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We study the formation of intermediate-mass ratio inspirals (IMRIs) triggered by the interactions between two stellar black holes (BHs) and an intermediate-mass BH (IMBH) inhabiting the centre of a dense star cluster. We exploit $N$-body models varying the IMBH mass, the stellar BH mass spectrum, and the star cluster properties. These simulations are coupled with a semi-analytic procedure to characterise the evolution of the remnant IMBH. The IMRIs formation probability attains values $sim 5-50%$, with larger values corresponding to larger IMBH masses. IMRIs map out the stellar BH mass spectrum, thus they might be used to unravel BH populations in star clusters harboring an IMBH. After the IMRI phase, an IMBH initially nearly maximal(almost non-rotating) tends to decrease(increase) its spin. If IMBHs grow mostly via repeated IMRIs, we show that only IMBH seeds sufficiently massive ($M_{rm seed} > 300$ M$_odot$) can grow up to $M_{rm imbh} >10^3$ M$_odot$ in dense globular clusters. Assuming that these seeds form at a redshift $zsim 2-6$, we find that around $1-5%$ of them would reach masses $sim 500-1500$ M$_odot$ at redshift $z=0$ and would exhibit low-spins, $S_{rm imbh} < 0.2$. Measuring the mass and spin of IMBHs involved in IMRIs could help unravelling their formation mechanisms. We show that LISA can detect IMBHs in Milky Way globular clusters with a signal-to-noise ratio SNR$=10-100$, or in the Large Magellanic Cloud with an SNR$=8-40$. We provide the IMRIs merger rate for LIGO ($Gamma_{rm LIG} = 0.003-1.6$ yr$^{-1}$), LISA ($Gamma_{rm LIS} = 0.02-60$ yr$^{-1}$), ET ($Gamma_{rm ET} = 1-600$ yr$^{-1}$), and DECIGO ($Gamma_{rm DEC} = 6-3000$ yr$^{-1}$). Our simulations show that IMRIs mass and spin encode crucial insights on the mechanisms that regulate IMBH formation and that the synergy among different detectors would enable us to fully unveil them. (Abridged)
Intermediate mass black holes (IMBHs) with a mass between $10^{2}$ and $10^{5}$ times that of the sun, which bridges the {mass gap between the} stellar-mass black holes and the supermassive black holes, are crucial in understanding the evolution of t
Massive young clusters (YCs) are expected to host intermediate-mass black holes (IMBHs) born via runaway collapse. These IMBHs are likely in binaries and can undergo mergers with other compact objects, such as stellar mass black holes (BHs) and neutr
We propose a new formation channel for intermediate mass black hole (IMBH) binaries via globular cluster collisions in the Galactic disc. Using numerical simulations, we show that the IMBHs form a tight binary that enters the gravitational waves (GWs
The second generation of gravitational-wave detectors are being built and tuned all over the world. The detection of signals from binary black holes is beginning to fulfill the promise of gravitational-wave astronomy. In this work, we examine several
Intermediate-mass black holes (IMBHs) could form via runaway merging of massive stars in a young massive star cluster (YMC). We combine a suite of numerical simulations of YMC formation with a semi-analytic model for dynamical friction and merging of