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We study the non-Gaussian features of the gravitational wave (GW) background generated by a population of inspiraling supermassive black hole (SMBH) binaries. We show that the SMBH GW amplitude distribution (GWAD) features a universal heavy power-law tail <inline-formula><mml:math><mml:mo>∝</mml:mo><mml:msup><mml:mi>A</mml:mi><mml:mrow><mml:mo>-</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:math></inline-formula>, while the low-amplitude tail depends on the SMBH merger rate and the energy-loss mechanisms of the binaries. The distribution of the induced timing residuals inherits this heavy tail. As a result, the ensemble averaged statistical moments of order three and higher diverge, limiting their usefulness as measures of non-Gaussianity, and the GW background from SMBH binaries exhibits the single loud source principle, according to which the strongest signals are more likely to be caused by a small number of loud sources. We confirm that the variance-averaged Gaussian approximation accurately describes the timing residual statistics. This approximation justifies a factored likelihood structure that combines standard Gaussian-process PTA posteriors with the non-Gaussian population prior, enabling consistent incorporation of non-Gaussian effects into SMBH model inference. We provide a fast and flexible Python implementation to compute the distribution of timing residuals from a given SMBH merger rate or GWAD.

Recent advances in the observation of black-hole candidates have renewed interest in probing their near-horizon structure and in searching for departures from the standard singular solutions of general relativity. In this context, significant effort has been devoted to regular black holes and to horizonless black-hole mimickers, motivated primarily by quantum-gravitational effects. Depending on the value of the regularization parameter relative to the object mass, typical spherically symmetric solutions can describe either of these two scenarios. Regular black-hole configurations generically feature an outer and an inner horizon surrounding a maximally symmetric core; the inner horizon in turn triggers mass inflation and semiclassical instabilities. The horizonless branch of the same solutions, by contrast, supports stable inner light rings when sufficiently compact, yet is itself subject to instabilities associated with long-lived quasinormal modes. Here, we investigate how to emulate these spacetimes in an analog-gravity platform based on surface-gravity waves in a shallow-water basin, with the aim of reproducing these instabilities experimentally. We begin by identifying the flow profiles and boundary conditions required to replicate the relevant effective geometries. In particular, we show that the inner-core metrics can be simulated with a nonrotating central-drainage configuration, and we propose a graded-drainage profile to connect them to an asymptotically flat exterior region. We then assess the experimental feasibility of studying the instabilities mentioned above with current technology. Our conclusion is that, while the required setup is realizable in principle, alternative media, such as Bose-Einstein condensates, may offer a more practical route to faithfully capturing the targeted physical features.