Binary-Disk Interaction and Its Effect on Multi-Messenger Signatures in Massive Black Holes

In the past five years, there has been renewed interest in the classic problem of binary-disk interaction, where two point masses interact with a surrounding accretion disk. This process influences the binary's growth rate, angular momentum exchange, and orbital evolution. Despite advancements in computational modeling, key aspects of this long-standing problem remain unresolved. Recent findings challenge the traditional view that binaries contract; instead, they may expand due to binary-gas coupling. This unexpected behavior has significant implications for the evolution of massive black hole binaries and their gravitational wave signatures. In this talk, I will address the 'outward migration' conundrum and reassess other established theories. I will also explore why this phenomenon went unnoticed for 30 years and consider potential physical processes that could still drive inward migration.