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Notice that the volume of the hyperbolic solid torus is not finite. Therefore this hyperbolic 3-manifold knot complement does not count as a “knot complement with hyperbolic structure” in the sense of Thurston’s classification of 3-manifolds_ (see also this MO discussion).
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Ingmar Akira Saberi, around Figure 4.3 of: Knots, Trees, and Fields: Common Ground Between Physics and Mathematics (doi:10.7907/Z9VX0DHZ, pdf)
(with generalization to p-adic string theory)
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Stefan Aminneborg, Ingemar Bengtsson, Dieter Brill, Soren Holst, Peter Peldan, Black Holes and Wormholes in 2+1 Dimensions, Class. Quant. Grav. 15 (1998) 627-644 (arXiv:gr-qc/9707036)
Dieter Brill, Black Holes and Wormholes in 2+1 Dimensions, In: Cotsakis S., Gibbons G.W. (eds) Mathematical and Quantum Aspects of Relativity and Cosmology. Lecture Notes in Physics, vol 537. Springer, Berlin, Heidelberg (arXiv:gr-qc/9904083, doi:10.1007/3-540-46671-1_6 )
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more on BTZ black holes in -adic AdS/CFT:
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