Ohio State’s trustees moved quickly this week, voting unanimously to appoint Executive Vice President and Provost Ravi Bellamkonda as the university’s president following Walter “Ted” Carter Jr.’s abrupt resignation. The board waived a national search and elevated an insider to steady the flagship campus after revelations about an ‘‘inappropriate relationship’’ involving the prior president, trustees said. Trustees framed the decision as an urgency move to preserve operational continuity; board chair John Zeiger told reporters the board wanted stability. The appointment makes Bellamkonda Ohio State’s fourth president since 2020 and ends speculation about an interim leader or prolonged search. The rapid elevation raises governance questions for trustees at large public universities about when to pause searches and when to install internal successors.