As large language models (LLMs) are increasingly deployed as black-box components in real-world applications, red teaming has become essential for identifying potential risks. It tests LLMs with adversarial prompts to uncover vulnerabilities and improve safety alignment. Ideally, effective red teaming should be adaptive to evolving LLM capabilities and explore a broad range of harmful topics. However, existing approaches face two limitations: 1) topic-based approaches rely on pre-collected harmful topics, limited in flexibility and adaptivity. 2) topic-free methods use reinforcement learning (RL), but they lack an explicit reward signal for exploration and tend to over-optimize a narrow objective, reducing topic diversity. To address these limitations, we propose RedTopic, a novel red teaming framework that generates topic-diverse adversarial prompts through a contextualized generation pipeline, an aggregate reward design, and a multi-objective RL training loop. Experiments show that RedTopic produces more effective and diverse adversarial prompts than existing methods, with notable improvements in integrated evaluation metrics. We believe RedTopic represents a step toward more adaptive and topic-diverse red teaming for large language models.