Tritone substitution: G#7 can be replaced by D7 (a tritone away). Both chords share the same tritone between the 3rd and 7th, resolving to the same tonic.
The augmented 11th forms a tritone with the root and avoids the close clash that a perfect 11th creates with the 3rd. The combination of major 3rd, minor 7th, and #11 matches the Lydian dominant scale.
Application
Lydian harmony
Jazz and fusion
Film scoring
Voicing & structure
Root position
v1G#(G#4)Bass
root
v2B#(B#5)M3from G#
v3D#(D#5)m3from B#
v4F#(F#5)m3from D#
v5A#(A#5)M3from F#
v6D(D6)M3from A#
Harmony
Compatible scales
All chord tones are contained in these scales — use them for improvisation.