The track is a collaboration with a pair of American cellists known as 2Cellos, and the video for the track sees Rivera performing the track in a set made to look like a spaceship along with the duo. The track maintains some of the rock elements of the Muse original in its production - but ups the cello considerably. It is taken from the 2Cellos album Intuition, which is due for release on 15 January.
Rivera has been a regular on Glee since its first series, playing the role of bitchy cheerleader Santana. She was reported to have signed a solo record deal in the summer of 2011 with Columbia Records in the US.
Glee has now enjoyed three TV series and is set to return next year with a fourth, in which Rivera will also star.
See the singer in her 'Supermassive Black Hole' cover below.
The original version of 'Supermassive Black Hole' appears on Muse's fourth studio album, Black Holes And Revelations and was written by Matt Bellamy. It reached No.4 in 2006 after it was released as the album's lead single.
At the time of the track's release, Bellamy told NME: "I was going out dancing in clubs around New York. That helped create tracks like 'Supermassive Black Hole'.
"Franz Ferdinand would have done it very well, with that dance type beat going on mixed with alternative guitar and I've always wanted to find that."
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