Rahane is out due to a minor left hamstring strain he picked up while fielding on the final day of the Kanpur Test. Jadeja's is a right forearm injury that required scans which revealed swelling. "He has been advised rest," stated a BCCI release.
Ishant, meanwhile, dislocated his left little finger on the final day in Kanpur, leaving the door open for Mohammed Siraj's return. Siraj had himself sustained a finger injury during the T20I series, but has now been deemed fit.
For Williamson, it's the recurrence of an old left-elbow problem that has troubled him for much of the year. Coach Gary Stead confirmed the injury had flared up during the first Test and with it failing to improve in the days following the match, the call was made to rule him out. In his absence. Tom Latham will lead the side.
"It's been a really tough time for Kane having to deal with such a persistent injury," Stead said. "While we've been able to manage the injury through the year and the T20 World Cup, the shift to Test cricket and the increased batting loading has re-aggravated his elbow.
"Ultimately the injury is still not right and while he got through the Kanpur Test, it was clear playing in the second Test wasn't an option."
Meanwhile, the absence of Rahane and Jadeja could leave India's team management contemplate a sixth batting option. If they go down this route, it could mean a debut for KS Bharat or Suryakumar Yadav at his home ground. Wriddhiman Saha was ruled fit by Virat Kohli a day before the match.