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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., Comment: 16 pages, 7 captioned figures

Einstenian cubic gravity (ECG) is a modified theory of gravity constructed with cubic contractions of the curvature tensor. This theory has the remarkable feature of having the same two propagating degrees of freedom of Einstein gravity (EG), at the perturbative level on maximally symmetric spacetimes. The additional unstable modes steaming from the higher order derivative dynamics are suppressed provided that we consider the ECG as an effective field theory wherein the cubic terms are seen as perturbative corrections of the Einstein-Hilbert term. Extensions of ECG have been proposed in cosmology and compact objects in order to probe if this property holds in more general configurations. In this work, we construct a modified ECG gravity in a five dimensional warped braneworld scenario. By assuming a specific combination of the cubic parameters, we obtained modified gravity equations of motion with terms up to second-order. For a thin 3-brane, the cubic-gravity corrections yield an effective positive bulk cosmological constant. Thus, in order to keep the 5D bulk warped compact, an upper bound of the cubic parameter with respect to the bulk curvature was imposed. For a thick brane, the cubic-gravity terms modify the scalar field potential and its corresponding vacuum. Nonetheless, the domain-wall structure with a localized source is preserved. At the perturbative level, the Kaluza-Klein (KK) tensor gravitational modes are stable and possess a localized massless mode provided the cubic corrections are small compared to the EG braneworld.

In this work, the influence of the boundary term $B$ is analyzed in a string-like thick brane scenario in the gravity context $f(T, B)$. For that, three models of $f(T, B)$ are proposed, i.e., $f_1(T, B)=T+k{B}^{n}$, $f_2(T, B)=T+k(-T+B)^{n}$ and $f_3(T, B)=T+k_1T^2+k_2{B}^2$, where $n$, $k$ and $k_{1,2}$ are parameters that control the deviation from the usual teleparallelism. The first relevant result obtained was the appearance of a super-located tower in the core for energy density. Furthermore, the greater the influence of the boundary term, the new maximums and minimums appear in the energy density. All this indicates the emergence of capable structures from split to the brane. The second relevant result was obtained by analyzing the gravitational perturbations, where the effective potential presents the supersymmetric form of quantum mechanics, leading to well-localized massless modes., Comment: 18 pages, 7 captioned figures

Adopting the premise that the expected value of the quantum fluctuating metric is linear, i.e., $\langle g^{\mu\nu}\rangle=\alpha g^{\mu\nu}$, we analyze the modified gravity theory induced by the Einstein-Hilbert action coupled to a matter field. This approach engenders the $f(R,T)$ gravity used to investigate the braneworld. In this scenario, considering a thick brane, the influence of metric fluctuations on brane dynamics is investigated. Consequently, one shows how the metric fluctuations influence the vacuum states. This influence has repercussions for modifying the brane energy and the asymptotic profile of the matter field. After noticing these modifications, we analyzed the most likely and stable structures from the matter field. One performs this analysis considering the theoretical measure of differential configurational entropy., Comment: 20 pages, 5 captioned figures. Updated version to match one to appear in EPJP

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 Schr\"{o}dinger-like approach., Comment: 18 pages, 5 figures, matches published version in PLB

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 $\phi^{4}$-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., Comment: 28 pages, 7 captioned figures, references added, Enhanced version to appear in European Physical Journal C

In the teleparallel $f(T)$ gravity scenario, we consider a five-dimensional thick brane. This scenario is interesting because this theory can provide explanations for inflation, radiation, and dark matter under certain conditions. It is convenient to assume, for our study, a polynomial profile of the function $f(T)$. Indeed, some polynomial profiles can produce internal structures for which a brane splitting occurs. For functions $f(T)$ with this capability, geometrically contracted matter field configurations are obtained. These contractions of the matter field for the profiles of $f(T)$ reproduce compact-like settings. To complement the study, we analyze the stability of the brane using the concept of Configurational Entropy (CE). The CE arguments are interesting because they tell us the most stable and likely configurations from the brane in this gravitational background. Therefore, we can indicate the best profile of the function $f(T)$., Comment: 22 pages, 15 captioned figures. To appear in International Journal of Modern Physics D

We investigate the influence of the matter field and the gauge field on the metric functions of the AdS$_3$ spacetime of the Maxwell-Higgs model. By considering a matter field with a solitonic profile with the ability to adjust the field variable from kink to compact-like configurations, the appearance of black hole solutions is noticed for an event horizon at $r_{+} \approx 1.5$. An interesting result is displayed when analyzing the influence of matter field compactification on the metric functions. As we obtain compact-like field configurations the metric functions tend to a ``linearized behavior''. However, the compactification of the field does not change the structure of the horizon of the magnetic black hole vortex. With the ADM formalism, the mass of the black hole vortex is calculated, and its numerical results are presented. By analyzing the so-called ADM mass, it is observed that the mass of the black hole vortex increases as the cosmological constant becomes more negative, and this coincides with the vortex core becoming smaller. Nonetheless, this mass tends to decrease as the solitonic profile of the matter field becomes more compacted. Then, the black hole temperature study is performed using the tunneling formalism. In this case, it is perceived that the cosmological constant, and the $\alpha$-parameter, will influence the Bekenstein-Hawking temperature. In other words, the temperature of the structure increases as these parameters increase., Comment: 22 pages, 7 captioned figures. Enhanced version to appear in European Physical Journal Plus

The topological structures that arise from two-dimensional models are relevant physically and the first step towards understanding more complex systems. In this work, one studies the kink-like solutions of the matter field that emerge in a two-dimensional dilaton gravity scenario. Considering this scenario, we examine the linear stability of the matter field and the translational mode. Due to the specific profile of the solutions found, a differential configurational complexity (DCC) analysis of the system was necessary to confirm the nature of the structures. Furthermore, we study the interforce and scattering process, considering a pair of kink-antikink-like solutions in a fixed time ($t=0$)., Comment: 21 pages, 10 captioned figures. Title changed. Abstract changed. Some new discussions. Results remain the same. To appear in Fortschritte der Physis / Progress of Physics

We propose a braneworld scenario in a modified symmetric teleparallel gravitational theory, where the dynamics for the gravitational field is encoded in the nonmetricity tensor rather than in the curvature. Assuming a single real scalar field with a sine-Gordon self-interaction, the generalized quadratic nonmetricity invariant $\mathbb{Q}$ controls the brane width while keeping the shape of the energy density. By considering power corrections of the invariant $\mathbb{Q}$ in the gravitational Lagrangian, the sine-Gordon potential is modified exhibiting new barriers and false vacuum. As a result, the domain wall brane obtains an inner structure, and it undergoes a splitting process. In addition, we also propose a non-minimal coupling between a bulk fermion field and the nonmetricity invariant $\mathbb{Q}$. Such geometric coupling leads to a massless chiral fermion bound to the 3-brane and a stable tower of non-localized massive states., Comment: 26 pages, 16 figures

The thick brane scenario built on the f(T,B) teleparallel gravity theory was considered for the study of phase transitions, internal structures, and new classes of solutions in a model. In this theory, T denotes the torsion scalar, and B is a boundary term. An interesting result was observed when brane splitting occurs, i. e., internal structures in the model arise as a consequence of the appearance of new domain walls in the theory. In fact, this preliminary result influences the profile of the matter field (from kink to multi-kink) so that for appropriate values of the parameters $k_{1,2}$ multiple phase transitions are identified. To perform this analysis, the Differential Configurational Entropy (DCE) which has the ability to predict the existence of phase transitions through critical points was used. Furthermore, the DCE is able to select the most stable solutions since it gives us details about the informational content of the field settings., Comment: 20 pages,10 captioned figures. Updated version to match accepted one in IJMPD. Title changed. Minor modifications

We study a spin 1/2 fermion in a teleparallel f(T) domain-wall thick braneworld. By assuming a non-minimal coupling of fermion to the torsion, a geometric alternative to the Yukawa coupling is found. The torsion parameters control the width of the massless Kaluza-Klein mode and the properties of the analogue quantum-potential near the origin. The non-normalized massive fermionic modes are also analyzed., Comment: 25 pages, 13 captioned figures. Updated version to match the one published in Annals of Physics

We introduced a generalized Maxwell-Higgs model in a $(3+1)$ isotropic spacetime, and we found their stationary solutions using the BPS approach in curved spacetime. In order to investigate the compact-like vortices, we assume a particular choice for the generalization term. The model is controlled by a potential driven by a single real parameter that can be used to change the vortex solutions profile as they approach their bound values. Resembling some flat spacetime vortex solutions, our model tends to compress the vortices when the parameter $l$ increases. Through numerical analysis, we also show the energy behavior and the magnetic field of the model., Comment: 17 pages, 5 figures. To appear in Annals of Physics

We investigated the effects of the spacetime curvature and extra dimensions on the excitations of a self-interacting vector field known as the bumblebee field. The self-interacting quadratic potential breaks the gauge invariance and the vacuum expectation value (VEV) of the bumblebee field $b_M$ violates the local particle Lorentz symmetry. By assuming the bumblebee field living in a $AdS_{5}$ bulk, we found an exponential suppression of the self-interacting constant $\lambda$ and the bumblebee VEV along the extra dimension. The fluctuations of the bumblebee upon the VEV can be decomposed into transverse and longitudinal modes with respect to $b_{M}$. Despite the curvature, the transverse mode acquires massive Kaluza-Klein towers, while the longitudinal mode acquires LV mass $\lambda b^{2}$. On the other hand, the current conservation law prevents massive Kaluza-Klein modes for the longitudinal mode. For a spacelike $b_{M}$ along the extra dimension and assuming a FRW 3-brane embedded in the $AdS_{5}$ yields to an additional dissipative term to the longitudinal mode. The cosmological expansion leads to decay of the longitudinal mode in a time $\Delta t \approx H^{-1}$, where $H=\dot{a}/a$ is the Hubble parameter and $a(t)$ is the scale factor. For a timelike $b_{M}$, the longitudinal mode does not propagate on the brane and its amplitude decays in time with $a^{-3}$ and in the extra dimension with $z^{-\lambda b^{2}l^{2}}$., Comment: 15 pages, no figure

In this paper, we study the thick brane scenario constructed in the recently proposed $f(T,\mathcal{T})$ theories of gravity, where $T$ is called the torsion scalar, and $\mathcal{T}$ is the trace of the energy-momentum tensor. We use the first-order formalism to find analytical solutions for models that include a scalar field as a source. In particular, we describe two interesting cases in which, in the first, we obtain a double-kink solution, which generates a splitting in the brane. In the second case, proper management of a kink solution obtained generates a splitting in the brane intensified by the torsion parameter, evinced by the energy density components satisfying the weak and strong energy conditions. In addition, we investigate the behavior of the gravitational perturbations in this scenario. The parameters that control the torsion and the trace of the energy-momentum tensor tend to shift the massive modes to the core of the brane, keeping a gapless non-localizable and stable tower of massive modes and producing more localized massless modes., Comment: 31 pages, 49 figures. Revised version to match published version in EPJC

After recent observational events like the LIGO-Virgo detections of gravitational waves and the shadow image of M87* supermassive black hole by Event Horizon Telescope (EHT), the theoretical study of black holes was significantly improved. Quantities as quasinormal frequencies, shadows, and light deflection become more important to analyze black hole models. In this context, an interesting scenario to study is a black hole in the bumblebee gravity. The bumblebee vector field imposes a spontaneous symmetry breaking that allows the field to acquire a vacuum expectation value that generates Lorentz-Violating (LV) into the black hole. In order to compute the quasinormal modes (QNMs) via the WKB method, we obtain the Reege-Wheeler's equation with a bell-shaped potential for this black hole. Both QNMs, the scalar and tensorial modes, are computed for the black hole in the bumblebee scenario. Moreover, the stability of the Schwarzschild-like solution and some bounds to LV parameters are analyzed., Comment: 12 pages, 10 figures

Braneworld models are interesting theoretical and phenomenological frameworks to search for new physics beyond the standard model of particles and cosmology. In this work, we discuss braneworld models whose gravitational dynamics are governed by teleparallel $f(T)$ gravities. Here, we emphasize a codimension two axisymmetric model, also known as a string-like brane. Likewise, in the 5D domain-walls models, the $f(T)$ gravitational modification leads to a phase transition on the perfect fluid source providing a brane-splitting mechanism. Furthermore, the torsion changes the gravitational perturbations. The torsion produces new potential wells inside the brane core leading to a massless mode more localized around the ring structures. In addition, the torsion keeps a gapless non-localizable and a stable tower of massive modes in the bulk., Comment: 15 pages, 11 figures. arXiv admin note: text overlap with arXiv:2006.06891

We study a spin 1/2 fermion in a thick braneworld in the context of teleparallel $f(T, B)$ gravity. Here, $f(T,B)$ is such that $f_1(T,B)=T+k_1B^{n_1}$ and $f_2(T,B)=B+k_2T^{n_2}$, where $n_{1,2}$ and $k_{1,2}$ are parameters that control the influence of torsion and the boundary term. We assume Yukawa coupling, where one scalar field is coupled to a Dirac spinor field. We show how the $n_{1,2}$ and $k_{1,2}$ parameters control the width of the massless Kaluza-Klein mode, the breadth of non-normalized massive fermionic modes, and the properties of the analogue quantum-potential near the origin., Comment: 12 pages, 7 figures. To appear in European Physical Journal C

In this paper, we explore the five-dimensional f(T,B) teleparallel modified gravity with f_1(T,B)=T+k_1B^{n_1} and f_2(T,B)=B+k_2T^{n_2} in the brane scenario. Asymptotically, the bulk geometry converges to an AdS_5 spacetime whose cosmological constant is produced by parameters that control torsion and boundary term. The analysis of the energy density condition reveals a splitting brane process satisfying the weak and strong energy conditions for some values of the parameters n_{1,2} and k_{1,2}. In addition, we investigate the behavior of the gravitational perturbations in this scenario. In the bulk, the torsion keeps a gapless non-localizable, and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells, leading to small amplitude massive modes and a massless mode localized for some values of the parameters n_{1,2} and k_{1,2}., Comment: 26 pages, 30 figures. Updated to match the published version to appear in Physical Review D. Some modifications in the text in order to clarify arguments but the results are unchanged

We obtain a static spherically symmetric wormhole solution due to the vacuum expectation value (VEV) of a Kalb-Ramond field. The Kalb-Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb-Ramond (VEV) and the Ricci tensor, we found an exact traversable wormhole solution sustained by matter sources with a negative isotropic pressure. The matter source satisfies the energy conditions at the throat for particular choices of the LSB parameter. Moreover, we employ the Gauss-Bonnet method to analyze the deflection angle of light in the weak limit approximation., Comment: 16 pages, 2 figures

We propose a codimension two warped braneworld model within the teleparallel $f(T)$ gravity. By assuming a global vortex as the source, we found a $l=0$ vortex solution that yields to a thick string-like brane. Asymptotically, the bulk geometry converges to an $AdS_6$ spacetime whose cosmological constant is produced by the torsion parameters. Furthermore, the torsion induces an $AdS-dS$ transition on the exterior region. Inside the brane core, the torsion produces an internal structure even for a single complex scalar field. As the torsion parameters vary, the brane undergoes a phase transition leading to the formation of ring-like structures. The bulk-brane Planck mass ration is modified by the torsion. The analysis of the stress energy condition reveals a splitting brane process satisfying the weak and strong energy conditions for some values of the parameters. In addition, we investigate the behaviour of the gravitational perturbations in this scenario. It turns out that the gravitational spectrum has a linear behaviour for small masses and is independent of the torsion parameters for large masses. In the bulk, the torsion keeps a gapless non-localizable and stable tower of massive modes. Inside the brane core the torsion produces new barriers and potential wells leading to small amplitude massive modes and a massless mode localized around the ring structures., Comment: 25 pages, 11 figures

We study the gravitation effects on a static and spherically symmetric spacetime due to the vacuum expectation value (VEV) of a Kalb-Ramond field. The Kalb-Ramond VEV is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb-Ramond (VEV) and the Ricci tensor, we obtain an exact parameter-dependent power-law modified black hole. For a particular choice of the LSB parameter, the Lorentz violation produces a solution similar to the Reissner-Nordstrom, despite the absence of charge. The near-horizon geometry is modified by including a new inner horizon and shifting the Schwarzschild horizon. Asymptotically, the usual Minkowski spacetime with a background tensor field is recovered. The vacuum configurations are studied considering the energy conditions and the Lorentz violating source properties. By means of the mercury perihelion test, an upper bound to the local Lorentz violation (LV) is obtained, and its corresponding effects on the black hole temperature is investigated., Comment: 9 pages. Published version

In this work, we study the symmetries of a Lorentz violating bipartite-Finsler spacetime. By using the Finslerian Killing equation for the bipartite-Finsler metric, we analyze how the anisotropy of the bipartite spacetime modifies the local Lorentz symmetries. The symmetries of the Finsler metric allow us to obtain the bipartite algebra and interpreted it as a deformed Lorentz algebra. Causality effects driven by the particle modified dispersion relations are investigated upon Minkowski and the Schwarzschild spacetimes. The background bipartite tensor yields to superluminal velocities and modifies the effective gravitational potential., Comment: 15 pages, 2 figures. Small modifications in the text to match the accepted version in Physics Letters B

We study the properties of gravity and bulk fields living in a torsion warped braneworld. The torsion is driven by a background vector whose norm provides a source for the bulk cosmological constant. For a vector as the derivative of a scalar field, we find new isotropic and anisotropic thick brane geometries. We analyse the features of bosonic and fermionic fields in this isotropic and in standing wave scenarios. The background vector provides nonminimal coupling between the field and the geometry leading to modifications in the Kaluza-Klein states. The spinor connection is modified by the torsion and a derivative Yukawa-like coupling is proposed. The effects of these new couplings are investigated., Comment: 19 pages, 12 figures. Modified text to match the accepted version in International Journal of Modern Physics D

In this work, we propose a standing wave braneworld based on Lyra geometry scenario. The Lyra displacement vector provides a modification in Einstein equations which can be interpreted as a noninteracting phantom scalar. From the Einstein's equation in Lyra manifold, a 5D standing wave braneworld is constructed in the presence of a cosmological constant. Unlike other standing wave solutions presented in the literature, no matter field is necessary to obtain these new solutions. We analyze the properties of the scalar, gauge vector and fermionic fields in this model, highlighting the relevance of geometric structure in the process of trapping matter., Comment: 16 pages, 1 figure

In this work, we calculate the quasi-normal frequencies from a bumblebee traversable wormhole. The bumblebee wormhole model is based on the bumblebee gravity, which exhibits a spontaneous Lorentz symmetry breaking. Supporting by the Lorentz violation parameter $\lambda$, this model allows the fulfillment of the flare-out and energy conditions, granted non-exotic matter to the wormhole. We analyze the parameters of bumblebee wormhole in order to obtain a Reege-Wheeler's equation with a bell-shaped potential. We obtain the quasi-normal modes (QNMs) via the WKB approximation method for both scalar and gravitational perturbations. All frequencies obtained are stable and the time domain profiles have decreasing oscillation (damping) profiles for the bumblebee wormhole., Comment: 14 pages, 10 figures

Over the last decades, many methods were developed to prove Hawking radiation. Recently, a semiclassical method known as the tunneling method has been proposed as a more straightforward way of derivating black hole thermodynamical properties. This method has been widely applied to a vast sort of spacetimes with satisfactory results. In this work, we obtain the black hole thermodynamics in the presence of a Lorentz symmetry breaking (LSB). We apply the Hamilton-Jacobi method to Schwarzschild-like black holes, and we investigate whether the LSB affects their thermodynamics. The results found show that the LSB not only changes the black hole thermodynamic quantities but also makes it necessary to modify the standard first law of thermodynamics., Comment: Title changed, section VI suppressed. Other slight modifications in order to match the accepted version to appears in Annals of Physics. 17 pages, no figures

In this work, we evaluate the Shannon-like entropic measure of spatially-localized functions for a five-dimensional braneworld generated by a double sine-Gordon (DSG) potential. The differential configurational entropy (DCE) has been shown in several recent works to be a configurational informational measure (CIM) that selects critical points and brings out phase transitions in confined energy models with arbitrary parameters. We select the DSG scenario because it presents an energy-degenerate spatially localized profile where the solutions to the scalar field demonstrate critical behavior that is only a result of geometrical effects. As we will show, the DCE evaluation provides a method for predicting the existence of a transition between the phases of the domain wall solutions. Moreover, the entropic measure reveals information about the model that is capable of describing the phase sector where we obtain resonance modes on the massive spectra of the graviton. The graviton resonance lifetimes are related to the existence of scales on which 4D gravity is recovered. Thus, we correlate the critical points defined by the {CIMs} with the existence of resonances and their lifetimes. To extend our research regarding this system, we calculate the corrections to Newton's Law coming from the graviton modes., Comment: 17 pages, 9 figures. Some modifications to match the published version in Annalen der Physik

In this work, we present a complete analysis of the quantisation of the classical Brans-Dicke Theory using the method of affine quantisation in the Hamiltonian description of the theory. The affine quantisation method is based on the symmetry of the phase-space of the system, in this case the (positive) half-plane, that is identified with the affine group. We consider a FLRW-type spacetime, and since the scale factor is always positive, the affine method seems to be more suited than the canonincal quantisation for our Quantum Cosmology. We find the wave function of the Brans-Dicke universe, and its energy spectrum. A smooth bounce is expected at the semi-classical level in the quantum phase-space portrait. We also adress the problem of equivalence between the Jordan and Einstein frames., Comment: 28 pages, 8 figures

We present in this work, the calculations of corrections in the Newton's law of gravitation due to Kaluza-Klein gravitons in five-dimensional warped thick braneworld scenarios. We consider here a recently proposed model, namely, the hybrid Bloch brane. This model couples two scalar fields to gravity and is engendered from a domain wall-like defect. Also, two other models the so-called asymmetric hybrid brane and compact brane are considered. As a matter of fact, these models are obtained from deformations of the phi4 and sine-Gordon topological defects. Then, we constructed the branes upon such defects, and the corresponding corrections in Newton's law of gravitation are computed. In order to attain the mass spectrum and its corresponding eigenfunctions which are the essential quantities for computing the correction to the Newtonian potential, we develop a suitable numerical technique., Comment: 7 pages, 3 figures, Proceedings of The XXVth International Conference on Integrable Systems and Quantum symmetries (ISQS-25)

In this work, we propose a new class of smooth thick string-like braneworld in six dimensions. The brane exhibits a varying brane-tension and an $AdS$ asymptotic behavior. The brane-core geometry is parametrized by the Bulk cosmological constant, the brane width and by a geometrical deformation parameter. The source satisfies the dominant energy condition for the undeformed solution and has an exotic asymptotic regime for the deformed solution. This scenario provides a normalized massless Kaluza-Klein mode for the scalar, gravitational and gauge sectors. The near-brane geometry allows massive resonant modes at the brane for the $s$ state and nearby the brane for $l=1$., Comment: 14 pages, 12 figures. Some modifications to match the published version in EPJC

In this work, we compute the corrections in the Newton's law of gravitation due to Kaluza-Klein gravitons in codimension-1 warped thick braneworld scenarios. We focus in some models recently proposed in the literature, the so-called asymmetric hybrid brane and compact brane. Such models are deformations of the $\phi^4$ and sine-Gordon topological defects, respectively. Therefore we consider the branes engendered by such defects and we also compute the corrections in their cases. We use suitable numerical techniques to attain the mass spectrum and its corresponding eigenfunctions which are the essential quantities for computing the correction to the Newtonian potential. Moreover, we discuss that the existence of massive modes is necessary for building a braneworld model with a phenomenology involved. We find that the odd eigenfunctions have non-trivial contributions and the first eigenstate of the Kaluza-Klein tower has the highest contribution. The calculation of slight deviations in the gravitational potential may be used as a selection tool for braneworld scenarios matching with future experimental measurements in high energy collisions., Comment: 24 pages, 15 figures. Replaced in order to match the modified version accepted to PRD. Minor text modifications

The so-called configurational entropy (CE) framework has proved to be an efficient instrument to study nonlinear scalar field models featuring solutions with spatially-localized energy, since its proposal by Gleiser and Stamapoulos. Therefore, in this work, we apply this new physical quantity in order to investigate the properties of degenerate Bloch branes. We show that it is possible to construct a configurational entropy measure in functional space from the field configurations, where a complete set of exact solutions for the model studied displays both double and single-kink configurations. Our study shows a rich internal structure of the configurations, where we observe that the field configurations undergo a quick phase transition, which is endorsed by information entropy. Furthermore, the Bloch configurational entropy is employed to demonstrate a high organisational degree in the structure of the configurations of the system, stating that there is a best ordering for the solutions., Comment: 14 pages, 8 figures, published in PLB

In this work, we derive an expression for the correction in the Newton's law of gravitation due to the gravitational Kaluza-Klein states in a general thick string-like braneworld scenario in six dimensions. In order to analyze corrections to Newton's law we study the gravity fluctuations in a 3-brane placed in a transverse resolved conifold and use suitable numerical methods to attain the massive spectrum and the corresponding eigenfunctions. Such braneworld model has a resolution parameter which removes the conical singularity. The correction has an exponentially suppressed mass term and depends on the values of the eigenfunctions and warp factors computed at the core peak of the brane. The spectrum is real and monotonically increased, as desired. However, the resolution parameter must assume moderate values to have physically acceptable states. Moreover, the trapped massless mode regains the 4D gravity and it is displaced from the origin, sharing similar profile with the energy density of brane for small values of resolution parameter. Finally, for the singular conifold, we found that a non-first eigenstate is a resonant mode. Such excited state is the largest contributor to corrections in the Newtonian potential., Comment: 21 pages, 12 figures. 5 new figures. Section V modified in order to include more details and analysis of experimental bounds. Some references added

In this paper, the problem of the self-adjointness for the case of a quantum minisuperspace Hamiltonian retrieved from a Brans-Dicke (BD) action is investigated. Our matter content is presented in terms of a perfect fluid, onto which the Schutz's formalism will be applied. We use the von Neumann theorem and the similarity with the Laplacian operator in one of the variables to determine the cases where the Hamiltonian is self-adjoint and if it admits self-adjoint extensions. For the latter, we study which extension is physically more suitable., Comment: Latex file, 12 pages. Small changes made in the paper, and a a new appendix added

A class of $k$-Essence cosmological models, with a power law kinetic term, is quantised in the mini-superspace. It is shown that for a specific configuration, corresponding to a pressureless fluid, a Schr\"odinger-type equation is obtained with the scalar field playing the r\^ole of time. The resulting quantum scenario reveals a bounce, the classical behaviour being recovered asymptotically., Comment: Latex file, 7 pages. Version to appear in the proceedings of the 31st International Colloquium on Group Theoretical Methods in Physics. Rio de Janeiro, Brazil, 19-25 june 2016

We investigate the properties of a real scalar field in the Finslerian Randers spacetime, where the local Lorentz violation is driven by a geometrical background vector. We propose a dynamics for the scalar field by a minimal coupling of the scalar field and the Finsler metric. The coupling is intrinsically defined on the Randers spacetime, and it leads to a non-canonical kinetic term for the scalar field. The nonlinear dynamics can be split into a linear and nonlinear regimes, which depend perturbatively on the even and odd powers of the Lorentz-violating parameter, respectively. We analyze the plane-waves solutions and the modified dispersion relations, and it turns out that the spectrum is free of tachyons up to second-order., Comment: 14 pages, 2 figures;shorted version, corrected typos, figures modified, results unchanged; version to appear in PLB

One simplified black hole model constructed from a semiclassical analysis of loop quantum gravity (LQG) is called self-dual black hole. This black hole solution depends on a free dimensionless parameter P known as the polymeric parameter and also on the $a_{0}$ area related to the minimum area gap of LQG. In the limit of P and $a_{0}$ going to zero, the usual Schwarzschild-solution is recovered. Here we investigate the quasinormal modes (QNMs) of massless scalar perturbations in the self-dual black hole background. We compute the QN frequencies using the sixth order WKB approximation method and compare them with numerical solutions of the Regge-Wheeler equation. Our results show that as the parameter P grows, the real part of the QN frequencies suffers an initial increase and then starts to decrease while the magnitude of the imaginary one decreases for fixed area gap $a_{0}$. This particular feature means that the damping of scalar perturbations in the self-dual black hole spacetimes are slower, and their oscillations are faster or slower according to the value of P., Comment: 17 pages, 5 figures. Some improvements with respect to the previous version. Final version to appear in Phys. Rev. D

We study the spin 1/2 and spin 3/2 fermion fields in a thick braneworld scenario in six dimensions called string-cigar model. This smooth string-like model has a source that satisfies the dominant energy condition and undergoes a Ricci flow. We propose a new coupling for the fermions with a background gauge field which allows a smooth and normalized massless mode in the brane with positive tension. By numerical methods the mass spectrum and the massive eigenfunctions are obtained. The Kaluza-Klein massive tower exhibits the usual increasing pattern and, in this scenario, the coupling term does not allow tachyonic Kaluza-Klein states. The brane core and the background gauge field alter the properties of the massive KK tower, enhancing the amplitude of the massive states near the origin and changing the properties of the analogue Schroedinger potential. Furthermore, we find massive modes as resonant states in this scenario for both fermionic fields., Comment: Final version to appear in Physical Review D. Section II substantially enlarged in order to do a comprehensive review of the thin string brane model and string cigar brane model. One section added for considering of the Rarita-Schwinger spinor field. Some references added. 35 pgs, 17 figs

We discuss the issue of unitarity in particular quantum cosmological models with scalar field. The time variable is recovered, in this context, by using the Schutz's formalism for a radiative fluid. Two cases are considered: a phantom scalar field and an ordinary scalar field. For the first case, it is shown that the evolution is unitary provided a convenient factor ordering and inner product measure are chosen; the same happens for the ordinary scalar field, except for some special cases for which the Hamiltonian is not self-adjoint but admits a self-adjoint extension. In all cases, even for those cases not exhibiting unitary evolution, the formal computation of the expectation value of the scale factor indicates a non-singular bounce. The importance of the unitary evolution in quantum cosmology is briefly discussed., Comment: Latex file, 17 pages

In this work we investigate the properties of an Abelian gauge vector field in a thin and in a smoothed string-like braneworld, the so-called string-cigar model. This thick brane scenario satisfies the regularity conditions and it can be regarded as an interior and exterior string-like solution. The source undergoes a geometric Ricci flow which is connected to a variation of the bulk cosmological constant. The Ricci flow changes the width and amplitude of the massless mode at the brane core and recover the usual thin string-like behavior at large distances. By numerical means we obtain the Kaluza-Klein (KK) spectrum for both the thin brane and the string-cigar. It turns out that both models exhibit a mass gap between the massless and the massive modes and between the high and the low mass regimes. The KK modes are smooth near the brane and their amplitude are enhanced by the string-cigar core. The analogue Schr\"odinger potential is also tuned by the geometric flow., Comment: The discussion about the Kaluza-Klein spectrum of the gauge field was improved. Numerical analysis was adapted to the conventional notation on Kaluza-Klein number. Some graphics were modified for considering other notation. Results unchanged. References added. Corrected typos. 17 pages. 6 figures. To match version to appears in Physics Letters B

Non-commutative corrections to the classical expression for the fuzzy sphere area are found out through the asymptotic expansion for its heat kernel trace. As an important consequence, some quantum gravity deviations in the luminosity of black holes must appear. We calculate these deviations for a static, spherically symmetric, black-hole with a horizon modeled by a fuzzy sphere. The results obtained could be verified through the radiation of black holes formed in the Large Hadron Collider (LHC)., Comment: 14 pages, 2 figures

In this work the gravitational Kaluza-Klein (KK) modes are analysed on string-like braneworlds in six dimensions, namely the thin string-like Gherghetta-Shaposhnikov (GS) and the thick string-cigar model. We find a new massless mode in both modes satisfying the respective Schroedinger equation. By means of numerical analysis for both models, a complete graviton spectrum and eigenfunctions is attained. Besides the linear regime, the KK spectrum exhibits a decreasing behavior with an asymmetric mass gap with respect to the massless mode. The discontinuity is bigger in the GS model, and it is invariant upon the geometrical flow. A massive mode is obtained in the GS model with a tiny mass which does not match in any regime. It turns out that in the string-cigar model, the core brane structure smoothes and amplifies the KK modes near the brane. Further, the presence of a potential well allows the existence of resonant massive gravitons for small masses in the string-cigar scenario., Comment: 15 pages, 12 figures

A six dimensional standing-wave braneworld model has been constructed. It consists in an anisotropic 4-brane generated by standing gravitational waves whose source is normal matter. In this model the compact (on-brane) dimension is assumed to be sufficiently small in order to describe our universe (hybrid compactification). The bulk geometry is non-static, unlike most of the braneworld models in the literature. The principal feature of this model is the fact that the source is not a phantom like scalar field, as the original standing-wave model that was proposed in five dimensions and its six dimensional extension recently proposed in the literature. Here it was obtained a solution in the presence of normal matter what assures that the model is stable. Also our model is the first standing wave brane model in the literature which can be applied successfully to the hierarchy problem. Additionally, we have shown that the zero-mode for the scalar and fermionic fields are localized around the brane. Particularly for the scalar field we show that it is localized on the brane, regardless the warp factor is decreasing or increasing. This is in contrast to the case of the local string-like defect where the scalar field is localized for a decreasing warp factor only., Comment: 26 pages, 6 figures. Revised to match accepted version in Physical Review D

We investigated the localization of the spinorial field in a braneworld built as a warped product between a 3-brane and a 2-cycle of the resolved conifold. This scenario provides a geometric flow that controls the singularity at the origin and changes the properties of the fermion in this background. Furthermore, due the cylindrical symmetry according to the 3-brane and a smoothed warp factor, this geometry can be regarded as a near brane correction of the string-like branes. This geometry allows a normalizable and well-defined massless mode whose decay and value on the brane depend on the resolution parameter. For the Kaluza-Klein modes, resolution parameter also controls the height of the barrier of the volcano potential., Comment: 14 pages, 12 figures. To appear in Physics Letters B

Considering quantum gravity within the framework of effective field theory, we investigated the consequences of spontaneous Lorentz violation for the gravitational potential. In particular, we focus our attention on the bumblebee models, in which the graviton couples to a vector $B_{\mu}$ that assumes a nonzero vacuum expectation value. The leading order corrections for the nonrelativistic potential are obtained from calculation of the scattering matrix of two scalar particles interacting gravitationally. These corrections imply anisotropic properties associated with the bumblebee background and also add a Darwin-like term for Newton's potential., Comment: 19 pages, 2 figures, new references added, Eqs. (30) and (34) are corrected, and results and conclusions are improved. Version published in Phys. Rev. D

This work deals with new results on the Kalb-Ramond (KR) field localization in braneworld models. We consider a five-dimensional warped spacetime with an embedded 4D thick brane which is generated by two real scalar fields coupled with gravity (the so called Bloch brane). We find a KR field zero mode localized with the inclusion of the dilaton coupling. Analyzing the massive spectrum, we detected a series of resonant modes that arise from the solutions of the Schr\"odinger-like equation for KR field. The effects of the brane thickness and of the dilaton coupling over the resonance structures are determined. Such analysis is extended to the resonance lifetimes of the massive modes, allowing a better understanding on the localization mechanism of the model., Comment: 18 pages, 6 figures

We present new results on the localization of gauge fields in thick brane models. The four-dimensional observable universe is considered to be a topological defect which is generated by two scalar fields coupled with gravity embedded in a five-dimensional space-time. Like other thick brane models, the Bloch brane setup is not capable of supporting gauge field localization. In order to circumvent this problem we include the dilaton field and, as a result, obtain normalizable solutions. In addition, by writing the equations of motion as Schroedinger-like equations, we have found new kinds of resonances in the massive spectrum which appear also for heavy modes. This is in sharp contrast to what is commonly found in previous analog studies, where only light modes become resonant. At specific energies, the wave solutions exhibit very high amplitudes within the membrane. The influence of the dilaton coupling and of the internal structure on the resonant modes are also discussed., Comment: 17 pages, 7 figures. Clarifying changes in Introduction and in Sections III, IV and V. Results unchanged

Recently Rizzo studied the Lorentz Invariance Violation (LIV) in a brane scenario with one extra dimension where he found a non-zero mass for the four-dimensional graviton. This leads to the conclusion that five-dimensional models with LIV are not phenomenologically viable. In this work we re-examine the issue of Lorentz Invariance Violation in the context of higher dimensional theories. We show that a six-dimensional geometry describing a string-like defect with a bulk-dependent cosmological constant can yield a massless 4D graviton, if we allow the cosmological constant variation along the bulk, and thus can provides a phenomenologically viable solution for the gauge hierarchy problem., Comment: 13 pages, 2 figures. To appear in Physics Letters B

Brane world six dimensional scenarios with string like metric has been proposed to alleviate the problem of field localization. However, these models have been suffering from some drawbacks related with energy conditions as well as from difficulties to find analytical solutions. In this work, we propose a model where a brane is made of a scalar field with bounce-type configurations and embedded in a bulk with a string-like metric. This model produces a sound AdS scenario where none of the important physical quantities is infinite. Among these quantities are the components of the energy momentum tensor, which have its positivity ensured by a suitable choice of the bounce configurations. Another advantage of this model is that the warp factor can be obtained analytically from the equations of motion for the scalar field, obtaining as a result a thick brane configuration, in a six dimensional context. Moreover, the study of the scalar field localization in these scenario is done., Comment: 15 pages, 5 figures. To appear in Physics Letters B