WASHINGTON—Defense Secretary Lloyd Austin declined to inform the White House both times he was hospitalized and transferred authority to run the Pentagon to his deputy, military officials said Monday, episodes that call into question Austin’s judgment amid heightened tensions in Asia, Europe and the Middle East. 

The secrecy behind his hospitalization Jan. 1—known only to a handful of aides and military officials by the next day, but not the White House or President Biden until Thursday—has raised the ire of Congress, including some Democrats, and privately frustrated the White House. 

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