The following article contains an answer for the question: Whose cryptic approach characterized the lyrics that often dealt with themes of existentialism, love, hedonism, spirituality and Christianity? , can you please find it? 

Audioslave's musical style has generally been regarded as hard rock, alternative metal, post-grunge, and alternative rock. By combining '70s style hard rock riffing with alternative rock, Audioslave created a distinctive sound. This mix was driven by Cornell's wide vocal range, Morello's innovative guitar solos and the robust rhythm section of Wilk and Commerford. Morello, although stating he "never felt musically limited" in Rage Against the Machine, did say that he had "a lot more scope to explore with Audioslave" and a "wider musical territory." This meant that the instrumentalists had the opportunity to write slow and melodic songs, something they had not done before.
As opposed to de la Rocha's lyrics, Cornell's were mostly apolitical; Morello referred to them as "haunted, existential poetry." They were characterised by his cryptic approach, often dealing with themes of existentialism, love, hedonism, spirituality and Christianity. Audioslave's first two albums drew influences from 1970s hard rock and heavy metal such as Led Zeppelin and Black Sabbath and from the members' previous bands (the grunge sound of Soundgarden and the funk metal sound of Rage Against the Machine). For Revelations, which was influenced by 1960s and '70s funk, soul and R&B music, Morello used vintage guitars and amplifiers and Cornell adopted his "seventies funk and R&B-flavor vocals." The guitarist also cited Sly & the Family Stone, James Brown and Funkadelic as a reason for the funk overtones on the album.Just as Rage Against the Machine did, Audioslave also included the statement "All sounds made by guitar, bass, drums and vocals" in their albums' booklets as Morello's guitar work often caused listeners to believe that the band used samples, synthesiser effects or different turntable techniques to produce certain sounds.

Cornell