Influence of dark matter on quantum entanglement and coherence in curved spacetime

Abstract: Dark matter (DM) remains undetected, and developing theoretical models such as the promising perfect fluid dark matter (PFDM) is a key challenge in modern cosmology. In this work, we investigate the quantum characteristics of PFDM by analyzing the behavior of quantum entanglement and coherence for both fermionic and bosonic fields near a Schwarzschild black hole embedded in a PFDM halo. Our results reveal that PFDM can either enhance or degrade quantum entanglement and coherence, depending sensitively on its density. Notably, bosonic entanglement shows greater susceptibility to PFDM effects compared to fermionic entanglement, while fermionic coherence exhibits a stronger dependence on PFDM than its bosonic counterpart. These findings highlight the necessity of selecting appropriate quantum probes for DM detection based on the type of quantum resources, as different quantum fields exhibit significantly different responses to PFDM in curved spacetime.

• The paper demonstrates that perfect fluid dark matter alters the Schwarzschild metric, leading to non-monotonic changes in quantum entanglement and coherence.
• It employs Einstein field equations along with Klein-Gordon and Dirac formulations, using l1-norm, REC, and logarithmic negativity to quantify quantum effects.
• The findings highlight distinct responses between bosonic and fermionic fields, suggesting tailored quantum probes for more effective dark matter detection.

Influence of Dark Matter on Quantum Entanglement and Coherence in Curved Spacetime

Introduction

The paper discusses the effects of perfect fluid dark matter (PFDM) on quantum entanglement and coherence in curved spacetime, specifically in the vicinity of a Schwarzschild black hole. PFDM is a theoretical model proposed to account for the elusive nature of dark matter, which remains undetected despite constituting a significant portion of the universe's mass-energy content. The study aims to explore how PFDM influences entanglement and coherence, comparing the susceptibility of fermionic and bosonic fields in this curved spacetime scenario.

Theoretical Framework

The study begins by setting a theoretical foundation, establishing the Einstein field equations with components for PFDM in a Schwarzschild black hole metric. The PFDM influences the effective gravitational field, modifying the standard Schwarzschild solution. The paper meticulously derives the quantized fields for bosonic and fermionic particles in this modified spacetime, employing the Klein-Gordon and Dirac equations. It details the transformation to Kruskal coordinates to evaluate how field modes behave near the event horizon of the black hole surrounded by PFDM.

Quantum Coherence and Entanglement Measures

The authors utilize two primary measures: the $l_1$-norm and the relative entropy of coherence (REC), for quantifying coherence in quantum states. Entanglement is assessed via the logarithmic negativity approach, which provides insights into the entanglement structure degradation or enhancement due to PFDM proximity.

Behavior of Quantum Resources

The paper investigates how PFDM influences the quantum properties of fields, demonstrating a non-monotonic dependency of entanglement and coherence on PFDM density. Initially, as PFDM density increases, quantum resources degrade due to augmented Hawking radiation effects, but a subsequent decrease in Hawking temperature leads to a recovery of these resources.

The study reveals a distinct contrast between bosonic and fermionic reactions: Bosonic entanglement is highly sensitive to PFDM, making it an effective probe for PFDM effects, while fermionic coherence demonstrates higher susceptibility compared to bosonic coherence, providing a robust scheme for coherence-based detection.

Practical Implications and Future Directions

The findings suggest potential experimental pathways for dark matter detection via quantum field responses. By choosing the appropriate quantum resources and understanding field-specific susceptibilities, experimental designs can be optimized for probing the dark matter’s mysterious effects. Such strategies can refine and enhance the sensitivity of upcoming quantum technologies aimed at detecting or constraining dark matter models.

Conclusion

This study underscores the nuanced interplay between dark matter, represented by the perfect fluid model, and quantum informational resources like entanglement and coherence in curved spacetime. These insights could guide the development of more sensitive detection methods for dark matter, contributing a significant piece to the puzzle of understanding the universe's dark sector. The results indicate that different quantum fields respond uniquely to PFDM, underscoring the importance of selecting appropriate quantum probes based on the quantum resource type, which could inform the direction of future theoretical and experimental research in cosmology and quantum information science.