The Steelers contend their lease requires the authority to pay about two-thirds of the $38 million the team expects it will cost to add the end zone seats and a new video scoreboard.
But the authority's attorney said that provision kicks in only if half of the NFL's stadiums have had similar expansions and at least 25 percent of the cost of those other expansions were funded with tax dollars. Authority attorney Walter DeForest said that hasn't happened.
The stadium now has 65,050 seats.
The Steelers sued when a deal to finance the authority's share with parking and ticket surcharges fell through.
The Allegheny County judge hasn't immediately ruled.