arXiv subjects

José Rodal

Publications and source records attributed to José Rodal.

6 recordsLinked to original sources

arXiv2026

Tamm-Rubilar branch diagnostics for Drummond-Hathrell photon propagation: Schwarzschild calibration and a Kerr weak-lensing benchmark

This paper develops a local Tamm-Rubilar branch diagnostic for supplied nondispersive, pair-symmetric constitutive tensors and uses it as a preprocessing layer for polarization-resolved ray transport. The diagnostic constructs the local quartic Fresnel polynomial, checks real ADM-oriented roots and root margins, and separates algebraic branch stability from the separate effective-field-theory question of when a Drummond-Hathrell low-frequency surrogate is applicable. For constitutive tensors with a reflection isometry, the adapted bivector matrix has an exact parity block form. The full parity-invariant Tamm-Rubilar polynomial is a quartic with coefficients even in the transverse momentum, while a restricted meridional SSSW-frame quartic is retained only as a compact analytic benchmark and root-margin test. In Schwarzschild, the Ricci-flat Drummond-Hathrell curvature sector factorizes and reproduces the standard radial no-shift and orbital polarization-split result. The rotating-spacetime benchmark is an infinity-to-infinity weak-lensing calculation in the linearized Kerr field. In a transported Born screen, the local slow-Kerr magnetic-Weyl eigenbasis tilt has zero leading endpoint mismatch, while the branch-delay split has a spin-odd term proportional to the angular momentum projected along the lens-plane normal. The resulting phase retardance is far below near-term detectability for representative compact-object grazing rays, so the Kerr calculation is presented as a reproducible scale-setting benchmark for the diagnostic and transport framework rather than as an observational claim.

gr-qc↗

arXiv2025

A Machian wave effect in conformal, scalar-tensor gravitational theory

Woodward proposed that driven mass-energy fluctuations could yield a frequency-dependent "Machian" gravitational response $\propto \partial_t^2 M_{\rm loc}(t)$, amplified by a Sciama-scale cosmic potential $Φ/c^2\sim -1$. We test this claim covariantly in (i) Einstein gravity and (ii) Hoyle-Narlikar (HN) conformal scalar-tensor gravity. In GR, the Landau-Lifshitz relaxed equations in harmonic gauge contain nonlinear terms of the form $H^{αβ}\,\partial_α\partial_βH^{μν}$, including a near-zone piece $H^{00}\,\partial_t^2 H^{μν}$. These terms are not independent matter sources; they arise from expanding the curved wave operator about a flat background. Moving them back to the left-hand side restores the quasilinear principal part, and for laboratory devices their size is suppressed by $\sim (U_N/c^2)(ωL/c)^2\ll 1$, with no enhancement by any cosmological potential. In HN theory, the conformal scalar satisfies $\nabla_a\nabla^a m + (R/6)m=λN$. For a localized device of size $L$ driven at angular frequency $ω$, $|(c^{-2}\partial_t^2 m_s)|/|\nabla^2 m_s|\sim (ωL/c)^2\ll 1$, so the response is effectively instantaneous (Poisson-like), not wave-amplified. Baryon-number conservation fixes the scalar charge, so the rest-mass monopole cannot oscillate; any radiating monopole requires nonconservative internal-energy variations, further suppressed by $E_{\rm int}/(M c^2)$ and by $M_{\rm dev}/M_H$. Thus any Mach-effect thrust is far too small for practical propulsion.

gr-qc↗

arXiv2025

Visualization and analysis of the curvature invariants in the Alcubierre warp-drive spacetime

In the Alcubierre warp-drive spacetime, we investigate the following scalar curvature invariants: the scalar $I$, derived from a quadratic contraction of the Weyl tensor, the trace $R$ of the Ricci tensor, and the quadratic $r1$ and cubic $r2$ invariants from the trace-adjusted Ricci tensor. In four-dimensional spacetime the trace-adjusted Einstein and Ricci tensors are identical, and their unadjusted traces are oppositely signed yet equal in absolute value. This allows us to express these Ricci invariants using Einstein's curvature tensor, facilitating a direct interpretation of the energy-momentum tensor. We present detailed plots illustrating the distribution of these invariants. Our findings underscore the requirement for four distinct layers of an anisotropic stress-energy tensor to create the warp bubble. Additionally, we delve into the Kretschmann quadratic invariant decomposition. We provide a critical analysis of the work by Mattingly et al., particularly their underrepresentation of curvature invariants in their plots by 8 to 16 orders of magnitude. A comparison is made between the spacetime curvature of the Alcubierre warp-drive and that of a Schwarzschild black hole with a mass equivalent to the planet Saturn. The paper addresses potential misconceptions about the Alcubierre warp-drive due to inaccuracies in representing spacetime curvature changes and clarifies the classification of the Alcubierre spacetime, emphasizing its distinction from class $B$ warped product spacetimes.

gr-qc↗

arXiv2025

A Closer Look at Natário's Zero-Expansion Warp Drive

We conduct a detailed analysis of Nat'{a}rio's ``zero-expansion'' warp drive spacetime, focusing on scalar curvature invariants within the 3+1 formalism. This paper has four primary objectives: First, we establish the Petrov type classification of Nat'{a}rio's spacetime, which has not been previously determined in the literature. We prove that Nat'{a}rio's spacetime is Petrov type I, not fitting the Class B warped product spacetime definition. Second, we assess the relative magnitude of the Weyl scalar curvature invariant and compare it with the amplitudes of Einstein's scalar and the Ricci quadratic and cubic invariants within the warp-bubble zone. Previous studies have focused on Ricci curvature and the energy-momentum tensor, neglecting the Weyl curvature, which we demonstrate plays a significant role due to the sharp localization of the form function near the warp-bubble radius. Third, we visualize several curvature invariants for Nat'{a}rio's warp drive, as well as momentum density, which we show as the critical physical quantity governing the orientation of the warp drive trajectory, overshadowing space volume changes. Fourth, we critically examine claims that Nat'{a}rio's warp drive is more realistic than Alcubierre's. We demonstrate that Nat'{a}rio's spacetime exhibits curvature invariant amplitudes 35 times greater than Alcubierre's, given identical warp-bubble parameters, making Nat'{a}rio's concept even less viable. Additionally, we address Mattingly et al.'s analysis, highlighting their underestimation of curvature invariant amplitudes by 21 orders of magnitude.

gr-qc↗

arXiv2025

A warp drive with predominantly positive invariant energy density and global Hawking-Ellis Type I

We present the first fully explicit, continuous, analytically derived warp-drive spacetime within General Relativity whose shift-vector flow is kinematically irrotational. Building on Santiago \emph{et al.} that scalar-potential, zero-vorticity warp fields are Hawking-Ellis Type I for unit lapse and flat spatial slices, we supply a closed-form scalar potential and smooth shift components with proper boundary behavior, together with a Cartan-tetrad analytic pipeline and high-precision eigenanalysis. Compared with the Alcubierre and Natário models (evaluated at identical parameters $ρ, σ, v/c$), our irrotational solution exhibits \emph{significantly reduced} local NEC/WEC stress: its peak proper-energy deficit is reduced by a factor of $\approx 38$ relative to Alcubierre and $\approx 2.6 \times 10^{3}$ relative to Natário, and its peak NEC violation is more than $60 \times$ smaller than Natário. Crucially, the stress-energy is \emph{globally} Hawking-Ellis Type I, with a well-defined timelike eigenvalue (proper energy density) everywhere. A fixed-smoothing vortical ablation confirms that this improvement is causally due to irrotational, curl-free kinematics rather than profile shaping: adding modest vorticity collapses the $E_{+} / E_{-}$ balance and drives large increases in the negative-energy magnitude $E_{-}$. We quantify the negative-energy requirement via a \emph{slice-integrated} (on $Σ_{t}$) negative-energy volume and tabulate global measures. A far-field extrapolation to $R \to \infty$ yields tail-corrected totals $|E_{+} - E_{-}| / (E_{+} + E_{-}) = 0.04\%$. Thus the net \emph{proper} energy is consistent with zero to four decimal places (in fractional units). We also establish regularity at $r=0$ for the irrotational construction.

gr-qc↗

arXiv2025

On the Infeasibility of Low-Energy Warp Drive via Metamaterial Gravitational Coupling

Recent ``low-energy'' warp-drive concepts propose replacing the constant gravitational coupling $κ_0$ with a spatially varying scalar field $κ(x)$ set by an engineered metamaterial's electromagnetic response. We show that the idea fails on both theoretical and experimental grounds. A prescribed, non-dynamical $κ(x)$ in the field equation $G^{μν} = κ(x)T^{μν}$ clashes with the contracted Bianchi identity, $\nabla_μG^{μν} \equiv 0$, forcing $\nabla_μT^{μν} \neq 0$ and thus violating local energy-momentum conservation. Making $κ(x)$ dynamical yields a scalar-tensor theory in which the scalar mediates a new long-range force that breaks the strong equivalence principle; Solar-System and pulsar-timing experiments already restrict $|γ- 1| \lesssim 10^{-5}$, excluding any technologically useful coupling. Junction-condition analysis further shows that any interface where $κ$ changes demands a $δ$-function layer of stress-energy, while even steep continuous profiles are ruled out by torsion-balance, lunar-laser, and spacecraft Doppler measurements. Hence the concept is untenable: a non-dynamical scheme violates conservation laws, and its scalar-tensor completion is falsified by existing data..

gr-qc↗