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We construct the off-shell recursion for gravity and the graviton current forthe perturbative double field theory (DFT). We first formulate the perturbativeDFT, which is equivalent but simpler to perturbative general relativity, toall-orders in fluctuations of generalised metric. The perturbative action andequations of motion (EoM) are derived to arbitrary order for pure gravity case.We then derive the graviton off-shell recursion, the gravity counterpart of theBerends-Giele recursion in Yang-Mills theory, through the so-called perturbinermethod using the EoM of the perturbative DFT. We solve the recursioniteratively and obtain the graviton off-shell currents explicitly. We thendiscuss the classical double copy for the off-shell currents. We present thecurrent KLT relation for gravity by extending the result proposed by Mizera andSkrzypek for the non-gravitational effective field theories. The relationrepresents graviton currents by squaring gluon currents with the KLT kernel upto gauge transformation and regular terms that do not have any pole. Finally wediscuss the off-shell conservation of currents for nonlinear gauge choices.

The Off-Shell Recursion for Gravity and the Classical Double Copy for currents