What is the test for an Eighth Amendment claim arising out of inadequate medical care?

"To establish an Eighth Amendment claim arising out of inadequate medical care, a prisoner must prove deliberate indifference to his serious medical needs." Chance v. Armstrong, 143 F.3d 698, 702 (2d Cir. 1998) (internal quotation marks and brackets omitted). "[N]egligence, even if it constitutes medical malpractice, does not, without more, engender a constitutional claim." Id. at 703. Deliberate indifference has objective and subjective components: "First, the alleged deprivation must be, in objective terms, sufficiently serious. Second, the defendant must act with a sufficiently culpable state of mind." Id. at 702 (internal quotation marks and citation omitted). To satisfy the subjective component, a plaintiff must establish the equivalent of criminal recklessness, i.e., "that the charged official act[ed] or fail[ed] to act while actually aware of a substantial risk that serious inmate harm will result." Salahuddin v. Goord, 467 F.3d 263, 280 (2d Cir. 2006).