Carson was last seen alive at 1:30 a.m. Wednesday, when she stayed home to do schoolwork while her roommates went out, authorities said. Officers found the body of a young woman about a mile from campus after neighbors reported hearing shots around 5 a.m.
"My information is she was an extraordinarily busy woman and it wasn't unusual for her to go to the office in the middle of the night," police Chief Brian Curran said. "But we don't know that's what she was doing."
The medical examiner said there was no indication that Carson had been sexually assaulted.
Curran said detectives had no evidence other than her car, which was found Thursday about a mile from where her body was discovered. Officers found the blue 2005 Toyota Highlander after receiving a tip from a witness who spotted it near the main drag though the college town about 45 minutes west of Raleigh.
Curran said police don't know what she was doing in the upscale residential area where her body was found. He told The News & Observer of Raleigh that police believe the killer was in Carson's car at some point.
University Chancellor James Moeser said there was nothing to link Carson's slaying to anyone on campus.
"We have lost someone whom we cherish and love," Moeser told a massive crowd on the school's quad at a memorial service, one of two held Thursday. "We're all in a state of shock."
A huge crowd of students, staff and faculty gathered on campus in the afternoon to remember Carson. Students passed out daisies and carnations, and large boards were erected for students to leave written memories. Dozens of counselors were available to talk to students.
A huge crowd of students, staff and faculty gathered on campus in the afternoon to remember Carson. Students passed out daisies and carnations, and large boards were erected for students to leave written memories. Dozens of counselors were available to talk to students.
Students met again after nightfall for a candlelight vigil at The Pit, a popular campus gathering spot.
"If they saw a smile on Eve's face, they were smiling," said Carly Swain of Charlotte. "If she was having fun, they had fun for a second because that's the kind of power she had over people."
Moeser said Friday that Carson's death had shaken the entire community.
"This is a place where students really bond to the university and to themselves," he told NBC's "Today." "We can only get through this by embracing each other."
Carson was a prestigious Morehead-Cain scholar and a North Carolina Fellow, taking part in a four-year leadership development program for undergraduates. A premed student, she majored in political science and biology, taught science at a Chapel Hill elementary school, studied abroad in Cuba and spent summers volunteering in Ecuador, Egypt and Ghana as part of a school program.
Moeser said he last saw Carson on Tuesday, at the Tar Heels men's basketball game against Florida State.
"This is a tragedy magnified and multiplied by the number and depth of relationships, many relationships that Eve Carson had on this campus," Moeser told the students. "This enormous throng is a testament to the many and deep relationships.
"Eve Carson personified the Carolina spirit."
Carson is the daughter of Bob Carson and Teresa Bethke. A man answering the phone at Bob Carson's business, Carson Advisory Inc. in Athens, said the family had no comment.
Maxine Easom, principal of Clarke Central High School in Athens, where Carson graduated as valedictorian in 2004 and was also elected student body president, said she and staff members learned of her death Thursday morning.
"We're devastated," Easom said. "Eve was just the most wonderful young woman you would ever want to know. She was brilliant. She was absolutely beautiful. Everything she did was aimed at helping other people. It's one of the greatest tragedies I've ever known. Eve was one of the young women who could change the world."
