The paper explores the entropic uncertainty relations in Schwarzschild space-time, a fundamental aspect of quantum mechanics. The authors propose a generalized entropic uncertainty relation for multiple observables in multipartite systems and derive a tighter lower bound by considering Holevo quality and mutual information. They discuss the implications of these relations in the context of Schwarzschild space-time, noting that Hawking radiation damages the coherence of the physically accessible region and increases uncertainty. The properties of uncertainty in Schwarzschild space-time are attributed to the system's purity and the redistribution of information between different regions. The findings provide insights into the generalized entropic uncertainty relations in multipartite systems, which may help understand the quantumness and information paradox of black holes. The study uses three-qubit states, including a W-like state and a Werner state, to verify the derived uncertainty relations and analyze the dynamics of uncertainty, coherence, and purity in the presence of Hawking radiation.The paper explores the entropic uncertainty relations in Schwarzschild space-time, a fundamental aspect of quantum mechanics. The authors propose a generalized entropic uncertainty relation for multiple observables in multipartite systems and derive a tighter lower bound by considering Holevo quality and mutual information. They discuss the implications of these relations in the context of Schwarzschild space-time, noting that Hawking radiation damages the coherence of the physically accessible region and increases uncertainty. The properties of uncertainty in Schwarzschild space-time are attributed to the system's purity and the redistribution of information between different regions. The findings provide insights into the generalized entropic uncertainty relations in multipartite systems, which may help understand the quantumness and information paradox of black holes. The study uses three-qubit states, including a W-like state and a Werner state, to verify the derived uncertainty relations and analyze the dynamics of uncertainty, coherence, and purity in the presence of Hawking radiation.