arXiv subjects

Tonatiuh Matos

Publications and source records attributed to Tonatiuh Matos.

At least 19 recordsLinked to original sources

arXiv2026

Potential-space geometry and scalar rigidity of the Plebański-Demiański ansatz without a cosmological constant

We analyze stationary, axisymmetric Einstein-Maxwell-dilaton theory with zero cosmological constant in the conformal Carter class, employing a generalized Ernst approach on the space of potentials. We begin by establishing a complete local correspondence between Plebański-Demiański principal coordinates and Weyl data, covering the electric, magnetic, and twist potentials as well as the 1-forms $A$, $B$, and $C$. In the source-free Weyl reduction, requiring the invariant area density to be harmonic singles out the $Λ=0$ sector, and the principal chiral splitting isolates both electromagnetic misalignment and the part due to acceleration. Next, we obtain the Einstein reconstruction equations for general local EMD configurations in this setting. In a physical Carter domain with an ordinary scalar, the bilinear factor $\Om=1-\acc pq$ enforces $C=0$ and $B_-=0$. With fixed $\alphao\neq0$, the scalar field equation further rules out the charged PD Coulomb-type 1-form. Lastly, assuming an exact quadratic Stäckel scalar 1-form, the conditions of exactness together with reconstruction restrict the system to a single aligned branch, but consistency with the full potential equations removes this branch for arbitrary smooth Carter structure functions. Consequently, within the quadratic Stäckel class studied here, there is no local nonconstant solution with an ordinary dilaton. This conclusion does not extend to phantom scalars, conformal factors of higher degree, or non-Stäckel 1-forms.

gr-qc↗

arXiv2026

Canonical Quantization and Constraint Algebra of Weyl-Invariant Gravity in a Conformal Gauge: Emergence of a Geometric Cosmological Term

We present the canonical quantization of Weyl-invariant gravity in a specific conformal gauge. Fixing the scale factor as $a(η) = 1/(H_0η)$ yields an effective geometric cosmological term $\mathcal{M}(η) = α/η^2$ on the left-hand side of the Einstein equations, guaranteeing an equation of state $w = -1$ by construction. The Bianchi identity requires a compensator scalar field; we show that this compensator is the conformal mode of the metric, a gauge artifact that does not propagate ghost instabilities in the full quantum theory. We develop the complete ADM Hamiltonian formulation and prove that the constraint algebra closes in standard first-class form. Canonical quantization yields a well-defined Wheeler-DeWitt equation where the $\mathcal{M}(η)$ term acts as a potential barrier dynamically suppressing the quantum creation of small-scale universes. The physical reduced Hamiltonian is demonstrated to be bounded from below, time evolution is strictly unitary in the physical Hilbert space, and microcausality is preserved. In the pure vacuum regime, the model admits an exact analytical solution with $Ω_{\text{DE}} = 1$, resolving the cosmic coincidence problem without fine-tuned parameters. In the matter-dominated era, the comoving horizon scales as $R_H \propto η$, so our result $\mathcal{M} \propto η^{-2} \propto R_H^{-2}$ reproduces the central Compton Mass Dark Energy (CMaDE) hypothesis from first principles and establishes $n = -2$ as the theoretical benchmark for the Conformal Holographic Dark Energy (CHDE) parametrization $\mathcal{M} \propto η^n$. From a pure conformal symmetry principle, the model delivers an effective geometric cosmological term that drives the accelerated expansion with $w = -1$, providing the missing action principle for CMaDE.

gr-qc↗

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 $\varepsilon_h=\frac{8πGρ_0r_0^2}{c^2}$. 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.

gr-qc↗

arXiv2026

Canonical Uncertainty Relations for Madelung Variables in Curved Spacetime: Relating Dark Matter Cores and Unruh Radiation

We establish fundamental uncertainty relations for the hydrodynamic variables arising from the Madelung representation of quantum fields in curved spacetime. Through canonical quantization of the density $n$ and phase $θ$ variables and their conjugate momenta, we derive exact uncertainty principles that depend on spacetime geometry through the lapse function $N$ and spatial metric $γ_{ij}$. These relations reveal how gravitational fields modulate quantum fluctuations and provide first-principles constraints for Scalar Field Dark Matter (SFDM) models and stochastic quantum gravity. We present two groundbreaking applications. First, By coupling the density-velocity uncertainty to the Newtonian condition of hydrostatic equilibrium, we derive the exact scaling law for the minimum core radius of a self-gravitating scalar field halo. We naturally find the scale $r_c \propto m^{-1/2}$ which is a testable prediction. Second, by evaluating the phase--momentum commutator in Rindler coordinates and relating the canonical momentum $Π_θ$ to the energy density via the Hamiltonian, we obtain the acceleration scale $k_B T = C\hbar a/c$. The proportionality constant $C=1/(2π)$ is fixed by the topological quantization of the Madelung phase circulation around the Euclidean horizon. This dual achievement demonstrates that quantum uncertainty on curved backgrounds is the unifying principle behind both galactic structure and black hole thermodynamics.

gr-qc↗

arXiv2026

Alternative explanation of Fermi Bubbles using Scalar Field Dark Matter

In recent times, the Scalar Field Dark Matter (SFDM) model (also called Fuzzy, Wave, Ultralight dark matter model) has received much attention due to its success in describing dark matter on both cosmological and galactic scales. Several challenges of the Cold Dark Matter (CDM) model can be explained very easily and naturally by the SFDM model. Two of these challenges are to describe the anomalous trajectories of satellite galaxies called the Vast Polar Structure (VPOS) and to explain the magnetic fields observed in our galaxy. In previous works an alternative explanation for VPOS and the magnetic fields of our galaxy was proposed using the SFDM excited states, explaining the anomalous trajectories in a natural and simple way. In this work we use the same dark matter endowed with a extremely small charge that explains the magnetic fields of our galaxy to show that these excited states of SFDM can provide a very simple and natural explanation for Fermi Bubbles (FBs). If this assumption is correct, we should see FBs in several more galaxies, these observations would take place in the near future and could be crucial to the ultimate answer to the nature of dark matter.

astro-ph.GA↗

arXiv2026

Energy Balance of a Bose Gas in Curved Spacetime

Classical solutions of the Klein-Gordon (KG) equation are used in astrophysics to model galactic halos of scalar field dark matter and compact objects such as cores of neutron stars. These bound solutions are interpreted as Bose-Einstein condensates whose particle number density is governed by the Gross-Pitaevskii (GP) equation. It is well known that the Gross-Pitaevskii-Poisson (GPP) system arises as the non-relativistic limit of the Klein-Gordon-Einstein (KGE) equations and, converselly, the KGE system may be interpreted as a generalization of the GPP equations in a curved space-time. In the present work, we consider a 3+1 ADM foliation of the space-time in order to construct a general-relativistic version of the GP equation. Besides, we derive a general energy balance equation for the boson gas in the hydrodynamic variables, where different energy potentials are identified as kinetic, quantum, electromagnetic and gravitational. In addition, we find a correspondence between the energy potentials in the balance equation and actual components of the scalar energy-momentum tensor. We also study the Newtonian limit of the hydrodynamic formulation and the balance equation. As an illustrative case, we study the effects in the energy potentials due to a relativistic correction in the GP equation.

gr-qc↗

arXiv2026

A Covariant Chiral-Hydrodynamic Formulation of the Dirac Equation in Curved Spacetime

The hydrodynamic formulation of the Dirac equation has historically been hindered by the inability to close the system of physical variables without resorting to infinite moment hierarchies. We resolve this longstanding issue by developing a fully covariant chiral-hydrodynamic formulation of the Dirac field in curved spacetime. Working in the Weyl representation, we introduce two independent null vectors, $P_L^μ$ and $P_R^μ$, which decouple the left and right chiral components. This allows us to define chiral geodesic and stochastic velocities, yielding a closed system of exactly eight real equations that corresponds directly to the Dirac field degrees of freedom. Remarkably, this formulation naturally isolates the spin-orbit coupling $(q/2)σ^{μν}F_{μν}$ while demonstrating the vanishing of the spin-gravity coupling in torsion-free general relativity. To demonstrate the analytical power of this framework, we specialize to the Schwarzschild geometry. We obtain exact radial solutions in terms of confluent Heun functions and directly compute the quasi-bound state spectrum (fermionic resonances), quasinormal mode frequencies, and greybody factors. Furthermore, by establishing an exact energy balance equation -- representing the first law of thermodynamics for Dirac fields -- we derive the Hawking radiation flux purely from chiral flux conservation at the event horizon. This work not only provides a closed hydrodynamic theory for spin-1/2 fluids but also establishes a unified framework for analyzing quantum information and fermion dynamics in strong gravitational backgrounds.

gr-qc↗

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 $(f,ε,ψ,χ,κ)$, 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 $ω$ and $A_φ$ follow from Noether charges along the Killing directions of $ε$ and $χ$, and are written using dual harmonic functions. We examine the electric and magnetic Lewis-Weyl-Papapetrou frames and their discrete map, which sends $κ\mapstoκ^{-1}$, $ψ\mapstoχ$, $χ\mapsto-ψ$, and $ε\mapstoε-ψχ$. 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 $k$, $ω$, and $A_φ$.

gr-qc↗

arXiv2026

Energy Balance of a Boson Gas at Zero Temperature in Curved Spacetime

We develop a comprehensive thermodynamic description for a zero-temperature boson gas in curved spacetime, integrating energy conservation with information-theoretic principles. Using the hydrodynamic Madelung representation within the ADM formalism, we establish two fundamental relationships: an energy balance equation representing the first law of thermodynamics from a spacetime perspective, and an information-theoretic constraint connecting Fisher entropy to the dynamical evolution of the boson density. This dual formulation clearly separates energy transport from information conservation while revealing how quantum information is preserved in curved backgrounds. The introduction of a stochastic velocity provides a bridge between quantum potential effects and underlying spacetime fluctuations. We demonstrate the consistency of our framework through detailed analyses of quantum systems in both Minkowski and Schwarzschild spacetimes. This work provides a unified foundation for studying relativistic bosonic systems, with direct relevance to boson stars and scalar field dark matter models.

gr-qc↗

arXiv2026

Topological Quantization of Complex Velocity in Stochastic Spacetimes

We establish a rigorous geometric framework for quantum fields on a stochastic gravitational background. Starting from a master partition function that averages over metric fluctuations, we define a matter amplitude $\mathcal{K}$, whose logarithmic derivative yields a complex velocity field $η_μ = π_μ - i u_μ$. This object, originating in Nelson's stochastic mechanics, is a section of the pullback bundle $E = π_2^*(T^*M)$ over the product of configuration space $\mathcal{C}$ and spacetime $M$. We prove that $η_μ$ defines a flat $U(1)$ connection with $\mathcal{K}$ as its horizontal section, and via a bundle isomorphism it maps to the symmetric logarithmic derivative of quantum estimation theory. The coupled dynamics collapse into $\mathcal{L}_ηη= d(|η|^2)$. We resolve the tension between flatness and multi-valuedness: although the connection is flat, the potential can be multi-valued from topological terms or branch cuts. The total phase satisfies $\frac{m}{\hbar}\oint_γη_μ dx^μ = 2πn + Δϕ_{\text{top}}$. We demonstrate this in a toy model: a scalar field on a conical spacetime with deficit angle $α$, computing the matter amplitude in the Gaussian approximation, deriving the complex velocity, and calculating its holonomy. The resulting topological offset receives a quantized stochastic correction depending on the variance of metric fluctuations, providing an experimental signature for atom interferometry. This framework geometrizes quantum mechanics without hidden variables: stochasticity imprints spacetime fluctuations on matter, preserving the wave function's probabilistic nature while giving a geometric origin for the Born rule.

gr-qc↗

arXiv2026

Stochastic Quantum Mechanics Trajectories Near Schwarzschild Horizon Black Holes

This work explores the possibility of applying stochastic quantum mechanics to curved spacetimes, with an emphasis on the Schwarzschild black hole. After reviewing the fundamental concepts of this approach, the quantum stochastic equations are extended to curved spacetime using a fully covariant treatment. Subsequently, the Klein-Gordon equation is solved for scalar perturbations, and the resulting stochastic trajectories are analyzed by varying parameters such as angular momentum, particle frequency, and computational integration time. In conclusion, we find that the trajectories are influenced by gravitational fluctuations in spacetime and that, depending on the variation of the fundamental parameters, different types of stochastic trajectories are obtained.

physics.gen-ph↗

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 $A_φ$ 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.

gr-qc↗

arXiv2026

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.

gr-qc↗

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, $ω\neq 0$. 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.

gr-qc↗

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.

gr-qc↗

arXiv2026

One-dimensional subspaces of the $SL(n,\mathbb{R})$ Chiral Equations

In this work we find solutions of the ($n+2$)-dimensional Einstein Field Equations (EFE) with $n$ commuting Killing vectors in vacuum. In the presence of $n$ Killing vectors, the EFE can be separated into blocks of equations. The main part can be summarized in the chiral equation $\ (αg_{, \bar{z}} g^{-1})_{, z} + \ (αg_{, z} g^{-1})_{, \bar{z}} = 0$ with $ g\in SL(n,\mathbb{R})$. The other block reduces to the differential equation $(\ln f α^{1-1/n})_{, z} = 1/2 αtr( g_{, z} g^{-1})^2$ and its complex conjugate. We use the ansatz $g = g(ξ) $, where $ξ$ satisfies a generalized Laplace equation, so the chiral equation reduces to a matrix equation that can be solved using algebraic methods, turning the problem of obtaining exact solutions for these complicated differential equations into an algebraic problem. The different EFE solutions can be chosen with desired physical properties in a simple way.

gr-qc↗

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.

gr-qc↗

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.

gr-qc↗