His death sentence was vacated by a different judge in 2005.
Slomsky will be deciding whether Hammer, 55, should be sentenced to death - again - or whether he should spend the rest of his life in prison.
The resentencing hearing began June 2. It was not heard yesterday, and the parties will reconvene June 23 after a one-week break.
Defense attorneys yesterday declined to comment on the case.
Federal prosecutors did not return calls or an email for comment.
Hammer has made national headlines, in part, because he has flip-flopped numerous times over whether to challenge his death sentence. He had expressed a wish to be executed, but has also filed appeals to avoid the death penalty.
Executive Director Richard Dieter of the Washington, D.C.-based Death Penalty Information Center, a national nonprofit resource center, said yesterday that mental illness "could well be playing a part" in the "ping-pong nature of the case."
He said he can't speak about Hammer's specific mental state, but said it could play a factor in the judge's decision.
According to the center, three federal inmates have been executed since the federal death penalty was reinstated in 1988.
The most recent was in 2003 when Louis Jones Jr. was executed for a Texas slaying.
In June 2001, Oklahoma City bomber Timothy McVeigh was executed as was Juan Garza, who murdered three people in Texas.
Dieter said there are currently 60 inmates on federal death row, including Hammer.
Hammer has surprised observers with his various courtroom decisions and his prison behavior over the years.
During his first-degree murder trial in June 1998 before U.S. District Senior Judge Malcolm Muir in the Middle District of Pennsylvania, Hammer, then 39, halted proceedings by pleading guilty.
He admitted strangling his cellmate, Andrew Marti, with a rope in April 1996 in the Allenwood Federal Penitentiary in central Pennsylvania after tying him to a bunk and choking him unconscious.
As required, Muir sentenced Hammer to death after a jury recommended the death penalty.
Since then, Hammer has changed his mind several times about whether he wants to die and has filed various appeals.
He was scheduled to die by lethal injection in June 2004, but the Third U.S. Circuit Court of Appeals in Philadelphia issued a stay, delaying his execution.
Later, in December 2005, Muir vacated his death sentence. The judge said prosecutors should have told Hammer's lawyers about the existence of four interviews that may have supported Hammer's claim that he used rope made from bed sheets for bondage sex, The Associated Press has reported.
The evidence could have led the jury to decide that Hammer did not engage in substantial planning before he killed Marti, the judge said, according to the AP.
In January 2011, Hammer's case was reassigned to Slomsky after Muir decided to discontinue courtroom work. Muir, 96, died in July of that year.
Hammer first entered the federal prison system in December 1993 after Oklahoma authorities asked federal prison officials to house him because of his behavior in state prison.
His pranks, threats and various unsubstantiated claims - among them, that he ordered killings from prison when there was no evidence to support the allegations - apparently got to be too much for state officials, who considered him too dangerous.
He is already serving terms totaling more than 1,200 years for crimes he committed during an early 1980s crime spree in his native Oklahoma.
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