Francisco Cleiton E. Lima

We construct an analytical thick-brane solution in linear teleparallel Gauss-Bonnet gravity using a first-order formalism generated by a sine-Gordon superpotential. The resulting asymptotically configurations exhibit brane splitting controlled by the dimensionless parameter . An analytical splitting condition is derived and combined with tensor-stability requirements to identify the physically viable parameter region. We show that the tensor spectrum is free of tachyonic instabilities and supports a normalizable graviton zero mode. The massive sector exhibits odd-parity gravitational resonances whose quasi-localization is significantly enhanced near the stability boundary. Our results establish a direct link between brane splitting, tensor stability, and gravitational resonances in teleparallel Gauss-Bonnet braneworlds.

We investigate an effective, operator-inspired description of gravity in which quantum correlations of geometric operators give rise to modified gravitational dynamics at the semiclassical level. In this framework, classical spacetime geometry is identified with the expectation value of the metric operator, while genuine quantum effects are encoded in correlation functions. Owing to the nonlinear nature of geometric quantities, quantum averaging does not generally commute with functional evaluation, leading naturally to higher-curvature corrections in the effective gravitational action. Focusing on this mechanism, we show that effective modified gravity of the f ( R ) type emerges generically from quantum geometric correlations, without introducing additional fundamental degrees of freedom or postulating modifications of general relativity at the microscopic level. The resulting effective dynamics is state-dependent and should be interpreted as a controlled semiclassical description rather than as a fundamental theory of quantum gravity. A minimal illustrative example is presented to make explicit how curvature fluctuations generate higher-curvature terms in the effective action. Our results clarify the geometric origin of effective modified gravity from quantum correlations and provide a transparent framework to explore semiclassical quantum geometric effects on classical spacetime dynamics.

Considering a non-canonical multi-field theory, we propose a mechanism of geometric expansion for Abrikosov–Nielsen–Olesen (ANO) vortices. One builds the general setup adopting a non-canonical O(3)-sigma model, non-minimally coupled through an anomalous magnetic dipole interaction to a gauge and real scalar field. By embracing a hyperbolic non-canonical extension, one finds that self-dual vortex configurations undergo geometric expansion, deforming ANO-like vortices into disk-like structures, mitigating their energy, and generating concentric energy rings around the core. Furthermore, these vortices exhibit quantized magnetic flux and degenerate solutions. Finally, we highlight that the analyzed vortices carry energy below the corresponding magnetic flux while preserving a singularity at their origin.

Modified Gravity Theories (MGTs) are extensions of General Relativity (GR) in its standard formulation. Therefore, within this framework, we will investigate a system composed of a black hole (BH) surrounded by Maxwell-Higgs vortices, forming the BH-vortex system. In the case of linear f ( R ) gravity it is adopted showing the existence of a three-dimensional ring-like BH-vortex system with quantized magnetic flux. Within this system, one notes the BH at r = 0 and its event horizon at , while the magnetic vortices are at . A remarkable result is the constancy of the Bekenstein-Hawking temperature ( T _H ), regardless of MGTs and vortex parameters. This invariance of T _H suggests that the BH-vortex system reaches thermodynamic stability. Unlike the standard theory of Maxwell-Higgs vortices in flat spacetime, in f ( R ) gravity, the vortices suffer the influence of the BH's event horizon. This interaction induces perturbations in the magnetic vortex profile, forming cosmological ring-like magnetic structures.

Considering the relativistic scenario, we dedicate our study to the relativistic quantum description of one-dimensional Majorana fermions. Thus, we focus on aspects related to exciton-like particles. Seeking to reach our purpose, one analyzes the relativistic quantum mechanical system characterized by an effective mass distribution. In this context, we adopt an exciton-like position-dependent mass without impurity, i.e., without electromagnetic interactions. From this perspective, one notes results of noteworthy interest as consequences of the theory adopted. For instance, we highlight that, even without interaction, exciton-like Majorana fermions manifest theoretically bound states. Also, we construct a Majorana fermion ensemble with effective mass immersed in a thermal reservoir. That allows for a thorough investigation of the thermodynamic properties of the system. Among the thermodynamic characteristics studied in the canonical ensemble, we focus on the Helmholtz free energy, mean energy, entropy, and heat capacity. The numerical results obtained for these thermodynamic properties corroborate the validity of the Dulong-Petit law for our system.

We investigated the influence of the massive scalar field on the information degradation concerning the Unruh-DeWitt (UDW) detectors. In this conjecture, we adopted a system with a finite and large interaction time. To accomplish our purpose, one examines the quantum coherence of a uniformly accelerated qubit and the probability of finding the detector in the ground state. In this framework, we consider a quantum interferometric circuit to obtain the probability, visibility, and coherence. Naturally, these measurements provide us with wave-like information. Besides, one modifies the circuit to describe the path distinguishability and the particle-like information. These results are promising, as they allow us to understand the influence of the Unruh effect on the wave-particle duality. Thus, our findings announce that the increase in the scalar field mass induces a decrease in information degradation. Finally, we noted that the information concerning the Unruh effect remains preserved when m ≥ Ω. Therefore, the detector cannot absorb particles with mass equal to or greater than its energy gap. These results indicate that the scalar field mass is a protective factor against information degradation for systems under high acceleration conditions.

We consider a two-dimensional Lorentz-invariant field model with a potential modified by a term that introduces asymmetries at the manifold space. In this framework, the model recovers its original symmetry only when p = 0. The asymmetry introduced in the potential suggests that, even when one of the minima diverges asymptotically, kink/antikink-like configurations emerge in the theory, shifting the critical point of the energy density away from the center of the kink-like solutions. Hence, we note that the model supports asymmetrical kink/antikink-like topological solutions. Furthermore, an analysis of the excitation spectrum of these solutions revealed the absence of vibrational modes. Finally, we examine the dynamical solutions for different values of initial velocity by verifying the effects of asymmetries on the collision properties.

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.