By AJ Willingham

CNN

(CNN) -- It has been a month since 15-year-old Elizabeth Thomas disappeared with her former teacher, 50-year-old Tad Cummins. What started as an Amber Alert in the small town of Culleoka, Tennessee, has evolved into a nationwide manhunt, and neither Thomas nor Cummins have been found.

Here's what we know about the disappearance, and the big questions that still need answering:

Have either been seen since the kidnapping?

Thomas and Cummins left Culleoka on March 13. Since then, there has been only one confirmed sighting of the pair. On March 15, surveillance footage captured them together at a Walmart in Oklahoma City. It looked as if both had changed their appearance: Cummins may have dyed his gray beard and hair darker, and Thomas may have dyed her hair red.

Where might they be now?

Authorities suspect the pair traveled to Decatur, Alabama, on their first day of flight, but other than that and the Oklahoma sighting, police have had no credible leads.

Maury County District Attorney Brent Cooper told CNN that Cummins takes blood pressure medication and might need a refill soon, which would obviously tip off police to their location.

For now, authorities say the pair could be "anywhere," but advised people to be particularly observant around rural and remote areas like campgrounds and parks.

Tennessee Bureau of Investigation (TBI) spokesman Josh DeVine told CNN authorities were also looking into any connections Cummins might have had outside the continental United States.

What is their relationship?

Cummins was Thomas' forensics teacher when she was a freshman at Culleoka Unit School in 2016.

Over time, signs point to some sort of romantic relationship developing.

A student reported seeing Thomas and Cummins kissing in a classroom in 2016, a claim both of them denied. However, the teen and the teacher both stated that Cummins gave Thomas emotional support and that they were close.

After the pair went missing, authorities discovered Cummins had conducted research on teen marriage, and the two exchanged romantic messages using the draft folder of Cummins' email.

Cummins' wife, Jill Cummins, initially pleaded for her husband to return home with the girl, saying "This is not who you are." However, a few weeks after their disappearance, Jill Cummins filed documents for divorce, saying her husband is "guilty of inappropriate marital conduct."

Did Thomas go with him willingly?

Even though the pair were engaged in some sort of relationship, the TBI says there's no way Thomas is not a victim.

"She may very well not know that she's a victim in all of this," DeVine said during a news conference. "So our message to her tonight, you are a victim. You're 15 years old. He's 50. We are going to do everything we can to bring you home."

Thomas' family provided more evidence that their daughter had been groomed by her teacher.

"He convinced her that he had been a secret agent and ... that he had all kinds of money," Anthony Thomas told HLN. "It was clear that he had really put a lot of notions into her head."

Has Cummins been charged?

He has. Cummins was charged with sexual contact with a minor, according to the TBI. Four days after their disappearance, Cummins was charged with aggravated kidnapping, since he may be armed. Cummins has also been added to Tennessee's "Top 10 Most Wanted" list.

Here's one thing that has people worried: Tennessee's kidnapping law is strangely lenient, so if the pair are caught and it is found that Thomas went with Cummins willingly, the kidnapping charge against him may not hold water.