A Georgia man is behind bars for allegedly strangling a woman and her toddler son earlier this week in Gwinnett County

Georgia Man Allegedly Strangles Woman and Her Toddler Son in Her Home — as Police Search for Motive

A Georgia man is behind bars for allegedly strangling a woman and her toddler son earlier this week, but investigators are still searching for a motive.

Authorities allege Brandon Williams, 32, strangled 30-year-old Natalie Nation — who was renting a room in his father’s home in Buford, Georgia — and her 2-year-old, Cole Nation.

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Williams is held without bond on multiple criminal counts, including one for felony murder and two for aggravated assault, according to a statement from police in Gwinnett County, Georgia.

Police were called to the home Sunday night by the suspect’s father.

Cole was pronounced dead soon after arriving at a local hospital; Natalie died not long after her son, according to police.

Williama’s arrest warrant — obtained by PEOPLE — alleges he used a towel to strangle Natalie, and an unidentified “offensive object” was used to kill Cole.

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There are no family ties between Williams and the victims, according to police.

Authorities are not commenting on unsubstantiated reports that Natalie was dating Williams’ father.

Image zoom Brandon Williams Gwinnett County Police

The arrest warrant alleges the slayings were committed while Williams’ dad was outside the home, working on an automobile.

Police arrested Williams not far from the crime scene. After the killings, the warrant alleges he walked to a nearby gas station, where he was detained without incident.

Williams has yet to enter a plea to the charges against him. It is likely he will face an additional felony murder charge following Natalie’s passing.