii of event and cosmological horizons, and the cosmological constant, requiring extensive numerical computations. They determined the rate of black hole production for each scenario, revealing extremely suppressed rates, ranging from e -1011 to e -1010 for post-inflationary scenarios, suggesting that black hole production is highly improbable under the considered conditions.

Singularities Resolved with Minimal Length Spacetime

Researchers developed a theoretical framework for black holes that addresses singularities and ultraviolet divergences, issues arising when applying conventional physics to extremely small scales. This work combines concepts from nonlinear electrodynamics and a minimal length scale, suggesting that spacetime itself has a granular structure at the Planck scale, resulting in electrically charged black holes that remain well-behaved even at these incredibly small distances. The team’s approach modifies both the electric and matter components of a black hole, introducing corrections that become significant as the size of the black hole approaches this minimal length, allowing the black hole to recover familiar properties at larger scales but exhibit different behavior at the Planck scale. Notably, the model predicts a unique relationship between the black hole’s electric and gravitational fields, akin to the behavior of a Van der Waals fluid. Further investigation reveals that these modified black holes can exist in both cosmological anti-de Sitter and de Sitter spaces, influencing their stability and potential for creation. The researchers explored the possibility of these black holes forming through quantum processes, specifically examining the rate at which pairs of these non-singular black holes could nucleate during and after cosmic inflation, offering a potential mechanism for the creation of primordial black holes in the early universe.

Planckian Black Holes and Dark Matter Production

This research presents a modified model of electrically charged black holes, incorporating principles of nonlinear electrodynamics and a minimal length scale, effectively resolving ultraviolet divergences. The resulting black hole solution recovers standard Maxwellian behaviour at larger scales while remaining well-behaved at extremely small distances, and investigates the production of these black holes within a de Sitter background, demonstrating a mechanism for their creation via quantum fluctuations, potentially contributing to the overall dark matter content of the universe. The calculations suggest that a significant number of these Planckian black holes, estimated around 10 60, could exist today, possessing a combined mass comparable to the observed dark matter. However, the authors acknowledge that this relies on extending the conjecture of pre-inflationary black hole production to the present epoch, a point requiring further investigation. The analysis utilizes an anisotropic fluid approach.