Intermediate-Mass Black Holes in Star Clusters and Dwarf Galaxies

Black holes (BHs) with masses between 100 to 100,000 times the mass of the Sun ($\rm{M}_{\odot}$) are classified as intermediate-mass black holes (IMBHs), potentially representing a crucial link between stellar-mass and supermassive BHs. Stellar-mass BHs are endpoints of the evolution of stars initially more massive than roughly 20 $\rm{M}_{\odot}$ and generally weigh about 10 to 100 $\rm{M}_{\odot}$. Supermassive BHs are found in the centre of many galaxies and weigh between $10^{6}$ to $10^{10} \ \rm{M}_{\odot}$. The origin of supermassive BHs remains an unresolved problem in astrophysics, with many viable pathways suggesting that they undergo an intermediate-mass phase. Whether IMBHs really stand as an independent category of BHs or rather they represent the heaviest stellar mass and the lightest supermassive BHs is still unclear, mostly owing to the lack of an observational smoking gun. The first part of this chapter discusses proposed formation channels of IMBHs and focuses on their formation and growth in dense stellar environments like globular and nuclear star clusters. It also highlights how the growth of IMBHs through mergers with other BHs is important from the point of view of gravitational waves and seeding of supermassive BHs in our Universe. The second part of the chapter focuses on the multi-wavelength observational constraints on IMBHs in dense star clusters and dwarf galactic nuclei. It also examines the potential insights that future gravitational wave detectors could offer in unraveling the mystery surrounding IMBHs.