Advocate depute John Scullion branded Carter a "cold-blooded man" who followed 42-year-old pharmaceutical manager Khanikporn Satjawat into the ladies toilet of the Clyde Auditorium and brutally killed her.
He told the jury that Carter showed no remorse for his actions and did "everything in his power" to avoid being caught.
Mr Scullion said that after the alleged murder, Carter's actions were "not those of a man trying to come to terms with committing a terrible act".
He said: "He showed no regret or remorse for what he had done and he made no attempt to assist Khanikporn Satjawat or get medical help in a building full of doctors."
He added: "Such was the lack of interest or concern for Khanikporn Satjawat's fate that minutes after beating her to death he was sitting in the rest area eating his sandwiches."
Carter, 35, from Motherwell, North Lanarkshire, is on trial at the High Court in Glasgow accused of murdering Miss Satjawat last November 12 when she was attending an HIV conference.
He admits culpable homicide on the grounds of diminished responsibility but the Crown rejects this.
Defence counsel Ian Duguid told the jury in his closing speech that the issue they have to decide is whether Carter was suffering from diminished responsibility when he killed Miss Satjawat.
Mr Duguid said that Carter suffers from a personality disorder - an emotionally unstable personality disorder of the impulse type - and claimed it was this that caused him to act the way he did.
The trial before judge Lord Matthews continues.