arXiv subjects

I. A. Sarmiento-Alvarado

Publications and source records attributed to I. A. Sarmiento-Alvarado.

8 recordsLinked to original sources

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

Exact lambdavacuum solutions in higher dimensions

In this work, we obtain exact solutions to the $(n+2)$-dimensional Einstein Field Equations with a non-zero cosmological constant for $n > 1$. These solutions depend on a set $\{ A_a, a=1,2,\ldots , m \}$ of pairwise commuting constant matrices in $\mathfrak{sl} ( n, \mathbb{R} )$ and on a constant matrix $g_0$ in $\mathcal{I} (\{ A_a, a=1,\ldots , m \})$, determined in previous work. Different choices of $\{ A_a, a=1,\ldots , m \}$ and $g_0$ correspond to different solutions. As examples, we show how to obtain the de Sitter metric, the Anti-de Sitter metric, the Birmingham metric, the Nariai metric and the Anti-Nariai metric in higher dimensions. The generalized Nariai and Anti-Nariai solutions are direct topological products of $AdS_{\frac{n}{2} + 1} \times H^{\frac{n}{2} + 1}$, $dS_{\frac{n}{2} + 1} \times S^{\frac{n}{2} + 1}$, $AdS_2 \times H^n$, $AdS_n \times H^2$, $dS_2 \times S^n$ and $dS_n \times S^2$. In addition, we study a solution in the context of cosmology.

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

Flat subspaces of the $SL(n,\mathbb{R})$ chiral equations

In this work, we introduce a method for finding exact solutions to the vacuum Einstein field equations in higher dimensions from a given solution to the chiral equation. When considering a $n + 2$-dimensional spacetime with $n$ commutative Killing vectors, the metric tensor can take the form $\hat g = f ( ρ, ζ) ( d ρ^2 + d ζ^2 ) + g_{μν} ( ρ, ζ) d x^μd x^ν$. Then, the Einstein field equations in vacuum reduce to a chiral equation, $( ρg_{, z} g ^{-1} )_{, \bar z} + ( ρg_{, \bar z} g ^{-1} )_{, z} = 0$, and two differential equations, $( \ln f ρ^{1-1/n} )_{, Z} = \fracρ{2} \operatorname{tr} ( g_{, _Z} g^{-1} )^2$, where $g \in SL( n, \mathbb{R} )$ is the normalized matrix representation of $g_{μν}$, $z = ρ+ i ζ$ and $Z = z, \bar z$. We use the ansatz $g = g ( ξ^a )$, where the parameters $ξ^a$ depend on $z$ and $\bar z$ and satisfy a generalized Laplace equation, $( ρξ^a _{, z} )_{, \bar z} + ( ρξ^a _{, \bar z} )_{, z} = 0$. The chiral equation to the Killing equation, $A_{a , ξ^b} + A_{b , ξ^a} = 0$, where $A_a = g_{, ξ^a} g^{-1}$. Furthermore, we assume that the matrices $A_a$ commute with each other; in this way, they fulfill the Killing equation.

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↗

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.

gr-qc↗

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 Lü 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.

gr-qc↗

arXiv2015

Analysis of the top-quark charged-current coupling at the LHeC

In the context of $SU(2)_L\times U(1)$ dimension six operators we study the potential of the LHeC to provide information on top quark effective interactions. We focus on single antitop production and how it is affected not only by the effective $tbW$ coupling but also by four-fermion operators. Compared to the LHC, the LHeC provides a cleaner environment to make a precise measurement of the top quark production cross section. Therefore, this machine would give a much better assesment of $V_{tb}$ in the context of the SM or $V_L$ in the context of higher dimension operators. The LHeC could also give a slightly better measurement for $V_R$. For $g_R$ the HL-LHC precise measurements of $F_L$ and $F_R$ (the $W$-boson helicity decay ratios of top) would yield better constraints than those obtained by the LHeC. Lepton-quark contact interactions would also be significantly better probed by the LHeC, since the only way of measuring them at the LHC would be through leptonic top decay which is hardly sensitive to these interactions.

hep-ph↗