arXiv subjects

Wen-Xiang Chen

Publications and source records attributed to Wen-Xiang Chen.

At least 37 records · Page 2Linked to original sources

arXiv2024

Verification of the First Law of Horizon Thermodynamics for Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman Black Holes in Four-Dimensional f(R) Gravity with Dual Scalar Fields

This paper demonstrates the validity of the first law of horizon thermodynamics for Schwarzschild, RN, Kerr, and Kerr-Newman (KN) black holes within the framework of four-dimensional f(R) gravity coupled with dual scalar fields. Starting from a five-dimensional membrane world scenario, we derive the four-dimensional effective f(R) gravity action and obtain the corresponding black hole solutions. We then verify that these solutions satisfy the first law of black hole thermodynamics by explicitly calculating the variations of thermodynamic quantities. The analysis confirms the robustness of the horizon thermodynamics framework in extended gravitational theories, providing insights into the interplay between higher-dimensional theories and four-dimensional black hole thermodynamics.

gr-qc↗

arXiv2024

Topological and Geometric Properties of Spherically Symmetric Black Hole Metrics: Connections to Bose-Einstein Condensation and Uniqueness in Einstein Gravity

This paper investigates the interplay between the geometric and topological properties of spherically symmetric black hole metrics within Einstein gravity, emphasizing implications for Bose-Einstein Condensation (BEC). By analyzing metric functions, scalar fields, and the cosmological constant, we reveal how these black hole solutions are intrinsically linked to the underlying spacetime topology. We establish the uniqueness of a general black hole solution that supports BEC and demonstrate the impossibility of BEC in Kerr black holes. Additionally, through Laurent series expansions, residue calculations, winding numbers, and contour integrals, we confirm the algebraic and dimensional consistency between double Kerr black hole collisions and specific scalar field black hole solutions. This work uncovers fundamental connections in black hole interactions, providing a robust mathematical framework for understanding the dynamics of complex black hole systems and their interactions with scalar fields.

physics.gen-ph↗

arXiv2024

Quantum-Corrected Black Hole Solutions from f(R) Gravity and Their Canonical Ensemble Analysis

This study investigates quantum-corrected black hole solutions derived from f(R) gravity and explores their thermodynamic properties using the canonical ensemble framework. By incorporating higher-order f(R) corrections into classical black hole metrics, we construct regular black hole solutions that eliminate classical singularities. Advanced canonical ensemble techniques, including path integral formulations and stability analyses, are employed to examine the thermodynamic stability, phase transitions, and critical phenomena of these f(R)-corrected black holes. The results indicate that f(R) corrections significantly alter the thermodynamic landscape, introducing novel phase structures and stability conditions. Additionally, numerical simulations are conducted to visualize the behavior of thermodynamic quantities under varying f(R) correction parameters. This work provides deeper insights into the interplay between modified gravity effects and black hole thermodynamics, contributing to the broader understanding of gravitational phenomena in strong gravitational fields.

physics.gen-ph↗

arXiv2024

The Schwarzschild black hole in f(R) can exist superradiation phenomenon

This paper explores the mechanism by which Schwarzschild black holes may exhibit superradiance when Bell's theorem is considered a fundamental principle. By integrating quantum field theory with general relativity under the constraints imposed by Bell's inequalities, we develop a comprehensive model that extends the classical understanding of black hole dynamics. The study further draws parallels between the superradiant phenomena in Schwarzschild black holes and those observed in $f(R)$ gravity theories. Our findings suggest a profound mathematical and conceptual linkage between Bell's theorem and $f(R)$ gravity, particularly in the manifestation of irreducible singularities and their associated residues. This work provides a novel framework bridging quantum non-locality with modified theories of gravity, offering potential insights into the quantum nature of spacetime and black hole physics.

physics.gen-ph↗

arXiv2024

Advanced Mathematical Techniques in Renormalization of Elastic Models: A Comprehensive Analysis

In this study, we delve into the intricate mathematical frameworks essential for the renormalization of effective elastic models within complex physical systems. By integrating advanced tools such as Laurent series, residue theorem, winding numbers, and path integrals, we systematically address divergent loop integrals encountered in renormalization group analyses. Furthermore, we extend our analysis to higher-order physical models, incorporating techniques from quantum field theory and exploring quantum coherent states in complex systems. This comprehensive approach not only enhances the precision of calculating elastic anomalous exponents but also provides deeper insights into the topological structures underlying phase transitions and fixed-point behaviors. The methodologies developed herein pave the way for future explorations into more intricate many-body systems.This paper presents an extensive mathematical framework aimed at enhancing the complexity and extending the theory of Fermi condensates to high-temperature regimes. By incorporating a range of mathematical formulations from thermodynamics, statistical physics, and quantum field theory, we derive key equations and their high-temperature modifications. The study encompasses corrections to the Fermi-Dirac distribution, thermodynamic quantities of Fermi condensates, pairing gap equations within the BCS theory, correlation functions, modified Hamiltonians, path integral representations, and hydrodynamic equations.

physics.gen-ph↗

arXiv2024

Advanced Mathematical Approaches to Symmetry Breaking in High-Dimensional Field Theories: The Roles of Laurent Series, Residues, and Winding Numbers

This paper explores the advanced mathematical frameworks used to analyze symmetry breaking in high-dimensional field theories, emphasizing the roles of Laurent series, residues, and winding numbers. Symmetry breaking is fundamental in various physical contexts, such as high-energy physics, condensed matter physics, and cosmology. The study addresses how these mathematical tools enable the decomposition of complex field behaviors near singularities, revealing the intricate dynamics of symmetry breaking. Laurent series facilitate the expansion of fields into manageable terms, particularly around critical points. Residues provide a direct link between local field behavior and global physical properties, playing a crucial role in effective action formulations and renormalization processes. Winding numbers offer a topological perspective, quantifying how fields wrap around singularities and identifying stable topological structures like vortices, solitons, and monopoles. Extending these methods to (3+1) dimensions highlights the complexity of symmetry breaking in higher-dimensional scenarios, where advanced group theory and topological invariants are necessary to describe non-linear interactions. The findings underscore the importance of integrating these mathematical techniques into modern theoretical physics, with potential applications in quantum gravity, string theory, and the study of topological phases of matter. Future directions include further exploration of higher-dimensional extensions and their implications for understanding the fundamental nature of symmetry, topology, and field dynamics.

physics.gen-ph↗

arXiv2024

Thermodynamic Topology of Quantum RN Black Holes

This paper presents a comprehensive exploration of the thermodynamics of black holes, focusing on foundational concepts such as free energy, entropy, and topological numbers, alongside a detailed examination of quantum RN black holes. By extending the discussion to encompass the symmetry groups SO(2), SO(3)/SO(2), and SO(3) within the framework of (f(R)) gravity, the paper offers a nuanced understanding of black hole physics. Key insights include the pivotal role of free energy and entropy in understanding the thermodynamic properties of black holes, the significance of topological numbers in determining thermodynamic stability and phase transitions, and the implications of quantum mechanics and (f(R)) gravity on traditional thermodynamic concepts. This exploration not only enriches our theoretical knowledge of black holes but also sets the stage for future empirical investigations, marking a pivotal contribution to our ongoing quest to decipher the universe's mysteries.

physics.gen-ph↗

arXiv2024

Thermodynamic geometric analysis of 3D charged black holes under f(R) gravity

This article investigates 3D charged black holes within the scope of f(R) gravity, focusing on their thermodynamic attributes. The research primarily examines minor fluctuations around these black holes' equilibrium states and delves into their modified thermodynamic entropy. Utilizing geometric thermodynamics (GTD), the study evaluates the curvature scalar's role in pinpointing phase transition points in these black holes. A key finding is that several 3D charged black holes under f(R) gravity display thermodynamic properties akin to an ideal gas when their initial curvature scalar remains constant. Conversely, with a non-constant curvature scalar and a cosmological constant term that includes a negative exponent, these black holes exhibit characteristics similar to a van der Waals gas. The article outlines general solutions for scenarios involving non-negative powers and specific solutions for cases with negative powers. Notably, under certain conditions, a phase transition resembling that of a van der Waals gas is observed, suggesting a strong correlation between the black hole's fate and the cosmological constant, extending beyond the parameters proposed by the no-hair theorem.The research provides insights into the swift decline of peaks linked to both large and small black holes, revealing new aspects of black hole transitional behaviors. In a three-dimensional space (for $d=3$) with a variable $k_1$ set to 1, and considering a $Λ$ term that adheres to SO(2) symmetry, the study uncovers a cusp catastrophe in the G-T function graph. This observation, within the specified metric, points to a distinct solution that characterizes the ``Phase Transition and Properties of Bose-Einstein Condensation" under specific conditions. Notably, this phase transition in Bose-Einstein condensation occurs due to the symmetry shift from SO(3) to SO(2).

physics.gen-ph↗

arXiv2024

Schwarzschild-f(R) Black Holes and the Absence of Black Hole Bomb Effect

In this paper, we analytically study the superradiant stability of Schwarzschild-f(R) black holes under charged massive scalar perturbation. Using an analytic method based on Descartes' rule of signs, we extend previous methods developed for higher-dimensional Reissner-Nordstrom black holes to the Schwarzschild-f(R) black hole cases. Our results show that Schwarzschild-f(R) black holes are superradiantly stable under charged massive scalar perturbation, implying the absence of the black hole bomb effect.

gr-qc↗

arXiv2024

Thermodynamic Properties of Modified Black Hole Metrics in $f(R)$ Gravity

To construct new Schwarzschild and Kerr-Newman metric solutions, we start from the Lagrangian in entropy and statistical mechanics, introducing $f(R)$ gravity theory and dark energy definitions. Through a series of calculations, we derive the corrected metric solutions under different forms of $f(R)$ gravity.

physics.gen-ph↗

arXiv2024

Thermodynamic geometric analysis of RN black holes under f(R) gravity

In this article, we explore the RN black hole under f(R) gravity and its thermodynamic properties. We begin by examining the small fluctuations around the equilibrium state and summarizing the expression for the modified thermodynamic entropy of this black hole. Additionally, we delve into the geometric thermodynamics (GTD) of black holes and investigate the suitability of the curvature scalar of the GTD method for the phase transition point of the black hole. Moreover, we investigate the effects of modified parameters on the thermodynamic behavior of black holes.Within the framework of $f(R)$ modified gravity theory, we discovered that several RN black holes demonstrate thermodynamic properties resembling those of an ideal gas when the initial curvature scalar of the black hole remains constant. However, if the initial curvature scalar is non-constant and the cosmological constant term possesses a negative exponent, the Reissner-Nordström (RN) black holes could exhibit characteristics akin to those of a van der Waals gas.We separately list the general solutions for the case of non-negative powers and the special solutions for the case of negative powers. We observe that, under certain conditions, the phase transition analogous to the Van der Waals gas exists for charged black holes under f(R) gravity.

physics.gen-ph↗

arXiv2024

Exploring the Dynamics of Mass Inflation: Implications for Cauchy Horizon Stability and Black Hole Physics in General Relativity and $f(R)$ Gravity

This article investigates the phenomenon of mass inflation and its consequential impact on the stability of Cauchy horizons within the framework of general relativity. Mass inflation, defined by an exponential surge in energy, is pivotal in preserving causality across solutions like the Kerr black hole, ensuring the singular nature of causality-violating regions. Through a nuanced examination, the study expands the traditional understanding of mass inflation beyond stationary geometries to include dynamic black hole configurations. This exploration is enriched with a mathematical analysis of Schwarzschild and Kerr-Newman metrics, alongside a discussion on $f(R)$ gravity's implications for black hole physics. The findings challenge existing paradigms, proposing new models that accommodate mass inflation, thereby inviting further inquiry into the interplay between general relativity, quantum mechanics, and $f(R)$ gravity.

physics.gen-ph↗

arXiv2023

Superradiant stability of the Kerr black hole

We know that Kerr black holes are stable for specific conditions.In this article, we use algebraic methods to prove the stability of the Kerr black hole against certain scalar perturbations. This provides new results for the previously obtained superradiant stability conditions of Kerr black hole. Hod proved that Kerr black holes are stable to massive perturbations in the regime $μ\ge \sqrt 2 m{Ω_H}$. In this article, we consider some other situations of the stability of the black hole in the complementary parameter region$ \sqrt 2 ω< μ< \sqrt 2 m{Ω_H}.$

gr-qc↗

arXiv2023

Refined Perspectives on the Kerr-Schild Double Copy:Harmonizing Gravity and Electromagnetism in Metric Formulations

This paper explores the Kerr-Schild double copy, a duality relating gravity and electromagnetism. We show how Einstein's vacuum solutions in four dimensions can be converted into Maxwell's solutions via a double copy procedure, employing tensor fields. This technique yields novel solutions to Einstein's equations, including Kerr, Schwarzschild, and RN black holes. Introduced by Kerr and Schild in 1965, the Kerr-Schild action decouples the gravitational and matter fields, surpassing the Einstein-Hilbert action in facilitating calculations. It holds significant value for studying gravitational waves, cosmology, and black hole thermodynamics. We further delve into the applications of the Kerr-Schild double copy in deriving black hole solutions, analyzing gravitational waves, exploring alternative cosmological theories, and understanding black hole thermodynamics. Moreover, we investigate the implications of this double copy under SO(3) and SU(2) symmetries on the Schwarzschild and Kerr-Newman black hole metrics.

gr-qc↗

arXiv2023

Superradiation of Dirac particles in KN black hole

In this article, we process the approximate wave function of the Dirac particle outside the horizon of the KN ds black hole to effective potential V, and then derive V (including real and imaginary parts). We know that fermions cannot produce superradiation, but we can prove that Dirac particles in the KN black hole background can have a special solution through a certain operation, forming a Cooper pair, thus producing superradiation.We deal with the real and imaginary parts separately. When V (real part or imaginary part) has a maximum value, there may be a potential barrier outside the field of view to have a chance to produce superradiation.

gr-qc↗

arXiv2023

The Quantum and thermodynamic properties of dyonic RN-like black holes

The effect of magnetic fields on black hole superradiance is an exciting topic with possible astrophysical applications. A dyonic RN-like black hole is not asymptotically flat. It describes a black hole immersed in an asymptotically uniform magnetic field. This paper discusses the superadditive stability of binary RN black holes, asymptotically flat, band-like black holes. This article introduces the above condition into dyonic RN-like black holes if a dyonic RN-like black hole satisfies the requirement of $μ=yω$, When $\sqrt{2(B^2+Q^2)}/{r^2_+}< ω< q\varPhi_H$,particularly $μ\ge \sqrt{2}(q\varPhi_H)$,the dyonic RN-like black hole is superradiantly stable at that time.Scalars can be seen as combinations of positive/negative powers of a base, much like the decimal system. This principle is key in math and computing, from number systems to Fourier series (linked to $e^{i x}$ ). Dyonic RN-like black holes show no phase transition.

physics.gen-ph↗

arXiv2023

The possibility of the no-hair theorem being violated

Recently, one of my articles presented intriguing findings on the superradiant stability of Kerr black holes. These findings drew conclusions that appear to challenge the established ``No Hair Theorem". As is widely known, the ``No Hair Theorem" stems from the principles of general relativity. In this paper, we thoroughly examine the nexus between Bell's theorem and the uncertainty principle. By delving deep into the theoretical underpinnings of both concepts, we illustrate that Bell's theorem occupies a more foundational stance within the landscape of uncertainty. This gives rise to a particular probability, shedding light on why the no-hair theorem might not hold in the face of quantum effects. It's possible that while the no-hair theorem remains valid, the combined effects of classical and quantum mechanics introduce additional variations to the three parameters of the black hole. This nuance could represent a modest advancement in cosmological research.

physics.gen-ph↗

arXiv2023

Fermions can also produce super-radiation phenomena

According to traditional theory, it is believed that Fermions do not exhibit superradiation. However, when predetermined boundary conditions are in place, there is a possibility of combining the wave function of coupled Fermions, which can result in the emergence of superradiation phenomena. This article presents a novel perspective, proposing that Fermions have the potential to display superradiation phenomena. This implies that there is a broader scope for investigating superradiation and its relationship with boundary conditions.

physics.gen-ph↗