Acceptance in PhD Program With Unfortunate Background
The pictures and the posts are rather different issues. Whether there are nude pictures of an applicant available on the internet is no business of an admissions committee, regardless of how they got there. This aspect is covered well in another question:
Can leaked nude pictures damage one&#39;s academic career?
For the racist comments however, the fact that you did not write them is essential. If you had written them, it would be very legitimate to hold it against you. If these show up on the first page of Google results for your name, you may want to include a statement with your applications that horrific comments with your name attached to them exist on the internet, and that you neither wrote them nor agreed with them.