Non-Commutative Schwarzschild Black Hole Achieves Particle Creation Estimates Using Tunneling

Researchers have investigated the quantum properties of black holes within a framework incorporating the principles of non-commutative geometry. A. A. Araújo Filho (Universidade Federal da Paraíba and Universidade Federal de Campina Grande, and Center for Theoretical Physics, Khazar University), alongside I. P. Lobo and P. H. M. Barros et al., present a novel analysis of a Schwarzschild black hole constructed using a Moyal twist, effectively modelling a non-commutative spacetime. Their work calculates particle creation rates near the black hole’s event horizon , utilising a tunnelling method and addressing divergent integrals , and importantly, estimates the black hole’s evaporation lifetime. By revisiting previous studies on gauge Schwarzschild black holes and applying constraints derived from solar-system tests, this research offers significant insights into the interplay between quantum field theory, general relativity, and the fundamental nature of spacetime itself.

Non-commutative Gravity and Black Hole Evaporation

Scientists have demonstrated a novel approach to understanding black hole physics by investigating quantum effects within a non-commutative gauge gravity framework. The team achieved a consistent formulation for a Schwarzschild-like black hole constructed using a specific Moyal twist, ∂t ∧∂θ, which crucially allows for a well-defined surface gravity, a key element for thermodynamic calculations. This research estimates particle creation rates for both bosons and fermions using the quantum tunneling method, addressing the challenge of divergent integrals through a residue prescription. The study unveils a detailed analysis of black hole evaporation, calculating emission rates and lifetimes, and revisits previously published results on gauge Schwarzschild black holes to refine the theoretical landscape.
The work establishes a modified Schwarzschild black hole solution derived from a corrected non-commutative gauge theory construction, building upon earlier research and addressing identified inconsistencies. Researchers meticulously reformulated the construction procedure, revealing a previously omitted contribution in the non-commutative sector, impacting the vierbein fields and ultimately the metric components. This refined approach allows for a consistent thermodynamic description, enabling the computation of crucial quantities like entropy, Hawking temperature, and heat capacity in this non-commutative setting. Experiments show that by focusing on the ∂t ∧∂θ Moyal twist, the surface gravity remains well-defined, overcoming limitations present in other configurations and facilitating a comprehensive analysis of particle emission and mass loss.

The study reveals that particle creation is estimated for both bosonic and fermionic fields, employing the quantum tunneling method to navigate the complexities of particle production near the black hole horizon. Divergent integrals encountered in these calculations are systematically handled using the residue prescription, ensuring physically meaningful results. Since the surface gravity is well defined for this configuration, the corresponding emission rates and evaporation lifetimes are also computed, providing insights into the black hole’s long-term behaviour and eventual decay. Furthermore, the research establishes constraints on the non-commutative parameter Θ by comparing theoretical predictions with solar-system tests, bridging the gap between theoretical models and observational data.

This breakthrough reveals a pathway to explore black hole physics beyond the classical geometric picture, incorporating the principles of non-commutative spacetime. The research opens new avenues for investigating the emergence of a smallest measurable length scale, a concept motivated by quantum gravity approaches. By revisiting and refining existing theoretical frameworks, the team has provided a robust foundation for future studies exploring the interplay between non-commutative geometry, black hole thermodynamics, and particle physics, potentially leading to a deeper understanding of the universe’s most enigmatic objects.

Non-commutative Black Hole Particle Creation and Lifetimes

Scientists investigated quantum aspects of a non-commutative gauge gravity formulation of a Schwarzschild-like black hole constructed using a Moyal twist ∂t ∧∂θ. The research team estimated particle creation for both bosonic and fermionic fields, employing the quantum tunneling method to model these processes precisely. Divergent integrals encountered during calculations were systematically addressed using the residue prescription, ensuring mathematically sound results. Since surface gravity was well-defined for this specific configuration, the study computed corresponding emission rates and evaporation lifetimes, providing insights into black hole dynamics.

Researchers revisited previously published results concerning gauge Schwarzschild black holes, critically evaluating existing literature and identifying potential inconsistencies. The work pioneered a refined construction procedure, demonstrating that earlier formulations were incomplete and omitted a crucial term: −1/16ΘνρΘλτh ωac ν ωcd λ DτRd5 ρμ + ∂τRd5 ρμ i. This omission significantly impacted the tetrad sector, leading to nontrivial modifications of the vierbein fields and altering the associated metric components. The team engineered a system to accurately model these changes, revealing how non-commutative corrections reshape the geometry of black holes.

Experiments employed a non-commutative parameter, Θ, to explore the effects of spacetime deformation at short distances, building upon the principle that quantum gravity may introduce a smallest measurable length. The approach enables the investigation of how departures from classical spacetime commutativity influence the dynamical evolution of black holes, particularly regarding particle emission and mass loss. Scientists harnessed the Seiberg, Witten map to deform the underlying symmetry content of the geometry, preserving gauge consistency while introducing non-commutative corrections. Furthermore, the study inferred constraints on the non-commutative parameter Θ from solar-system tests, including analyses of perihelion precession of Mercury, deflection of light, and time delay of light, achieving a connection between theoretical predictions and observational data. These calculations, performed with meticulous precision, provide a means to test the validity of the non-commutative gauge gravity framework against established astrophysical observations and potentially constrain the magnitude of non-commutative effects.

Non-commutative Black Hole Emission and Lifetime Calculations

Scientists achieved a refined formulation of a Schwarzschild-like black hole within a non-commutative gauge framework constructed via the Moyal twist ∂t ∧∂θ, addressing inconsistencies found in prior literature. The research meticulously estimated particle creation for both bosonic and fermionic fields, employing the quantum tunneling method and utilising the residue prescription to handle divergent integrals, a crucial step for accurate calculations. Experiments revealed that, with the surface gravity well-defined for this specific configuration, corresponding emission rates and black hole evaporation lifetimes could be consistently computed, overcoming limitations of previous studies. Data shows the team revisited previously reported results on gauge Schwarzschild black holes, providing a robust foundation for their new findings and ensuring consistency with existing knowledge.

The team measured particle creation. Measurements confirm that the modified Schwarzschild black hole geometry, obtained through a revised construction procedure, exhibits distinct characteristics compared to classical solutions. The study meticulously calculated the non-commutative parameter Θ, inferring constraints from solar-system tests, specifically, analysing perihelion precession of Mercury, deflection of light, and time delay of light. Data shows that the analysis of perihelion precession yielded precise bounds on Θ, while observations of light deflection and time delay provided independent verification of these constraints, strengthening the robustness of the results. Tests prove that the revised construction procedure successfully addresses shortcomings in earlier formulations, providing a more accurate and physically consistent description of non-commutative black hole physics. Researchers.