Renormalized Stress-Energy Tensor Reveals Instabilities in Horizonless Bardeen Spacetime Vacuum Fluctuations

The subtle quantum fluctuations of empty space, known as vacuum polarization, present a long-standing challenge to our understanding of gravity, particularly around exotic objects. Andrés Boasso and Francisco D. Mazzitelli, from Centro Atómico Bariloche and Instituto Balseiro, investigate these fluctuations in the unique environment surrounding a horizonless Bardeen spacetime, a theoretical alternative to black holes. Their work reveals that the behaviour of vacuum energy differs markedly depending on how the quantum field interacts with gravity, exhibiting distinct patterns at various distances, and importantly, predicts potential instabilities leading to exponential growth of these fluctuations under certain conditions. This research offers crucial insights into the interplay between quantum field theory and gravity, potentially refining our understanding of how gravity responds to quantum effects and challenging conventional expectations around compact objects.

Investigation reveals that vacuum fluctuations differ significantly between conformally and non-conformally coupled fields, both in magnitude and in their behaviour at short and intermediate distances. At large distances, the research recovers the universal asymptotic behaviour previously observed in black hole and Newtonian star backgrounds. Extending beyond the weak-field regime, the findings demonstrate that, for certain parameter ranges, the modes of the field can develop imaginary frequencies, leading to instabilities and an exponential growth of vacuum fluctuations.

Vacuum Polarization and Curved Spacetime Analysis

This research presents a comprehensive analysis of quantum field theory in curved spacetime, focusing on the Bardeen model and its implications for vacuum polarization, particle creation, and the nature of compact objects. The study explores how quantum fields behave in the presence of gravity, leading to phenomena like vacuum polarization and Hawking radiation. A central focus is understanding how strong gravitational fields affect the vacuum state of quantum fields and induce particle creation. The Bardeen model, a solution describing a regular black hole without a singularity, serves as a key test case, allowing researchers to investigate quantum effects without the complications introduced by a singularity.

The paper emphasizes the importance of using a nonlocal effective action, which accounts for long-range correlations, unlike simpler local approximations. The research also touches upon the concept of quantum hair, the idea that quantum effects can leave unique imprints on the spacetime geometry. Key findings demonstrate the importance of nonlocal effective actions for accurately describing quantum effects in curved spacetime. The Bardeen model proves to be a valuable tool for investigating quantum effects in a singularity-free environment. The research suggests that regular black holes like the Bardeen model may exhibit quantum hair, meaning their quantum properties can distinguish them from other objects with the same classical characteristics.

The work provides a rigorous mathematical framework for calculating the nonlocal effective action and analyzing the behaviour of quantum fields in curved spacetime. This research contributes to the ongoing effort to develop a consistent theory of quantum gravity, reconciling quantum mechanics with general relativity. The findings have implications for our understanding of compact objects, their formation, and their evolution. The concepts explored could also be relevant to cosmology, particularly the study of the early universe. The research could potentially lead to experimental tests of quantum gravity.

Quantum Fluctuations Around Horizonless Compact Objects

Researchers have investigated the behaviour of quantum fields in the curved spacetime surrounding a compact object, specifically using the Bardeen metric, which describes an object without an event horizon. The study focuses on the renormalized stress-energy tensor and how it differs depending on the field’s coupling to gravity. The results demonstrate significant differences in these fluctuations between fields that respond strongly to curvature and those that do not, particularly at shorter and intermediate distances. Importantly, the team found that at very large distances, the behaviour of quantum fluctuations is surprisingly universal, mirroring that found around both black holes and ordinary stars, provided the field is either minimally or conformally coupled to gravity.

This suggests a fundamental robustness in how quantum fields interact with gravity at large scales. The calculations were performed using a perturbative approach, confirming the expected decay of energy density with distance. Beyond the standard weak-field approximation, the research explored scenarios where the chosen vacuum state might become unstable. The team discovered that under certain conditions, the field modes can develop imaginary frequencies, leading to an exponential growth of vacuum fluctuations. This instability suggests that the vacuum state is not always as stable as assumed and can be significantly affected by strong gravitational fields.

Furthermore, the study compared its findings with those obtained using an alternative method based on the anomaly-induced effective action. The researchers found discrepancies between the two approaches, suggesting limitations in the anomaly-induced effective action, particularly in accurately capturing the long-distance behaviour of the stress-energy tensor. This highlights the importance of employing multiple theoretical tools to fully understand the complex interplay between quantum fields and gravity in curved spacetime. The work provides valuable insights into the nature of quantum vacuum fluctuations and their response to strong gravitational fields.

Bardeen Spacetime Alters Quantum Vacuum Fluctuations

This research investigates vacuum fluctuations of quantum fields within the horizonless Bardeen spacetime, a model designed to mimic black hole characteristics without an event horizon. The study demonstrates significant differences in these fluctuations between fields that respond differently to the curvature of spacetime, both in terms of their overall magnitude and their behaviour at varying distances from the central object. Importantly, the calculations reveal the potential for instabilities and exponential growth of these fluctuations under certain conditions. The team found that the Bardeen metric results in a regular stress-energy tensor and exhibits a complex energy density structure around a characteristic radius. While previous work suggested a stable vacuum state for specific parameters, this analysis confirms stability within those limits and identifies regions where instabilities can arise. Future research will focus on refining the understanding of the stress-energy tensor’s behaviour over time and exploring the implications of these findings for the broader study of quantum fields in curved spacetime.