This paper presents a thin acoustic metamaterial with acoustic black hole (ABH) profiles for broadband sound absorption. The metamaterial, called the multi-pancake absorber, consists of periodically arranged thin annular cavities separated by plates and connected by a main pore. The main pore's radius is varied to achieve broadband absorption. An analytical model based on the transfer matrix approach and lumped elements is proposed to predict the acoustic properties. The model is validated through thermo-visco-acoustic finite element simulations and impedance tube measurements. The study investigates various main pore profiles, including linear and non-linear decreasing radii, to balance losses and achieve broadband absorption. The complex frequency plane representation is used to analyze the balance of losses and improve absorption. The results show that varying the main pore radius can significantly enhance the absorption coefficient across a broad frequency range. The study also highlights the importance of balancing losses in the metamaterial to achieve perfect absorption. The findings demonstrate that ABH profiles can be used to create thin, broadband sound absorbers with high absorption coefficients. The results suggest that non-linear ABH profiles can accentuate losses and achieve absorption peaks of similar amplitude. The study provides insights into the design of ABH profiles for broadband sound absorption and the role of geometric parameters in achieving optimal acoustic performance. The results validate the effectiveness of the proposed ABH metamaterial for broadband sound absorption.This paper presents a thin acoustic metamaterial with acoustic black hole (ABH) profiles for broadband sound absorption. The metamaterial, called the multi-pancake absorber, consists of periodically arranged thin annular cavities separated by plates and connected by a main pore. The main pore's radius is varied to achieve broadband absorption. An analytical model based on the transfer matrix approach and lumped elements is proposed to predict the acoustic properties. The model is validated through thermo-visco-acoustic finite element simulations and impedance tube measurements. The study investigates various main pore profiles, including linear and non-linear decreasing radii, to balance losses and achieve broadband absorption. The complex frequency plane representation is used to analyze the balance of losses and improve absorption. The results show that varying the main pore radius can significantly enhance the absorption coefficient across a broad frequency range. The study also highlights the importance of balancing losses in the metamaterial to achieve perfect absorption. The findings demonstrate that ABH profiles can be used to create thin, broadband sound absorbers with high absorption coefficients. The results suggest that non-linear ABH profiles can accentuate losses and achieve absorption peaks of similar amplitude. The study provides insights into the design of ABH profiles for broadband sound absorption and the role of geometric parameters in achieving optimal acoustic performance. The results validate the effectiveness of the proposed ABH metamaterial for broadband sound absorption.