Geodesic completeness and photon propagation in a superconducting T-duality black hole
Abstract
The purpose of this article is twofold. First, we study the geodesic completeness of the string T-duality black hole with the Raychaudhuri equation, for radial massive particles of arbitrary specific energy ε. Exact proper-time quadratures reveal three classes of observers: supercritical observers reach the regular centre in finite proper time through a caustic and pass through it, critical observers (ε=1) approach it only asymptotically with finite expansion, and subcritical observers are reflected at a fold caustic. Because the lapse is analytic and even in r, geodesics continue regularly through the centre, and all three classes are complete on the stipulated maximal extension. A diverging expansion therefore signals a caustic of the congruence rather than an endpoint of the geodesics, in contrast with Schwarzschild spacetime. Second, radial Maxwell rays are likewise complete but form a single class, since a massless ray carries no energy scale. We propose to model the black-hole core itself as a superconductor, with London response μ2=4πκρ attributed to the existing source. A symmetry-breaking potential with a vacuum-energy offset reproduces the de Sitter core and its photon mass exactly at the centre and approximately in the inner core; since no static scalar theory reproduces the anisotropic source further out, the full radial response remains phenomenological. The resulting Hamiltonian rays follow timelike geodesics of μ2gμν up to reparametrisation and reproduce the three classes, separated by the central mass μ0, while the density gradient of the core adds a defocusing contribution near the centre. We also distinguish Hamiltonian completeness from completeness of the conformal metric.
Related
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BibTeX
@misc{jusufi2026geodesic,
title = {{Geodesic completeness and photon propagation in a superconducting T-duality black hole}},
author = {Kimet Jusufi},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05630},
eprint = {2611.05630},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05630},
}
RIS
TY - UNPB
TI - Geodesic completeness and photon propagation in a superconducting T-duality black hole
AU - Kimet Jusufi
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05630
UR - https://arxiv.org/abs/2611.05630
AB - The purpose of this article is twofold. First, we study the geodesic completeness of the string T-duality black hole with the Raychaudhuri equation, for radial massive particles of arbitrary specific energy ε. Exact proper-time quadratures reveal three classes of observers: supercritical observers reach the regular centre in finite proper time through a caustic and pass through it, critical observers (ε=1) approach it only asymptotically with finite expansion, and subcritical observers are reflected at a fold caustic. Because the lapse is analytic and even in r, geodesics continue regularly through the centre, and all three classes are complete on the stipulated maximal extension. A diverging expansion therefore signals a caustic of the congruence rather than an endpoint of the geodesics, in contrast with Schwarzschild spacetime. Second, radial Maxwell rays are likewise complete but form a single class, since a massless ray carries no energy scale. We propose to model the black-hole core itself as a superconductor, with London response μ^2=4πκρ attributed to the existing source. A symmetry-breaking potential with a vacuum-energy offset reproduces the de Sitter core and its photon mass exactly at the centre and approximately in the inner core; since no static scalar theory reproduces the anisotropic source further out, the full radial response remains phenomenological. The resulting Hamiltonian rays follow timelike geodesics of μ^2g_μν up to reparametrisation and reproduce the three classes, separated by the central mass μ_0, while the density gradient of the core adds a defocusing contribution near the centre. We also distinguish Hamiltonian completeness from completeness of the conformal metric.
ER -