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We take into account higher derivative R4 corrections in M-theory andconstruct quantum black hole and black string solutions in 11 dimensions up tothe next leading order. The quantum black string is stretching along the 11thdirection and the Gregory-Laflamme instability is examined at the quantumlevel. Thermodynamics of the boosted quantum black hole and black string arealso discussed. Especially we take the near horizon limit of the quantum blackstring and investigate its instability quantitatively.

Boosted Quantum Black Hole and Black String in M-theory, and Quantum Correction to Gregory-Laflamme Instability