arXiv subjects

Leonel Bixano

Publications and source records attributed to Leonel Bixano.

13 recordsLinked to original sources

arXiv2026

A Lie-Jordan Geometric Formulation of Lindblad Dynamics

We develop a Lie-Jordan geometric formulation of finite-dimensional open quantum dynamics, building on the algebraic framework introduced in our previous work (arXiv:2606.26477). The Hilbert-Schmidt operator space is endowed with an orthonormal Hermitian basis, in which the commutator and anticommutator are encoded by the structure tensors $C_{\mu\nu}{}^\lambda$ and $B_{\mu\nu}{}^\lambda$. Within this formulation, the von Neumann and Gorini-Kossakowski-Lindblad-Sudarshan equations admit a direct component representation. Our central result is the identification of a basis-independent universal trilinear dissipative map, $ \mathcal D(X,Y)Z=XZY-\frac12\{YX,Z\}, $ whose components define a universal operator-space tensor depending only on the Lie-Jordan structure tensors. The physical dissipator is obtained by contracting this tensor with the expansion coefficients of the Lindblad operators and the Kossakowski matrix, thereby separating the universal algebraic structure from the model-dependent physical information. We further show that the combinations $(B+C)$ and $(B-C)$ generate internal left and right transports, allowing the elementary dissipative map to be expressed as a left-right bimodule action corrected by an ordered Jordan contribution. The universal map satisfies basis-independent trace and Hermitian-conjugation identities, from which trace preservation, Hermiticity preservation of the complete dissipator, and the reality of its component representation in a Hermitian Hilbert-Schmidt basis follow. We also derive its Hilbert-Schmidt adjoint and illustrate the formalism for a qubit with pure dephasing and amplitude-damping channels. This construction provides a tensorial and affine-geometric interpretation of the universal superoperator structure derived in arXiv:2606.26477 while keeping the algebraic and model-dependent sectors explicitly separated.

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arXiv2026

Algebraic structures of the Lindblad equation

We investigate the algebraic structure underlying the Lindblad equation for finite-dimensional open quantum systems. By introducing a suitable operator representation of the Liouville superoperator, we show that the dynamics can be formulated in terms of a closed algebra of Hermitian operators that is independent of the particular physical model. This formulation reveals that dissipative dynamics requires a substantially richer algebraic structure than purely unitary evolution, thereby providing a clear characterization of the additional complexity introduced by the Lindbladian. The resulting framework naturally leads to parametrizations of the dynamical map and to differential equations governing its evolution. We further derive recursion relations that enable the efficient construction of the algebra for systems of increasing dimension. Because the algebraic basis is universal, while all model-dependent information enters through a single set of coefficients, the proposed approach significantly reduces the computational cost of constructing the Liouville superoperator compared with direct methods. To facilitate the implementation of the method, we provide a Mathematica notebook containing a one-qubit example that can be systematically extended to an arbitrary number of qubits. The proposed framework therefore provides both a general mathematical description of finite-dimensional Lindblad dynamics and a practical foundation for efficient analytical and numerical implementations.

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arXiv2026

Determination of the metric of a Schwarzschild black hole surrounded by a halo of dark matter

Following the landmark acquisition of the first image of a black hole, systems comprising a black hole enveloped by a dark matter halo have attracted considerable attention. This work implements a novel method to analyze the structure of a system composed of a Schwarzschild black hole and a dark matter halo modeled as an anisotropic fluid, while ensuring that the proposed metric constitutes an exact solution of the Einstein field equations. Numerical results show that the connection between the temporal and radial metric functions preserves an inverse relationship, namely $A(r) \approx 1/B(r)$. Furthermore, we analytically demonstrate that the resulting functions satisfy $A(r)B(r) = 1 + \mathcal{O}(10^{-6})$, in excellent agreement with the numerical findings. In addition, the Einstein equations imply that the variation of the product $A(r)B(r)$ is governed by the factor $\varepsilon_h=\frac{8\pi G\rho_0r_0^2}{c^2}$. Finally, we show that the interior Schwarzschild region and the exterior dark matter halo can be joined smoothly via a regular Darmois Israel junction, without generating any thin shell curvature steps. To assess the observational implications of the model, we compare its theoretical predictions for the pericenter precession of the S2 star and the angular size of the shadow of Sgr A*. In both cases, the predicted deviations remain within the observational uncertainties reported by the GRAVITY Collaboration and the Event Horizon Telescope (EHT), respectively. These results demonstrate that the proposed black hole dark matter halo configuration is not only mathematically consistent, but also compatible with current observational constraints.

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arXiv2026

Potential Space Symmetries in Ernst-like Formulations of Einstein-Maxwell/ModMax-Scalar field Theories

We complete the visible, hidden, sectorial, and discrete symmetries of Ernst-like potential spaces in stationary, axisymmetric Einstein-Maxwell-Scalar Field (EMSF) and Einstein-ModMax-Scalar Field (EMMSF) theories. In the real potential space $(f,\epsilon,\psi,\chi,\kappa)$, we determine the exact visible symmetries and their solvable Lie algebra. We characterize the hidden symmetries on invariant subspaces: Ehlers acts in the gravito-rotational sector, while electric and magnetic Harrison transformations act in static electromagnetic sectors. In the frozen EMMSF regime, $v=v_0,\ w=w_0$, we show how EMSF sectorial transformations are deformed in ModMax theory. We also show that coexistence of electric and magnetic sectorial Harrison transformations imposes $d w=0$ and $d[(v^2+w^2)/w]=0$, selecting precisely the frozen ModMax sector. We study the Hamiltonian formulation, Noether charges, and Casimir invariants of the sectorial algebras. In harmonic branches of the $A,B,C$ one-forms, the affine geodesic energy is constant, so the quadrature for $k$ is controlled by the affine-geodesic Hamiltonian. The functions $\omega$ and $A_\varphi$ follow from Noether charges along the Killing directions of $\epsilon$ and $\chi$, and are written using dual harmonic functions. We examine the electric and magnetic Lewis-Weyl-Papapetrou frames and their discrete map, which sends $\kappa\mapsto\kappa^{-1}$, $\psi\mapsto\chi$, $\chi\mapsto-\psi$, and $\epsilon\mapsto\epsilon-\psi\chi$. Finally, we apply the sectorial transformations to harmonic scalar--acuum Weyl seeds with independent gravitational and scalar harmonics. Frozen-ModMax Harrison maps generate charged branches, while Ehlers generates the gravito-rotational branch. For these solutions we give the final quadratures for $k$, $\omega$, and $A_\varphi$.

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arXiv2026

Exact rotating dilatonic branch in ModMax electrodynamics without Maxwell analogue

We present a novel class of rotating dilatonic solutions within the framework of Einstein-ModMax-type gravity. The configuration belongs to the nonlinear sector characterized by $\mathcal F/\mathcal G=\mathrm{const}$ and carries nontrivial electric and magnetic potentials, with both $A_t$ and $A_\varphi$ turned on, together with a nontrivial gravitomagnetic structure. We show that this solution does not admit continuation to the Maxwell framework of our parametrization, so it is intrinsically tied to the nonlinear ModMax regime. It includes both a NUT geometry and a NUT-free asymptotically flat limit, and it is valid for a broad class of dilatonic couplings, including the low-energy string and Kaluza-Klein cases. Moreover, in the prolate sector we identify a genuine black-hole regime in which the exterior region satisfies the null energy condition while the curvature singularity remains hidden behind the event horizon. These results provide an exact rotating dilatonic ModMax configuration with no Maxwell analog and a physically well-behaved exterior black-hole sector.

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arXiv2026

Generalized Einstein-ModMax-ScalarField theories and new exact solutions

We present a generalized Ernst-type framework for stationary, axisymmetric spacetimes in which a scalar field is coupled to the electrodynamic field, with a particular focus on the ModMax theory. Our approach relies on the Weyl stationary-axisymmetric ansatz and explicitly allows for a nonzero rotational metric function, $\omega\neq 0$. The resulting setup is broad enough to encompass wide classes of scalar couplings, including dilatonic and phantom-like sectors, and can be tailored to specific models such as Einstein-ModMax, Kaluza-Klein theories, low-energy string-inspired scenarios, entanglement relativity and related generalizations. Within this scheme, we derive two novel families of exact rotating solutions in the sector where the electromagnetic invariants obey $\mathcal F/\mathcal G=\mathrm{constant}$. This regime is particularly significant for ModMax, as it preserves genuinely nonlinear features while still admitting an analytically manageable description.

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arXiv2026

On the Possibility of the Existence of Wormholes in Nature

To date, many exotic predictions of Einstein's equations have been corroborated, with one exception: wormholes (WHs). In this work, we analyse a new exact solution combination to the Einstein-Maxwell-Dilaton or Phantom equations, which represent rotating WHs with magnetic and electric fields. The solution contains a ring singularity that, like other solutions, satisfies Wormhole Cosmic Censorship; that is, the singularity is causally disconnected by the WH throat. We show that this WH is traversable through regions close to the poles, where the tidal forces and magnetic field are reasonably small. We satisfy the energy conditions for the dilaton-like solution. We argue that if dilaton-like interactions can exist in nature, for example, if extra dimensions exist as in superstring theory, WHs are a natural realistic prediction of Einstein's equations, and we should be able to observe them somehow, probably as black hole mimics.We present several examples of realistic WH that may occur in nature, and we also introduce a new exact black hole solution.

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arXiv2026

Generalized Ernst Potentials for arbitrary Dilatonic Theories

In this work, we generalize Ernst potentials to the Einstein-Maxwell-Dilaton case and explicitly write the corresponding potential space metric. Since this metric is five-dimensional in potential space, we generalize the corresponding Newman-Penrose coefficients for this metric and compare this formalism with previous approaches to show that this formulation is very convenient for analyzing these spacetimes and finding new exact solutions. We show how to obtain old exact solutions and some new ones with very interesting properties.

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arXiv2026

Axially symmetric wormholes

In this work, we derive an exact vacuum solution to the Einstein field equations that depends on three constant parameters: the throat radius $r_0$, a parameter $q$, which is closely associated with the Komar mass, and a parameter $s$, which introduces axial topological defect while avoiding the emergence of conical singularities. We employ the cut-and-paste construction to generate wormhole geometries from this solution for $q \neq 0$. In addition, we perform a detailed analysis of the embedding diagrams, the wormhole throat, the occurrence and structure of trapped surfaces, the behavior of geodesics, the associated tidal forces, the Petrov algebraic classification, the Newman-Penrose spin coefficients, and the corresponding invariant conserved charges.

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arXiv2026

A Brief Review of Wormhole Cosmic Censorship

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formulated by Penrose. Here we review another type of CC where spacetime singularities are causally disconnected from the universe, because the throat of a wormhole ``sucks in'' the geodesics and prevents them from making contact with the singularity. In this work, we present a series of exact solutions to the Einstein--Maxwell--Dilaton equations that feature a ring singularity; that is, the curvature invariants are singular in this ring, but the ring is causally disconnected from the universe so that no geodesics can touch it. This extension of CC is called Wormhole Cosmic Censorship.

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arXiv2025

Wormholes exact solutions in high dimensions General Relativity

In the present work, we develop and examine a series of exact solutions to Einstein's 5-dimensional field equations in the vacuum, which depend on two constant parameters, $p$ and $q$, which generalize the solutions of L\"u and Mei [8] belonging to our class $p=2$. This category of solutions can be split into two sections: when $p$ is odd, it represents a compact object that may have naked singularities. However, the intriguing outcome occurs when $p$ is even, as asymptotically Ricci flat wormholes emerge in this scenario. The Kreschman invariant of these solutions depends on the constant parameter $l = 1 + \frac{3 q^2 - p^2}{4}$. When $l = 0$ and $l \leq -\frac{1}{2}$, the solutions are regular. For the specific cases where $l \leq 0$, or $l > 0$ such that $q < 0$ for $p \geq 2$, $q \leq \frac{1}{3}$ for $p = 2$, and $q \leq \frac{1 + \sqrt{2}}{3}$ for $ p \geq 4$, this class of wormholes adheres to Wormhole Cosmic Censorship, implying that the throat effectively obscures all causal anomalies and singularities. In our analysis, we investigated the embedded geometry, geodesics, singularities, potential event horizons, ergoregions, and the wormhole throat.

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arXiv2025

The space-time structure of an untouchable naked singularity in superstrings theory

According to the Cosmic Censorship Conjecture, naked singularities are believed to be forbidden in nature and must remain hidden by an event horizon. In this work, we present the causal structure of an exact solution to the Einstein-Maxwell-Dilaton equations with five parameters: mass, angular momentum, electric and magnetic charges, and a scale, satisfying constraint equations. For one of the constraints, the solution represents a wormhole (WH), and for the other, a black hole (BH), both with an untouchable ring singularity causally disconnected from the rest of the universe. After topologically defining the concept of Wormhole Cosmic Censorship (WCC), we analyze its metric functions in Papapetrou coordinates to verify metric analyticity in spacetime, construct the Carter-Penrose diagram, and use Boyer-Linquist coordinates to visualize the cladding of the ring singularity by the throat. We conclude that the ring singularity in this WH is clad by the throat, similarly to how the event horizon clads the ring singularity in the Kerr-Newman black hole, thus satisfying the WCC Conjecture. In this work, we show that the topology of the WH throat is such that the two sides of the throat are separated by the singularity but topologically identified, resulting in an instantaneous connection between these two regions. These results are applicable to various theories, including Kaluza-Klein and superstring theory. We provide a rigorous proof that, in the black hole case, the domain of outer communication includes a chronology-violating region and thus supports the existence of closed timelike curves outside the event horizon.

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arXiv2025

Einstein-Maxwell-Dilaton Wormholes that meet the Energy Conditions

One of the latest predictions of Einstein's theory is the existence of Wormholes (WH). In this work, we present exact solutions of the Einstein-Maxwell-Dilaton equations representing traversable Wormholes. These solutions satisfy the energy conditions and have a ring singularity satisfying the cosmic censorship of WHs, i.e. we show that, as in previous solutions, geodesics cannot touch the singularity. We find that the most optimal input regions for the first class of solutions traversing these wormholes are near the poles and near the equatorial plane for the second class. We also find that the solution associated with the first class is physically feasible, while for the second class it presents the problem of not being asymptotically flat when considering a dilatonic-type scalar field. Finally, we give examples of realistic astrophysical objects that could fulfill these conditions.

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