can they be found in captivity as well?
Rarely: a few are "Nandi" (uShaka Marine World); "Zeus" (The Atlantis resort); and those in the Okinawa Churaumi Aquarium.
Manta ray
One notable individual is "Nandi", a manta ray which was accidentally caught in shark nets off Durban, South Africa, in 2007. Rehabilitated and outgrowing her aquarium at uShaka Marine World, Nandi was moved to the larger Georgia Aquarium in August 2008, where she resides in its 23,848 m (6,300,000 US gal) "Ocean Voyager" exhibit. A second manta ray joined that aquarium's collection in September 2009 and a third was added in 2010.

The Atlantis resort on Paradise Island, Bahamas, hosted a manta named "Zeus" that was used as a research subject for 3 years until it was released in 2008. The Okinawa Churaumi Aquarium also houses manta rays in the "Kuroshio Sea" tank, one of the largest aquarium tanks in the world. The first manta ray birth in captivity took place there in 2007. 
do manta rays have barbs on their tails UNANSWERABLE what is this animal? These are large rays belonging to the genus "Mobula". where can it be found? They are found in warm temperate, subtropical and tropical waters. which species is it? "Manta birostris"
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Manta ray [SEP] Aquariums
Due to their size, mantas are rarely kept in captivity and few aquaria currently display them. One notable individual is "Nandi", a manta ray which was accidentally caught in shark nets off Durban, South Africa, in 2007. Rehabilitated and outgrowing her aquarium at uShaka Marine World, Nandi was moved to the larger Georgia Aquarium in August 2008, where she resides in its 23,848 m (6,300,000 US gal) "Ocean Voyager" exhibit. A second manta ray joined that aquarium's collection in September 2009 and a third was added in 2010. The Atlantis resort on Paradise Island, Bahamas, hosted a manta named "Zeus" that was used as a research subject for 3 years until it was released in 2008.