Black hole correspondences of quasi-topological gravity : Shadows, quasinormal modes, graybody factors

Within the framework of quasi-topological gravity, we systematically investigate the correspondences among three classes of observables—the shadow, the quasinormal modes, and the graybody factors—of regular black holes in $D=5$ dimensions. Using the WKB approximation and GrayHawk numerical integration, we test the applicability of the GBF–QNM correspondence and the shadow–GBF correspondence in the low-mode ($l=2$) and higher-dimensions ($D=5$): the difference between the GBF–QNM correspondence and the numerical results remains small in magnitude; we apply the known Langer correction (replacing $l$ by the effective angular momentum $\kappa =\sqrt{l(l+D-3)}\simeq l+(D-3)\mathrm{/}2$), which reduces the error of the shadow–GBF correspondence at low modes to a level comparable with that of the GBF–QNM correspondence. Our work extends the shadow–GBF correspondence to higher-dimensional regular black holes, providing a viable route to predict the black hole spectrum and the Hawking radiation profile from a single observable, and thereby to realize multi-messenger tests of gravity.