The longissimus muscle is a spinal extensor which attaches to the back of the sacrum and it will pick up the slack if your transversus abdominis (TVA) and multifidus are not pulling their weight! If overactive, longissimus can increase tension in the thoracolumbar fascia (TLF) and nutate the sacrum, potentially contributing to low back pain.
Similarly iliocostalis – another spinal extensor – can pull the pelvis into anterior rotation (and the sacrum into counternutation) and contribute to sacroiliac joint (SIJ) instability.
Both muscles are important to consider in the context of low back and/or SIJ pain.