This is a distinctive bracing system used inside certain Gretsch hollowbody guitars. It is intended to increase sustain and decrease feedback. Gretsch developed trestle bracing and first used it in the late 1950s.
Most hollowbody instruments use an internal support method called “sound-post bracing,” in which a vertical wooden dowel located directly under the bridge connects the top of the guitar to the back. The sound post itself doesn’t add much mass, so it has little impact on sustain. Since the sound post takes up very little space inside the guitar, the feedback characteristics of the body remain largely unchanged.
Trestle bracing consists of two bridge-like spruce braces with a wide “U” shape. These run parallel to each other down the center of the instrument interior from the neck joint to the center of the body, ending directly under the bridge. They’re between the f-holes, just beneath the sides of the pickups and bridge. Since each rigid trestle brace has two “feet,” there are four points of attachment that are glued to the back of the guitar. The intention is to enable a solid-body-like response to sustain and feedback while preserving the tonal effect of a hollow body.