We construct Kaluza-Klein monopole solutions with scalar hair provided by a massive complex scalar field multiplet that minimally couples to five-dimensional Einstein gravity. Writing the scalar field multiplet in terms of the Wigner D-matrices, we introduce the ansatz of the scalar multiplet compatible with the symmetries of the Gross-Perry-Sorkin monopole, on which the scalar hair grows. We give the ansatz for a multiplet with arbitrary number of components, whereas we show numerical solutions of the hairy Kaluza-Klein monopole specifically for the cases of scalar triplet and quadruplet. These generalize the preceding study on a doublet [<a href="http://dx.doi.org/10.1007/JHEP01(2024)181">J. High Energy Phys. 01 (2024) 181</a>]. We find that the range of the mass and angular momentum of the hairy solutions are larger for higher multiplets.

Japan

Takaaki Ishii

Keiju Murata

Keita Sugawara

Kaluza-Klein monopole with scalar multiplet hair

Gauge fields in extra compact dimensions can drive inflation in the four-dimensional (4D) non-compact spacetime, a scenario known as $\textit{extra-natural inflation}$. A time-dependent gauge field configuration generates the electric field along the compact dimension, enabling the production of Kaluza-Klein (KK) particles charged under the field via the Schwinger effect. We construct the extra-natural inflation model within a five-dimensional (5D) quantum electrodynamics (QED) framework coupled to gravity including matter fields that generate the inflationary one-loop effective potential. In general, multiple charged fields can exist, and we show that KK particle production occurs under these conditions. Since KK momentum is conserved, the produced KK particles may become superheavy dark matter or dominate the universe, depending on the model parameters. Furthermore, we show that even when the gauge field acts not as the inflaton but as a spectator field, its post-inflationary oscillations, initiated when the Hubble friction becomes negligible, can also generate superheavy KK modes. This suggests that KK particle production is a generic outcome when gauge potentials along compact dimensions are light.

South Korea

Yusuke Yamada

Extra-natural production of superheavy Kaluza-Klein particles

We show that the energy of a Kaluza-Klein bubble of nothing is unbounded from below even if the size of the circle at infinity and the size of the minimal sphere at the bubble are fixed. We demonstrate this by presenting a family of explicit time-symmetric initial data satisfying these boundary conditions with arbitrarily negative energy. In particular, this is true for very small bubbles, indicating that the standard Kaluza-Klein vacuum is more unstable than previously thought.

United States

Gary T. Horowitz

Guanyu (Ricky) Lu

Arbitrarily negative energy for small Kaluza-Klein bubbles

One-dimensional scattering of a wave packet of a relativistic fermion under a temporally oscillating electric field superimposed on a potential step is discussed by using the Furry-picture perturbation theory, where the oscillating electric field is treated as a perturbation. Reflection and transmission probabilities of the wave packet, which in its single-mode limit are consistent with those in the stationary scattering off the potential step alone, are investigated up to the second order. We show that even in the absence of the so-called Klein region, a positive-frequency incoming wave can penetrate the negative- frequency region below the potential step by emitting its energy to the oscillating electric field with a finite tunneling probability.

Makoto Ochiai

Shunsuke Shibayama

Dynamically assisted Klein tunneling in the Furry picture

We examine the thermal and statistical properties of the one-dimensional Klein–Gordon oscillator within two prominent Doubly Special Relativity (DSR) frameworks: Amelino-Camelia and Magueijo–Smolin. Using the modified dispersion relations specific to each formulation, we derive the positive energy spectra, construct the partition function via the Euler–Maclaurin method, and compute key thermodynamic quantities, including the specific heat Cv, as functions of temperature and the deformation scale. Planck-scale corrections produce distinct, theoretically resolvable shifts in both the position and magnitude of the Cv peak in the two models. An accompanying entropy analysis reveals that these peaks correspond to smooth Schottky-type anomalies: the specific heat curves remain analytic and positive across the explored temperature range, and thus do not indicate latent or continuous thermodynamic phase transitions. These comparative results provide a robust diagnostic framework for differentiating DSR prescriptions in relativistic quantum systems and reinforce the transition-free character of their thermal response.

Algeria

Abdelmalek Boumali

Kazakhstan

Azerbaijan

Nosratollah Jafari

Bekdaulet Shukirgaliyev

Fadila Serdouk

Thermal properties of Klein–Gordon oscillator in the context of Amelino-Camelia and Magueijo–Smolin doubly special relativity (DSR) frameworks

An Solution of exact Black Hole (BH) is developed within the framework of Kaluza-Klein (KK) gravity, featuring the existence of massive vector fields in its surroundings. KK gravity in 4D (four Dimension) is significantly noteworthy because it indicates the spectrum of states of particle comprising not only the massless spin-2 gravitons found in context of General Relativity (GR) but also some additional spin-0 and spin-1 graviton modes. This article develop a solution which is encompassed by massive spin-1 gravitons in context of KK gravity. This solution is influenced by spin-1 graviton mass with an extra parameter that represents refinement to Newton’s constant, along with interaction between mass of black hole and massive vector field. In this article, We explained the motion of massive and massless particles by investigating their effective potential <math altimg='si9.svg'><msub><mi>V</mi><mrow><mi>e</mi><mi>f</mi><mi>f</mi></mrow></msub></math>, event horizon <math altimg='si1.svg'><msub><mi>r</mi><mi>h</mi></msub></math>, photon orbit <math altimg='si5.svg'><msub><mi>r</mi><mrow><mi>p</mi><mi>h</mi></mrow></msub></math>, and inner circular orbit <math altimg='si10.svg'><msub><mi>r</mi><mrow><mi>I</mi><mi>S</mi><mi>C</mi><mi>O</mi></mrow></msub></math>. It has been shown that Black Hole parameters <math altimg='si2.svg'><mi>&#955;</mi></math> and <math altimg='si3.svg'><mi>&#947;</mi></math> produces a prominent impact. We also explore the phenomenon of weak gravitational lensing, employing a detailed approach to observe the deflection angle.The aim behind this work highlights promising directions for further exploration into the fundamental principles underlying gravitational theories.

Pakistan

Sikander Mehmood

Uzbekistan

Allah Ditta

Waleed Ahmad

Fahad Pervaiz

Wajiha Tanveer

Saudi Arabia

Awad A. Ibraheem

India

Rana Muhammad Zulqarnain

Exploring black hole phenomena in Kaluza-Klein gravity with massive vector fields discussing the particle dynamics and gravitational deflection of light

This work considers the dynamics of the gauge vector and inflaton (dilaton) fields inspired by Kaluza–Klein theory in an inflationary universe with Bianchi type-I spacetime. The inverse power-law potential of the inflaton field is used to study dynamical system analysis. As a result, all fixed points in the autonomous system are non-hyperbolic fixed points, and one cannot determine their stability. Therefore, a center manifold theory is required to analyze the stability of the dynamical system properly. Interestingly, we found an isotropic attractor point which means that the universe undergoes accelerated expansion (inflation) from an anisotropic phase to an isotropic phase of the universe. According to the dynamical system analysis of the anisotropic Bianchi type-I universe with the inspired Kaluza–Klein model, our results supported the isotropization of the observed universe.

Thailand

Jaturaporn Watanakampolkij

Patinya Ma-ardlerd

Natthason Autthisin

Pornpatara Chuvala

Nutthaphat Lunrasri

Chakrit Pongkitivanichkul

Daris Samart

Kaluza–Klein inspired a model of the inflation with the inverse power law potential in Bianchi type-I universe

In the decay process of metastable vacua in quantum field theories, the bounce solution, a classical solution in Euclideanized theories, is helpful in calculating the decay rate. Recently, the bounce solution with a conical singularity has attracted wide attention and revealed physical importance. In this paper, we discuss the bubble of nothing solution, which describes the decay process of a five-dimensional Kaluza-Klein vacuum, and study the consequence of including conical singularity. We found that the bounce solution with singularities has a higher decay rate than those without. This effect suggests that a singular solution can play a dominant role in vacuum decay of theories with compact internal space. We also discuss the enhanced decay rate from a thermodynamic perspective.

Yutaka Ookouchi

Ryota Sato

Sohei Tsukahara

Decay of Kaluza-Klein vacuum via singular instanton

We explore the phase emergence and corresponding phase transitions of charged dilaton $$\text {AdS}$$ black holes in the gauged Kaluza–Klein theory in the context of the generalized free energy. The black hole solutions are asymptotic to the AdS $$_D$$ geometry, and one can obtain them from the dimensional reduction of gauged supergravities on the compact internal manifolds, leading to the restriction as $$4\le D\le 7$$ . In the canonical ensemble, we classify the black hole thermodynamics into three different classes as follows: (i) $$D=4$$ , (ii) $$D=5$$ , and (iii) $$D=6,7$$ . In the grand canonical ensemble, the black hole thermodynamics is independent on the number of spacetime dimensions and the pressure, but it depends on the chemical potential $$\Phi $$ . As a result, we classify the black hole thermodynamics as follows: (i) $$\Phi <1$$ , (ii) $$\Phi >1$$ , and (iii) $$\Phi =1$$ . In addition, we show that the asymptotically AdS solutions can provide a scenario where our Universe lives on a nucleated bubble mediating the decay of unstable AdS space. We point out a minimum value for the scale factor in the case of a neutral bubble by which the initial curvature singularity can be removed. We obtain a dS universe corresponding to the late-time evolution of the nucleated bubble, avoiding the constraint of the dS conjecture.

Vietnam

Tran Hung

Cao Nam

Generalized free energy of black holes and nucleated bubbles in the gauged Kaluza–Klein theory

We investigate the scattering amplitudes of massive Kaluza-Klein (KK) states in compactified five-dimensional warped gauge and gravity theories. Focusing on tree-level 2 → 2 processes, we analyze the leading-order amplitudes involving bulk KK matter fields and KK gauge/gravitational Goldstone bosons. By imposing the gauge theory equivalence theorem (GAET) and the gravitational equivalence theorem (GRET) within warped KK theories, we systematically reconstruct the leading-order amplitudes for physical KK gauge bosons and gravitons, thereby circumventing the intricate energy cancellations inherent in physical amplitudes. Within this framework, the correspondence between GAET and GRET arises as a direct manifestation of the leading-order double-copy relation in the high-energy expansion. This connection provides a foundation for extending the BCJ double-copy construction to four-point amplitudes involving bulk KK matter fields, and further generalizes to arbitrary $\textit{N}$-point cases, enabling a systematic derivation of the corresponding gravitational amplitudes with consistent incorporation of KK matter fields at leading order.

Kezhu Guo

Yanfeng Hang

Equivalence theorems and double-copy structure in scattering amplitudes of massive Kaluza-Klein states with matter interactions