arXiv subjects

Vilson T. Zanchin

Publications and source records attributed to Vilson T. Zanchin.

At least 19 recordsLinked to original sources

arXiv2026

On the quasiblack-hole limit of rotating charged fluids

We investigate the extremal quasiblack-hole (QBH) limit of stationary, axisymmetric charged perfect fluids in rigid or differential rotation, with and without pressure. We emphasize Weyl-type configurations, whose redshift factor is functionally related to the generalized electromagnetic potential. In this limit, the redshift factor vanishes throughout the fluid interior and the boundary becomes a quasihorizon. We require regular matter and electromagnetic fields and smooth matching to the exterior. Under suitable convergence assumptions, electromagnetic regularity and the approach to uniform rotation imply a constant generalized electromagnetic potential throughout the connected fluid interior, independently of the Weyl ansatz. With additional integrability conditions, the mass formula reduces to the extremal Kerr-Newman Smarr relation. For rigid rotation, we examine charged dust obeying a linear Weyl relation and fluids with pressure obeying the Kloster-Das or Guilfoyle relations. The linear Kloster-Das subclass becomes pressureless in the limit, whereas the general Guilfoyle case allows nonzero pressure. The Islam ansatz obstructs a regular limit when its coupling parameter, limiting potential, and limiting charge density are nonzero. For differential rotation, we analyze configurations with an identically vanishing Lorentz-force term and a linear Weyl subclass whose regularity requires control of angular-velocity gradients. Our results show that rotating Weyl-type systems admit extremal QBH limits much like their static counterparts, extending analyses of rotating dust distributions and identifying conditions for more general rotating charged fluids to be compatible with this limit.

gr-qc↗

arXiv2026

A Lagrangian formulation for Rastall gravity and a covariant formulation for unimodular gravity

We propose a Lagrangian formulation for a non-conservative gravity model in which the divergence of the energy-momentum tensor in curved spacetime does not vanish. This is accomplished by introducing an arbitrary vector field that couples with the gradient of the Ricci curvature scalar. We first derive the field equations using the Palatini variational approach. Because the connection and the metric tensor are independent in the Palatini framework, the auxiliary vector field dictates whether the manifold geometry is Weyl or Riemannian. By assuming certain physically reasonable conditions on this vector field, the resulting field equations reduce to those of Rastall gravity. Furthermore, slightly different conditions on the vector field furnish unimodular gravity. For comparison, we also employ the standard metric variational approach to obtain the field equations, demonstrating that the same models can be recovered under appropriate conditions. Our key results are the derivation of a covariant Lagrangian formulation for Rastall gravity and a new Lagrangian formulation for unimodular gravity.

gr-qc↗

arXiv2025

Transport coefficients and quasinormal modes in Einstein-dilaton holographic QCD

In this paper, we investigate the transport coefficients of a strongly coupled plasma in the context of holographic QCD models based on Einstein-dilaton gravity that are compatible with linear confinement at zero temperature. At finite temperature, the holographic model is characterized by an asymptotically anti-de Sitter (AdS) black hole coupled to a scalar field, the dilaton, which is quadratic in the radial direction. The inclusion of the scalar field results in an explicit breaking of the conformal symmetry in the dual field theory. In such systems, the Hawking temperature of the black hole corresponds to the plasma temperature in the dual field theory. We confirm the existence of a minimum temperature $T_{\min}$, above which two distinct classes of black hole solutions emerge: one corresponding to large black holes and the other to small black holes. We calculate some thermodynamic quantities -- such as entropy, specific heat, and speed of sound -- and find results that are consistent with similar holographic models. We calculate the quasinormal modes (QNM) of the tensor and vector sectors using the pseudospectral method. In the hydrodynamic regime, we derive the dispersion relation for the vector sector, from which we extract the shear viscosity and the ratio $η/s=1/4 π$. The bulk viscosity is calculated using the Kubo formula in the scalar sector. Finally, our results for the speed of sound are compared with the Lattice QCD predictions, and our results for the bulk viscosity are compared with those reported by the JETSCAPE collaboration.

hep-th↗

arXiv2025

Kerr-Newman outside a rotating de Sitter-type core: A rotating version of the Lemos-Zanchin electrically charged solution

A rotating version of the solution of the Einstein-Maxwell system of equations modeling static electrically charged regular black holes by Lemos and Zanchin [Phys. Rev. D 83, 124005 (2011)] is obtained in the present work. The full rotating geometry consists of the Kerr-Newman exterior geometry outside a rotating de Sitter-type core, with an electrically charged spheroidal shell at the boundary. The properties of the entire rotating solution, such as electromagnetic charge and current distributions, curvature regularity, energy-momentum tensor, and energy conditions, are thoroughly examined, revealing various types of charged rotating objects. We also study in detail the possible electromagnetic fields allowed in the interior region of the spheroidal shell of charge. By assuming that the interior geometry is described by the Gürses-Gürsey metric with an arbitrary mass function, we show that no well-behaved electromagnetic field is allowed in the interior region if it is devoid of electromagnetic sources. We also note that, although the overall electric charge of the static solution is preserved, the arbitrariness of the algorithm allows us to propose different electromagnetic fields and charge distributions for the same geometry of the interior region, together with different charge densities on the rotating boundary shell, without changing the exterior Kerr-Newman solution. For a particular choice of the interior electromagnetic fields, we show that it is possible to interpret the rotating de Sitter fluid as being electrically polarized due to the presence of the rotating charged spheroidal shell, despite the absence of net electric charge within the interior region, which is instead concentrated solely on the charged shell, with the interior medium behaving as a perfect conductor with infinite conductivity.

gr-qc↗

arXiv2025

Regular Kerr black holes: Junction conditions and the matter content across the ring

Regular rotating black holes are usually described by a metric of the Kerr-Schild form with a particular mass function that is chosen to avoid the ring singularity of the Kerr metric and which approaches the Kerr metric at the asymptotic limit. However, as is well known, even for a class of well-behaved mass functions, the curvature scalars present a discontinuity in the equatorial plane at the ring. This discontinuity has been associated with the presence of a string of matter that joins the interior and exterior regions along the equatorial plane. By using the Darmois-Israel junction conditions, we analyze all four possible combinations of the normal vector orientations on each side of the ring, construct the complete stress-energy momentum tensor of the string, and interpret each resulting solution. We show that, out of the four possibilities, only one of the four models for the string solution at the ring yields the appropriate asymptotic geometry. In such a case, the string bears a fluid with nonzero pressure, but with a vanishing line energy density, and it does not rotate at all. Finally, taking an appropriate metric for the exterior region, we also discuss a different scenario in which the matter source at the ring is a rotating lightlike fluid.

gr-qc↗

arXiv2024

Comment on "Apparent horizons of the Thakurta spacetime and the description of cosmological black holes"

The findings discussed in "Apparent Horizons of the Thakurta Spacetime and the Description of Cosmological Black Holes" deviate from prior research, particularly our study in Phys. Rev. D 95, 084031 (2017). We clarify this inconsistency, which arises from employing a coordinate transformation covering a distinct region of spacetime -- specifically one considered inaccessible due to its location beyond a singularity, making it unreachable from infinity. Additionally, we provide a concrete example where the distinct horizons and spacetime regions are readily discernible.

gr-qc↗

arXiv2024

Compact regular objects from an electrified Tolman-like density: A new interior region for the Kerr-Newman spacetime

Charged static and rotating objects as solutions of the Einstein-Maxwell field equations are obtained and studied in the present work. The full spacetime geometry is obtained by matching two spacetime regions, an interior region containing electrified matter and an exterior electrovacuum region. In the static case, the interior region contains a spherically symmetric distribution of matter constituted by a de Sitter-type perfect fluid with electric charge, whose energy density profile is given by a Tolman-like relation. The interior solution is smoothly matched with the exterior Reissner-Nordström electrovacuum solution, thus producing different kinds of objects, such as charged regular black holes and overcharged tension stars, that we analyze in detail. We also investigate the connection between the present static solution and the regular black holes with a de Sitter core presented in the work by Lemos and Zanchin [Phys. Rev. D 83, 124005 (2011)]. We then employ the Gürses-Gürsey metric and apply the Newman-Janis algorithm to construct a charged rotating interior geometry from the static interior solution. The resulting interior metric and the electromagnetic field are smoothly matched to the exterior Kerr-Newman electrovacuum solution, thus producing a regular interior for the exterior Kerr-Newman geometry. The main properties of the complete rotating solution are analyzed in detail, showing that different kinds of rotating objects, such as charged rotating black holes and other charged rotating objects, also emerge in this solution.

gr-qc↗

arXiv2023

Third-order relativistic fluid dynamics at finite density in a general hydrodynamic frame

The motion of water is governed by the Navier-Stokes equations, which are complemented by the continuity equation to ensure local mass conservation. In this work, we construct the relativistic generalization of these equations through a gradient expansion for a fluid with conserved charge in a curved $d$-dimensional spacetime. We adopt a general hydrodynamic frame approach and introduce the Irreducible-Structure (IS) algorithm, which is based on derivatives of both the expansion scalar and the shear and vorticity tensors. By this method, we systematically generate all permissible gradients up to a specified order and derive the most comprehensive constitutive relations for a charged fluid, accurate to third-order gradients. These constitutive relations are formulated to apply to ordinary, non-conformal, and conformally invariant charged fluids. Furthermore, we examine the hydrodynamic frame dependence of the transport coefficients for a non-conformal charged fluid up to the third order in the gradient expansion. The frame dependence of the scalar, vector, and tensor parts of the constitutive relations is obtained in terms of the field redefinitions of the fundamental hydrodynamic variables. Managing these frame dependencies is challenging due to their non-linear character. However, in the linear regime, these higher-order transformations become tractable, enabling the identification of a set of frame-invariant coefficients. An advantage of employing these coefficients is the possibility of studying the linear equations of motion in any chosen frame and, hence, we apply this approach to the Landau frame. Subsequently, these linear equations are solved in momentum space, yielding dispersion relations for shear, sound, and diffusive modes for a non-conformal charged fluid, expressed in terms of the frame-invariant transport coefficients.

hep-th↗

arXiv2023

Rotating regular black holes and other compact objects with a Tolman type potential as a regular interior for the Kerr metric

We obtain a new class of stationary axisymmetric spacetimes by using the Gürses-Gürsey metric with an appropriate mass function in order to generate a rotating core of matter that may be smoothly matched to the exterior Kerr metric. The same stationary spacetimes may be obtained by applying a slightly modified version of the Newman-Janis algorithm to a nonrotating spherically symmetric seed metric. The starting spherically symmetric configuration represents a nonisotropic de-Sitter type fluid whose radial pressure $p_r$ satisfies an state equation of the form $p_r=-ρ$, where the energy density $ρ$ is chosen to be the Tolman type-VII energy density [R. C. Tolman, Phys. Rev. {\bf 55}, 364 (1939)]. The resulting rotating metric is then smoothly matched to the exterior Kerr metric, and the main properties of the obtained geometries are investigated. All the solutions considered in the present study are regular in the sense they are free of curvature singularities. Depending on the relative values of the total mass $m$ and rotation parameter $a$, the resulting stationary spacetimes represent different kinds of rotating compact objects such as regular black holes, extremal regular black holes, and regular starlike configurations.

gr-qc↗

arXiv2023

Rotating charged fluids: Theorems and results for Weyl-type systems

We perform a systematic study of rotating charged fluids, and extend several well known theorems regarding static Weyl-type systems which were recently compiled by Lemos and Zanchin [Phys. Rev. D 80, 024010 (2009)] to rotating and axisymmetric systems. Static Weyl-type systems are composed by static charged fluid configurations obeying the Newton-Maxwell or the Einstein-Maxwell systems of equations in which the electric potential $ϕ$ and the timelike metric potential $g_{tt}\equiv - W^ 2$ satisfy the Weyl hypothesis, i.e., $W=W(ϕ)$. In the present analysis, both the Newton-Maxwell and Einstein-Maxwell theories that describe non-relativistic and relativistic systems, respectively, are used to perform a detailed analysis of the general properties of rotating charged fluids rotating charged dust as well as rotating charged fluids with pressure in four-dimensional spacetimes. In comparison to the static (nonrotating) systems, two additional potentials, a metric potential related to rotation and an electromagnetic potential related to the magnetic field, come into play for rotating systems. In each case, constraints between the fluid quantities and the metric and electromagnetic potentials are identified in order to generalize the theorems holding for static charged systems to rotating charged systems. New theorems regarding equilibrium configurations with differential rotation in both the Newtonian and the relativistic theories are stated and proved. For rigidly rotating charged fluids in the Einstein-Maxwell theory, a new ansatz involving the gradient of the metric potentials and the gradient of the electromagnetic potentials is considered in order to prove new theorems. Such an ansatz leads to new constraints between the fluid quantities and field potentials, so implying new equations of state for the charged fluids.

gr-qc↗

arXiv2023

Stability of electrically charged stars, regular black holes, quasiblack holes, and quasinonblack holes

The stability of a class of electrically charged fluid spheres under radial perturbations is studied. Among these spheres there are regular stars, overcharged tension stars, regular black holes, quasiblack holes, and quasinonblack holes, all of which have a Reissner-Nordström exterior. We formulate the dynamical perturbed equations by following the Chandrasekhar approach and investigate the stability against radial perturbations through numerical methods. It is found that (i) under certain conditions that depend on the adiabatic index of the radial perturbation, there are stable charged stars and stable tension stars; (ii) also depending on the adiabatic index there are stable regular black holes; (iii) quasiblack hole configurations formed by, e.g., charging regular pressure stars or by discharging regular tension stars, can be stable against radial perturbations for reasonable values of the adiabatic index; (iv) quasinonblack holes are unstable against radial perturbations.

gr-qc↗

arXiv2022

Revisiting the quasinormal modes of the Schwarzschild black hole: Numerical analysis

We revisit the problem of calculating the quasinormal modes of spin $0$, $1/2$, $1$, $3/2$, $2$, and spin $5/2$ fields in the asymptotically flat Schwarzschild black hole spacetime. Our aim is to investigate the problem from the numerical point of view, by comparing some numerical methods available in the literature and still not applied for solving the eigenvalue problems arising from the perturbation equations in the Schwarzschild black hole spacetime. We focus on the pseudo-spectral and the asymptotic iteration methods. These numerical methods are tested against the available results in the literature, and confronting the precision between each other. Besides testing the different numerical methods, we calculate higher overtones quasinormal frequencies for all the investigated perturbation fields in comparison with the known results. In particular, we obtain purely imaginary frequencies for spin $1/2$ and $3/2$ fields that are in agreement with analytic results reported previously in the literature. The purely imaginary frequencies for the spin $1/2$ field are exactly the same as the frequencies obtained for the spin $3/2$ field. In turn, the quasinormal frequencies for the spin $5/2$ perturbation field are calculated for the very first time, and purely imaginary frequencies are found also in this case. We conclude that both methods provide accurate results and they complement each other.

gr-qc↗

arXiv2021

Effective holographic models for QCD: Thermodynamics and viscosity coefficients

A finite temperature extension of the effective holographic models for QCD (EHQCD), proposed in Ref.[1], is investigated in the present work. EHQCD models are characterized by two parameters, the conformal dimension of the relevant operator that deforms the CFT and the associated coupling. We find that black hole solutions appear at temperatures higher than some temperature $T_{min}$ and can be categorized in two classes: large and small black holes. A large black hole is thermally stable and it is therefore interpreted as the gravity dual of a non-conformal plasma. A small black hole, on the other hand, is thermally unstable. We show that thermodynamic quantities such as the entropy density $s$, specific heat $C_V$, and speed of sound $c_s$ are sensitive to the model parameters. We investigate perturbations of the black hole solutions and calculate the viscosity coefficients of the corresponding dual non-conformal plasma. For the shear viscosity, we confirm that the ratio $η/s$ is given by the universal result $1/4π$. For the bulk viscosity, the ratio $ζ/s$ varies with the temperature, displaying a rapid growth close to $T_{min}$, and it is sensitive to the model parameters. We compare our results for the thermodynamic quantities with the lattice $SU(N_C)$ results and find that they are compatible as long as the coupling is fixed appropriately as a function of the conformal dimension. We also compare our results for the viscosity coefficients against the JETSCAPE results that are obtained from the analysis of experimental data on heavy ion collisions.

hep-th↗

arXiv2021

Stability of regular black holes and other compact objects with a charged de Sitter core and a surface matter layer

The stability and other physical properties of a class of regular black holes, quasiblack holes, and other electrically charged compact objects are investigated in the present work. The compact objects are obtained by solving the Einstein-Maxwell system of equations assuming spherical symmetry in a static spacetime. The spacetime is split in two regions by a spherical surface of coordinate radius $a$. The interior region contains a nonisotropic charged fluid with a de Sitter type equation of state, $p_r = -ρ_m$, $p_r$ and $ρ_m$ being respectively the radial pressure and the energy density of the fluid. The charge distribution is chosen as a well behaved power-law function. The exterior region is the electrovacuum Reissner-Nordström metric, which is joined to the interior metric through a spherical thin shell (a thin matter layer) placed at the radius $a$. The matter of the shell is assumed to be a perfect fluid satisfying a linear barotropic equation of state, ${\cal P}=ωσ$, with ${\cal P}$ and $σ$ being respectively the pressure and energy density of the shell, with $ω$ being a constant. The exact solutions obtained are analyzed in some detail by exploring the interesting regions of parameter space, complementing the analysis of previous works on similar models. This is the first important contribution of the present study. The stability of the solutions are then investigated considering perturbations around the equilibrium position of the shell. This is the second and the most important contribution of this work. We find that there are stable objects in relatively large regions of the parameter space. In particular, there are stable regular black holes for all values of the parameter $ω$ of interest. Other stable ultracompact objects as quasiblack holes, gravastars, and even overcharged stars are allowed in certain regions of the parameter space.

gr-qc↗

arXiv2021

Generalized nonconservative gravitational field equations from Herglotz action principle

We present an alternative nonconservative gravitational theory based on the Herglotz variational principle in a fully covariant form. The present model may be seen as an improvement of the theory proposed in Ref. [Lazo et al, Phys. Rev. D 95, 101501 (2017)], whose resulting theory is meaningful just in particular coordinate systems. In the present work, we report a new theory that is free from such a restriction. It is also obtained using the Herglotz variational principle and by taking advantage of the restricted equivalence between Lagrangian functions in the scope of such action principle. The more restricted class of equivalent Lagrangian functions, in comparison with the Hamilton variational principle, is the key point to find a Lagrangian that furnishes a new alternative gravitational theory that is fully covariant. Once the equations that govern the dynamics of the gravitational field are obtained, a few simple cosmological models are investigated. It is found that the Herglotz gravitational field reduces to a single function that, under certain conditions, plays the role of the cosmological constant in general relativity, turning unnecessary the use of dark energy to explain the accelerated expansion of the universe. The linearized version of the theory is also investigated and it is verified that the theory shows a dissipative character in regard to gravitational waves. From observational data, in both scenarios, the Herglotz vector field is estimated.

gr-qc↗

arXiv2020

Plethora of relativistic charged spheres: The full spectrum of Guilfoyle's static, electrically charged spherical solutions

We show that Guilfoyle's exact solutions of the Einstein-Maxwell equations for spherical symmetric static electrically charged matter with a Reissner-Nordström exterior possess a bewildering plethora of different types of solutions. For the parameter space of the solutions we use two normalized variables, $q^2/R^2$ and $r_0/R$, where $q$ is the total electric charge, $r_0$ is the radius of the object, and $R$ is a length representing the square root of the inverse energy density of the matter. The two other parameters, the mass $m$ and the Guilfoyle parameter $a$, both dependent on $q$, $r_0$ and $R$, are analyzed in detail. The full parameter space of solutions $q^2/R^2\times r_0/R$ is explored with the corresponding types of solutions being identified and analyzed. The different types of solutions are regular charged stars, including charged dust stars and stars saturating the Buchdahl-Andréasson bound, quasiblack holes, regular charged black holes with a de Sitter core, regular black holes with a core of phantom charged matter, other exotic regular black holes, Schwarzschild stars, Schwarzschild black holes, Kasner spacetimes, pointlike and planar naked singularities, and the Minkowski spacetime. Allowing for $q^2<0$, in which case it is not possible to interpret $q$ as electric charge, also yields new solutions, some of which are interesting and regular, others are singular. Some of these types of solutions as well as the matter properties have been previously found and studied, here the full spectrum being presented in a unified manner.

gr-qc↗

arXiv2020

New regular black hole solutions and other electrically charged compact objects with a de Sitter core and a matter layer

The main objective of this work is the construction of regular black hole solutions in the context of the Einstein-Maxwell theory. The strategy is to match an interior regular solution to an exterior electrovacuum solution. With this purpose, we first write explicitly the Einstein field equations for the interior regular region. We take an electrically charged nonisotropic fluid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure $p_r$ is equal to the negative of energy density $ρ$, $p_r=-ρ$. Then, two solutions for the Einstein equations are built, a regular interior solution for the region with matter satisfying a de Sitter equation of state, and an external solution for the region outside the matter, that corresponds to the Reissner-Nordström metric. To complete the solution we apply the Darmois-Israel junction conditions with a timelike thin shell at the matching surface. It is assumed that the matching surface is composed by a thin shell of matter, i.e., a surface layer in the form a perfect fluid obeying a barotropic equation of state, $\mathcal{P}=ωσ$, $P$ and $σ$ being the intrinsic pressure and energy density of the shell, respectively, and $ω$ a constant parameter. We show that there are electrically charged regular black hole solutions and other compact objects for specific choices of $ω$ and of the other parameters of the model. Some properties of the objects are investigated.

gr-qc↗

arXiv2020

Phase diagram and compact stars in a holographic QCD model

A holographic model is used to investigate the thermodynamics and the phase diagram of a heavy quarks system. From such a model we obtain an equation of state and explore its applicability in astrophysical conditions. For this objective, we work in the context of the Einstein-Maxwell-Dilaton (EMD) holographic model for quantum chromodynamics (QCD). At first, we show the existence of a critical point where the first-order transitions line ends, later on, we calculated an analytic expression for the equation of state. Additionally, with the aim of investigating the global properties of compact stars, such as the total gravitational mass and radius, the equation of state is used to solve the Tolman-Oppenheimer-Volkov (TOV) equations for stellar structure. The numerical results show that our equation of state is able to reproduce the expected behavior of hybrid stars. Our main conclusion is that, by using an equation of state emerging in the framework of the EMD holographic model for QCD, it is possible to obtain quark matter properties and that it is also possible to extend the procedure to astrophysical applications.

hep-th↗