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We construct Type IIB string theory setups which, via double holography,realize two gravitational systems in separate AdS spaces which interact witheach other and with a non-gravitational bath. We employ top-down string theorysolutions with concrete field theory duals in the form of 4d $\mathcal N=4$ SYMBCFTs and a first-principles notion of double holography. The setups are usedto realize pairs of `near' and `far' black holes from the perspective of thebath, which exchange Hawking radiation with each other and radiate into thebath. We identify three phases for the entropy in the bath characterized as noisland, partial island and full island, and discuss the entropy curves. Thesetups differ from the black hole binaries observed in gravitational waveexperiments but may capture certain aspects.

Binary AdS black holes coupled to a bath in Type IIB