Geometric and wave optics analysis of BTZ-like charged wormholes with disclinations

Abstract

We study the geometric and wave-optical properties of a charged BTZ wormhole (BTZCWH) spacetime carrying disclinations. The metric function \(f(r)=1-b_0/r-\mathcal {Q}^2 r^2/4\) has two positive zeros, an inner throat \(r_0\) and an outer zero \(r_*\) ; the static Lorentzian description holds only on the finite domain \(r_0\le r\le r_*\) , beyond which the signature changes and the radial direction becomes timelike. Inside this patch we analyse null geodesics (NGs) and show how the disclination parameter \(\alpha\) , the wormhole (WH) shape parameter \(b_0\) , and the Neveu–Schwarz (NS) charge \(\mathcal {Q}\) shape the photon paths. The orbit equation follows from the canonical angular momentum, and the bending of light is defined through a finite-domain integral between the closest approach and the outer boundary, with the topological deficit and the explicit NS-charge correction displayed separately. We then reduce the scalar Helmholtz equation (HE) to a Schrodinger-type radial problem and, to avoid the coordinate divergence at the boundaries, state it directly in the proper-distance coordinate. With self-adjoint boundary conditions the problem is a regular Sturm–Liouville system with a discrete spectrum, so standing waves exist. The associated quantity n ( r ) is a radial WKB index for a given mode, not a universal optical index; the geometric-optics limit is recovered as \(\omega \rightarrow \infty\) when \(\omega ^2\gg |R|\) . The results clarify the optical content of the BTZCWH geometry and connect it to analogue gravity.