arXiv subjects

William Julius

Publications and source records attributed to William Julius.

5 recordsLinked to original sources

arXiv2026

Stationary Particle Creation and Entanglement in the Rotating Teo Wormhole: A Quantum Mode-Mixing Approach

Rotating traversable wormholes allow the effects of frame dragging and rotation to be studied in the absence of event horizons. We develop a quantum field theoretic treatment of massless scalar perturbations in the rotating Teo spacetime. This spacetime is an exact, stationary, horizonless wormhole connecting two asymptotically flat regions. Using the Bogoliubov transformation formalism, we construct ``in'' and ``out'' mode solutions defined on the two asymptotic regions and compute the Bogoliubov coefficients that quantify vacuum mode mixing. The effective radial potential induced by rotation and frame dragging forms an asymmetric scattering barrier. This geometric asymmetry allows an exact analytic evaluation of reflection and transmission amplitudes via the barrier-penetration exponent. This results in closed-form expressions for the Bogoliubov coefficients, the mean particle number, and the two-mode entanglement entropy as functions of the rotation parameter. The resulting amplification arises at the level of quantum Bogoliubov mode mixing and vacuum squeezing, rather than classical superradiant flux enhancement. Since this spacetime is stationary, particle creation originates from geometric asymmetry and boundary conditions, and not from explicit time dependence. Co-rotating and counter-rotating modes experience inequivalent scattering. This renders the process intrinsically non-reciprocal. We identify this mechanism as a stationary, geometric analogue of the Asymmetric Dynamical Casimir Effect (ADCE). In the rotating Teo geometry, rotation and frame dragging play the role that moving boundaries play in the dynamical Casimir effect, acting as the source of asymmetric vacuum mode mixing.

gr-qc↗

arXiv2026

Coupled-Channel Spectral Theory for a Non-Separable Rotating Geometry: Normal Modes and Two-Boundary Response in the Rotating AdS-Teo Wormhole

We investigate scalar perturbations of a rotating asymptotically anti-de Sitter (AdS)Teo traversable wormhole with a controlled nonseparable angular deformation. The geometry retains a regular wormhole throat and the required AdS asymptotics, while explicit quadrupolar deformation generates angular-channel coupling in the intermediate region. A sufficient condition is derived for an ergoregion free parameter regime in which the spectral analysis is performed. Projecting the geometry derived Klein Gordon equation onto spherical harmonics yields a matrix valued Sturm Liouville system and an associated quadratic operator pencil. Throat regularity together with normalizable AdS boundary conditions leads to a determinant quantization condition for the discrete normal mode spectrum. Two, four, and six channel calculations demonstrate systematic numerical convergence of the retained low lying normal mode frequencies under enlargement of the angular basis. The complete finite generalized eigenspectrum is also examined without imposing a near reality selection criterion, and no growing scalar mode is found within the ergoregion free parameter range and numerical resolutions studied. The six channel rotation continuation exhibits a finite interior level repulsion feature accompanied by collective redistribution of the multichannel eigenvectors. The same coupled spectral framework formally defines a matrix valued two boundary response whose poles are selected by the normal-mode matching condition, the response plots presented here illustrate this structure using the reduced two channel effective model rather than a numerical reconstruction of the full six channel response.

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arXiv2026

Gauge-Invariant Gravitational Wave Polarization in Metric f(R) Gravity with Cosmological Implications

We develop a fully gauge invariant analysis of gravitational wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model, whose constant curvature solution provides a natural deSitter background for both early and late time cosmology. Linearizing the field equations around this background, we derive the Klein Gordon equation for the curvature perturbation and show that the scalar propagating mode acquires a mass, highlighting how the same scalar degree of freedom governs inflationary dynamics at high curvature and the propagation of gravitational waves in the current accelerating Universe. Using the scalar vector tensor (SVT) decomposition and a decomposition of the perturbed Ricci tensor, we obtain a set of fully gauge invariant propagation equations that isolate the contributions of the scalar, vector, and tensor modes in the presence of matter. We find that the tensor sector retains the two transverse traceless polarizations of General Relativity, while the scalar sector supports a massive breathing-longitudinal mode determined by the massive scalar propagating mode. Through the geodesic deviation equation, computed both in a local Minkowski patch and in fully covariant de Sitter form, we independently recover the same polarization content and identify its tidal signatures. The resulting framework connects the extra scalar polarization to cosmological observables, providing a unified, gauge invariant link between gravitational wave phenomenology and the cosmological implications of metric f(R) gravity.

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arXiv2024

An Intrinsic Coordinate Reference Frame Procedure I: Tensorial Canonical Weyl Scalars

Canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space and time into a 3+1 formalism. Such a simplification may appear to come at the cost of general covariance. This requires tangential and perpendicular infinitesimal diffeomorphisms generated by the symmetry group under the Legendre transformation of the given action. This gauge generator, along with the fact that Weyl curvature scalars may act as ``intrinsic coordinates" (or a dynamical reference frame) which depend only on the spatial metric $g_{ab}$ and the conjugate momenta $p^{cd}$, allow for an alternative approach to canonical quantization of gravity. In this paper we present the tensorial solution of the set of Weyl scalars in terms of canonical phase-space variables.

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arXiv2020

Curvature Invariants for the Alcubierre and Nat\'ario Warp Drives

A process for using curvature invariants is applied to evaluate the metrics for the Alcubierre and the Natario warp drives at a constant velocity.Curvature invariants are independent of coordinate bases, so plotting these invariants will be free of coordinate mapping distortions. As a consequence, they provide a novel perspective into complex spacetimes such as warp drives. Warp drives are the theoretical solutions to Einstein's field equations that allow the possibility for faster-than-light (FTL) travel. While their mathematics is well established, the visualisation of such spacetimes is unexplored. This paper uses the methods of computing and plotting the warp drive curvature invariants to reveal these spacetimes. The warp drive parameters of velocity, skin depth and radius are varied individually and then plotted to see each parameter's unique effect on the surrounding curvature. For each warp drive, this research shows a safe harbor and how the shape function forms the warp bubble. The curvature plots for the constant velocity Natario warp drive do not contain a wake or a constant curvature indicating that these are unique features of the accelerating Natario warp drive.

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