William Julius

Rotating traversable wormholes provide a horizonless setting in which to investigate wave dynamics beyond the separable structures familiar from black-hole perturbation theory. We study scalar perturbations in the rotating AdS-Teo wormhole and show that the absence of separability naturally leads to a coupled-channel formulation in which the angular harmonic modes interact through a matrix-valued Sturm-Liouville operator. Imposing regularity at the wormhole throat together with asymptotically anti-de Sitter boundary conditions yields a determinant quantization condition that determines a discrete normal-mode spectrum. A controlled two-channel truncation illustrates how angular-channel mixing produces frequency shifts, spectral repulsion, and collective mode reorganization. From the asymptotic solutions, we construct a matrix-valued boundary response function whose poles coincide with the bulk normal-mode frequencies, while its off-diagonal components provide a direct signature of rotation-induced channel mixing. We further investigate the renormalized vacuum polarization, whose interference terms reveal local quantum signatures of non-separability, and examine semiclassical geodesic correlators as complementary probes of two-boundary connectivity. These results suggest that coupled-channel spectral theory provides a natural organizing principle for rotating, non-separable geometries, replacing conventional mode separability with a framework based on collective normal modes, matrix-valued response functions, and coupled quantum observables.

Wedevelop a fully gauge-invariant analysis of gravitational-wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model f(R) = R +αR² −2Λ, whose constant curvature solution R_d = 4Λ provides a natural de Sitter 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 δR and show that the scalar propagating mode acquires a mass m_ψ² = 1/(6α), highlighting how the same scalar degree of freedom governs inflationary dynamics at high curvature and the ropagation of gravitational waves in the current accelerating Universe. Using the scalar–vector–tensor 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.

The canonical quantization of gravity in general relativity is greatly simplified by the artificial decomposition of space-time into a 3+1 formalism. Such a simplification appears to come at the cost of general covariance. This quantization procedure 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 gab and the conjugate momenta pcd, 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.

Two perfectly conducting, infinite parallel plates will restrict the electromagnetic vacuum, producing an attractive force. This phenomenon is known as the Casimir effect. Here we use electromagnetic field correlators to define the local interaction between the plates and the vacuum, which gives rise to a renormalized stress-energy tensor. We then show that a Lorentz boost of the underlying electric and magnetic fields that comprise the correlators will produce the correct stress-energy tensor in the boosted frame. The infinite surface divergences of the field correlators will transform appropriately, such that they cancel out in the boosted frame and produce the desired finite result.