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F. M. Belchior

Publications and source records attributed to F. M. Belchior.

12 recordsLinked to original sources
arXiv2026

Five-dimensional thick branes in the scalar representation of $f(Q,B)$ gravity

One examines a codimension-one thick braneworld in the scalar representation of $f(Q,B)$ gravity, where $Q$ is the nonmetricity scalar, and $B$ is the boundary term satisfying $R=Q-B$. We write the gravitational sector in terms of two auxiliary scalar fields, $φ=f_Q$ and $ψ=f_B$, and an interaction potential $U(φ,ψ)$ obtained by a Legendre transformation from the $f(Q,B)$ function. Working in the coincident gauge and assuming a five-dimensional warped geometry with four-dimensional Poincaré symmetry, we derive the complete set of brane equations sourced by a canonical bulk scalar field. To accomplish our purpose, we address two models of smooth asymptotically AdS thick brane with localized scalar profiles. Furthermore, we also analyze tensor perturbations and demonstrate the localization and stability of the massless graviton.

gr-qc↗
arXiv2026

One-loop contributions in Lorentz-violating scalar QED with nonminimal coupling

In the context of pertubative aspects of Lorentz-violating theories, we study the divergent one-loop two-point functions of a Lorentz-violating (LV) extension of scalar QED containing a dimension-five CPT-odd nonminimal coupling. The model is defined through a generalized covariant derivative involving a constant background vector and the dual electromagnetic field strength. After expanding the action, we derive the full set of vertices relevant for the photon and scalar self-energies, including the mixed minimal-nonminimal seagull interaction diagram required by the gauge invariance. Using dimensional regularization, we compute the divergent parts of the vacuum polarization and scalar self-energy. The complete photon two-point function is shown to be transverse since the mass-dependent pieces generated by the mixed and purely nonminimal bubble graphs cancel against the corresponding seagull graphs, leaving higher-derivative CPT-odd and CPT-even LV gauge counterterms. The scalar self-energy generates LV kinetic and higher-derivative counterterms. The calculation confirms that gauge invariance is preserved, while the nonminimal interaction should be understood within an effective-field-theory expansion.

hep-th↗
arXiv2026

Nonlocal four-fermion theory

In this work, we formulate and analyze a nonlocal four-fermion theory in which the usual Dirac operator is deformed by an entire nonlocal form factor. After introducing an auxiliary scalar field, we derive the mean-field effective action and the corresponding gap equation for the dynamical mass. A central technical point of the analysis is that the nonlocal form factor is a matrix function of the Dirac operator, so the inverse propagator must be treated as an element of the closed algebra generated by the identity and $\not{\!p}$ operators, rather than as a purely scalar quantity. We obtain explicit expressions for the gap kernel for two representative choices of a form factor, $f_{I}(\not{\!\partial})=e^{-\not{\partial}/Λ}$ and $f_{II}(\not{\!\partial})=e^{-i\not{\partial}/Λ}$. Following the IR/UV matching method used in the recent Dirac-like nonlocal spinor theory [1], the momentum integral is split at an intermediate scale $M\ll Ω\ll Λ$, expanded analytically in the infrared and ultraviolet regions, and compared with the usual local NJL/Gross-Neveu result. We show that the hyperbolic form factor enhances the gap integral and lowers the critical coupling, whereas the oscillatory form factor suppresses it and raises the critical coupling. The finite-temperature and finite-density extension is formulated through Matsubara sums and a corrected contour representation, with the local thermal gap equation recovered in the limit $Λ\to\infty$.

hep-th↗
arXiv2026

Geodesics and Thermodynamics of a Schwarzschild Black Hole with Hernquist Dark Matter

In this work, we investigate the physical and geometrical properties of a Schwarzschild black hole (BH) immersed in a Hernquist dark matter halo. To accomplish our purpose, one builds the BH metric by incorporating the Hernquist dark matter profile into the Schwarzschild geometry. In addition, we verify the null geodesic solutions and the Halo effect on photon dynamics. Within this framework, one examines the corresponding light trajectories to determine the deformation of photon paths generated by the dark matter distribution. Furthermore, the thermodynamic properties of the system are studied by deriving expressions for the black hole mass, the horizon condition, the Hawking temperature, the entropy, the Gibbs free energy, and the heat capacity. Our results show that the dark matter halo modifies the thermal structure and stability conditions of the black hole configuration. Finally, we investigate the scalar perturbations to examine the influence of the Hernquist halo on the dynamical propagation of scalar fields in the BH background. In this framework, the results obtained demonstrate that the dark matter parameters yield nontrivial corrections to the optical, thermodynamic, and perturbative properties of the Schwarzschild black hole, producing deviations from the standard vacuum solution.

gr-qc↗
arXiv2026

Thick branes and fermion localization in five-dimensional $f(T,T_G)$ gravity

We investigate thick-brane configurations in five-dimensional $f(T,T_G)$ modified teleparallel gravity. In five dimensions, the torsional Gauss-Bonnet invariant $T_G$ contributes dynamically, leading to genuinely new effects even at linear order. Within a warped geometry supported by a scalar field, we construct explicit solutions and show that the $T_G$ sector significantly modifies the brane structure. In particular, the coupling parameter controls the deformation of the warp factor and energy density, allowing for the emergence of brane splitting and nontrivial internal structure. We further analyze the localization of spin-$1/2$ fermions via a Yukawa coupling. The system admits a normalizable chiral zero mode, while the opposite chirality remains delocalized. The massive Kaluza-Klein spectrum is strongly affected by the torsional Gauss-Bonnet term, which modifies the effective potentials and leads to the appearance of resonant quasi-localized states.Our results show that $f(T,T_G)$ gravity provides a richer framework for braneworld models, where torsional higher-order corrections play a key role in shaping both geometry and field localization.

hep-th↗
arXiv2026

Scattering, absorption and greybody factor of scalar particles by Lorentz-violating charged black holes

In this work, we investigate the scattering and absorption of spin 0 particles for electrically charged black holes in two gravity models with spontaneous Lorentz symmetry breaking. The first one is the so-called bumblebee model that involves a vector field with a nonvanishing vacuum expectation value (VEV), while the second one involves a self-interacting Kalb-Ramond field coupled to gravity. For our purpose, we employ the partial waves method to compute the scattering cross-section and the absorption for these charged black holes. Moreover, we calculate the greybody factors (GFs) for spin 0 particles, showing the influence of both the LV parameter and electric charge.

gr-qc↗
arXiv2025

Fermionic greybody factors and strong gravitational lensing by Lorentz-violating global monopole

In this work, we study the greybody factors (GFs) of spin 1/2 and spin 3/2 fermions for a black hole with global monopole in self-interacting Kalb-Ramond gravity with Lorentz symmetry violation. For our purpose, we consider the Dirac and Rarita-Schwinger equations in curved spacetime by proceeding with separating these equations into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schrödinger-like wave equations with potentials are derived by decoupling the radial wave equations using the tortoise coordinate. Moreover, we calculate the angular deflection of light in the strong field limit. With the expression for angular deflection in the strong field limit, we compute the positions as well as magnification of the respective relativistic images. We compute the shadows cast by the Lorentz-violating (LV) black hole with a global monopole and analyze how the LV parameter and the monopole charge affect the shadows.

gr-qc↗
arXiv2025

Global monopole in a Ricci-coupled Kalb-Ramond bumblebee gravity

In this paper, we investigate black hole solutions in Einstein-Kalb-Ramond (EKR) bumblebee gravity sourced by a global monopole characterized by the charge $η$. This modified theory of gravity possesses the notable feature of incorporating local Lorentz symmetry breaking (LSB) via a spontaneous symmetry-breaking mechanism. We solve the field equations for a static and spherically symmetric metric with the Kalb-Ramond (KR) field fixed at its VEV, thereby obtaining new black hole solutions. These solutions simultaneously exhibit the LSB effects, codified by the $γ$ parameter, and the global monopole effects, codified by the charge $η$. Next, we study the impact of the global monopole and LSB corrections on two classical tests, namely, the advance of Mercury's perihelion and the light deflection. Furthermore, we compute the Hawking temperature, black hole shadows, and greybody factors. Ultimately, we estimate an upper bound for $η$ by comparing the theoretical results provided by the EKR model with observational data from the advance of Mercury's perihelion and light deflection.

gr-qc↗
arXiv2025

On the singular position-dependent mass

Revisiting the issue associated with Position-Dependent Mass (PDM), we reaffirm that the appropriate framework for addressing a generic PDM is the symmetrization proposed by BenDaniel and Duke. To accomplish this result adopts the effective mass Hamiltonian proposed by von Roos, corrected by a symmetrized kinematic term. After verifying the appropriate ordering to approach the PDM issue, one investigates a crystalline lattice with a defect described by a singular PDM. The singular mass profile proves intriguing as it yields an atom's cluster in the neighborhood of the singularity. Considering that a restoring force acts on the atoms, one notes that the confluent Heun function describes the quantum states. Furthermore, one highlights that when the effective mass distribution tends to a constant profile, we recover a system similar to the harmonic oscillator.

quant-ph↗
arXiv2024

On the asymmetric non-canonical braneworld in five dimensions

Revisiting Einstein's gravitational theory, we build a five-dimensional braneworld. Within this framework, one announces the appearance of symmetric and asymmetric domain walls. Furthermore, it examines the emergent four-dimensional gravity from a theory with non-canonical dynamics. Exploring the physical and mathematical aspects, e.g., brane's energy density and the Kaluza-Klein (KK) spectrum, one verifies that brane splitting is absent in the canonical and non-canonical theories. Additionally, we note the localization of the four-dimensional fluctuation projection on the 3-branes, which ensures the theory's stability. Thereby, one can conclude that the behavior of gravitational perturbations of the domain wall maintains a profile similar to a stable and non-localizable tower of massive modes. In contrast, within the brane core, the matter sector generates new barriers and potential wells, resulting in massive modes with approximately symmetric amplitudes. However, the non-canonical dynamics generate massive modes with asymmetric amplitudes far from the 3-brane.

gr-qc↗
arXiv2023

5D Elko spinor field non-minimally coupled to nonmetricity in $f(Q)$ gravity

This paper aims to investigate the localization of the five-dimensional spinor field known as Elko (dual-helicity eigenspinors of the charge conjugation operator) by employing a Yukawa-like geometrical coupling in which the Elko field is non-minimally coupled to nonmetricity scalar $Q$. We adopt the braneworld scenarios in which the first-order formalism with sine-Gordon and linear superpotentials is employed to obtain the warp factors. A linear function supports the zero-mode trapping within the geometric coupling, leading to the same effective potential as the scalar field. Moreover, an exotic term must be added to obtain real-valued massive modes. Such modes are investigated through the Schrödinger-like approach.

gr-qc↗
arXiv2023

Localization of abelian gauge fields with Stueckelberg-like geometrical coupling on $f(T,B)$-thick brane

In the context of $f(T,B)$ modified teleparallel gravity, we investigate the influence of torsion scalar $T$ and boundary term $B$ on the confinement of both the gauge vector and Kalb-Ramond fields. Both fields require a suitable coupling in five-dimensional braneworld scenarios to yield a normalizable zero mode. We propose a Stueckelberg-like geometrical coupling that non-minimally couples the fields to the torsion scalar and boundary term. To set up our braneworld models, we use the first-order formalism in which two kinds of superpotential are taken: sine-Gordon and $ϕ^{4}$-deformed. The geometrical coupling is used to produce a localized zero mode. Moreover, we analyze the massive spectrum for both fields and obtain possible resonant massive modes. Furthermore, we do not find tachyonic modes leading to a consistent thick brane.

gr-qc↗