  We study the structure of scattering amplitudes of massive Kaluza-Klein (KK)
states in the compactified 5-dimensional warped gauge and gravity theories. We
present systematic formulations of the gauge theory equivalence theorem (GAET)
and the gravitational equivalence theorem (GRET) for warped KK theories in
$R_\xi^{}$ gauge, where the GAET connects the scattering amplitudes of
longitudinal KK gauge bosons to that of the corresponding KK Goldstone bosons
and the GRET connects the scattering amplitudes of KK gravitons of
helicity-zero (helicity-one) to that of the corresponding gravitational KK
Goldstone bosons. We analyze the structure of 3-point and 4-point scattering
amplitudes of massive KK gauge bosons and of massive KK gravitons as well as
their corresponding Goldstone bosons. We first prove the GAET and GRET
explicitly for the fundamental 3-point KK gauge/gravity scattering amplitudes.
We then demonstrate that the validity of the GAET and GRET for 4-point
gauge/gravity scattering amplitudes can be reduced to the validity of GAET and
GRET for 3-point gauge/gravity scattering amplitudes at tree level. With these,
we study the double-copy construction of KK scattering amplitudes in the warped
gauge/gravity theories. We newly realize the double-copy for massive 3-point
full gauge/gravity amplitudes at tree level under proper correspondences of
color-kinematics and of gauge/gravity couplings, whereas we can construct the
double-copy for 4-point KK gauge/gravity amplitudes to the leading order (LO)
of high energy expansion. We further demonstrate that this LO double-copy
construction can be extended to $N$-point KK scattering amplitudes with
$N\geqslant 4$.
