TsT, black holes, and $$ T\overline{T} $$ + $$ J\overline{T} $$ + $$ T\overline{J} $$

A bstract We generate a class of string backgrounds by sequence TsT transformations the NS1-NS5 system that we argue are holographically dual to states in single-trace $$ T\overline{T} T ¯ + J\overline{T} J T\overline{J} -deformed CFT 2 . The new include general rotating black hole solutions with two U(1) charges as well smooth solution without horizon is interpreted ground state. As evidence for correspondence ( i ) derive long spectrum and relate it field theory; ii show thermodynamics can be reproduced from CFTs; iii energy state matches vacuum theory. also study geometric properties these spacetimes find some choices parameters three-dimensional Ricci scalar Einstein frame become positive region outside before reaching closed timelike curves singularities.