Now that they have captured the man charged with abducting a missing University of Virginia student, police face two other major challenges: making the charge stick and, most important, finding Hannah Graham.

Jesse Leroy Matthew Jr. agreed Thursday not to fight his extradition from Texas, where he was arrested the previous day on a charge of abduction with intent to defile the 18-year-old Graham. Before turning up on a beach near Galveston, the 32-year-old Matthew was last seen speeding away from police, who had him under surveillance in Charlottesville on Saturday.

Charlottesville Police Chief Timothy Longo said at a news conference Thursday that investigators still have no information on the whereabouts of Graham, who vanished early Sept. 13. And he acknowledged that the longer Graham remains missing, the dimmer the hope she will be found alive.

"I can't lose hope until I have to, until I need to," Longo said. "I have hope, I think Hannah's mom and dad have hope. We all know, though, how as each day goes by that hope will diminish."

The search for the sophomore from northern Virginia has expanded to rural areas outside the college town of 40,000, Longo said. The Department of Emergency Management, which is coordinating searches by up to six two-person teams every day, estimates the crews have spent 44 hours in the field since a massive search involving more than 1,000 volunteers last weekend.

Longo appealed to land owners to search their properties, and to real estate agents to check vacant houses.

"We still have no idea whatsoever where she is, despite our best efforts," Longo said. "We have an obligation to bring her home, one way or the other. That's what we promised to do."

Meanwhile, the hunt for Matthew ended Wednesday in the Texas beach town of Gilchrist, 1,260 miles from Charlottesville and about a seven-hour drive from the border, when a deputy sheriff responding to a suspicious-person report found him camping on the beach and identified him by running a license plate check.

Authorities had been concerned he would try to cross into Mexico, according to a person familiar with the search who spoke with The Associated Press on condition of anonymity because the person isn't authorized to publicly discuss the investigation.

Police said they had probable cause to support the charge against Matthew after twice searching his apartment and gathering evidence they have not described. Police said a crime lab is testing clothing they recovered through search warrants, but they haven't said whose clothing that was.

"Defile," in a legal context, means "sexually molest."

"It's a crime that's much easier to charge than it is to prove," said Steve Benjamin, past president of the National Association of Criminal Defense Lawyers. "The fact that someone is the last person to have been in Hannah's company proves that the defendant had the opportunity to abduct, but it proves not much more."

He said the "great unknown" is what evidence police found in searches of Matthew's vehicle and apartment and added that Matthew did not help his case by running.

"Certainly flight from a jurisdiction where you know police want to talk to you is a circumstance in which you can infer a consciousness of guilt," Benjamin said. "That's a standard jury instruction."

Benjamin said the next step after Matthew gets back to Charlottesville will be an initial appearance in General District Court next week to ensure he has a lawyer and to schedule a preliminary hearing.

Police have refused to disclose their evidence but have released several surveillance videos capturing some of Graham's movements the night she vanished. Authorities say she met friends at a restaurant for dinner Sept. 12 before stopping by two off-campus parties. She left the second party alone and eventually texted a friend saying she was lost, authorities said.

Recorded images show her walking unsteadily and even running at times, past a pub and a service station and then onto the Downtown Mall — a seven-block pedestrian strip including the Tempo Restaurant. That's where she apparently met Matthew, and Longo said Thursday that police have no reason to believe they knew each other beforehand.

Tempo Restaurant owner Brice Cunningham told the AP on Thursday that his staff told police Graham could barely walk without support when she left with Matthew. He said Matthew briefly entered the bar where credit card records show he ordered what appeared to be two beers before rejoining the teenager outside. An employee then watched them walk off with Matthew's arm around her, Cunningham said.

"She was not seen and she was not served" inside the restaurant, he said.

Longo, who had said Graham went into the bar with Matthew, declined to challenge Cunningham's version but added: "I will tell you we have at least one witness who will put her in that restaurant."

Matthew attended Liberty University from 2000 to 2002, said officials with the Lynchburg school founded by the late Rev. Jerry Falwell. The school's athletics website listed him as a defensive lineman on the football team.

More recently, he volunteered to help coach football at The Covenant School, a private Christian grade school in Charlottesville, where officials said he had passed background and reference checks.

Matthew has had some past brushes with the law, but their details aren't public. Online court records show Matthew was convicted of trespassing in 2010, and charged but not prosecuted with assault and attempted grand larceny in a 2009 case. He had a state taxi permit from 2007 to 2010, and picked up several traffic infractions, records show.