Is the word autor the same in Brazilian and European Portuguese?

Yes

The word "autor" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only difference lies in pronunciation. In Brazil, the pronunciation of the final "r" varies significantly by region (ranging from a retroflex "r" in the countryside to an aspirated "h" sound in Rio de Janeiro), and vowels are generally more open. In Portugal, the "r" is typically a distinct alveolar tap, and vowels are generally more closed or reduced in unstressed positions.

Brazilian Portuguese Examples:

1. Esse autor é muito famoso no Brasil. (That author is very famous in Brazil.)
2. Eu adoro o estilo desse autor. (I love that author's style.)
3. Quem é o autor dessa música? (Who is the author of that song?)
4. Esse autor escreve livros de suspense. (That author writes suspense novels.)
5. Você já leu algo desse autor? (Have you ever read anything by that author?)

Portuguese (Continental) Examples:

1. Este autor é muito famoso em Portugal. (This author is very famous in Portugal.)
2. Eu adoro o estilo deste autor. (I love this author's style.)
3. Quem é o autor desta música? (Who is the author of this song?)
4. Este autor escreve livros de suspense. (This author writes suspense novels.)
5. Tu já leste algo deste autor? (Have you [informal] read anything by this author?)