exigent

adj. demanding; urgent, pressing

An exigent circumstance, in the American law of criminal procedure, allows law enforcement to enter a structure without a warrant, or if they have a "knock and announce" warrant, without knocking and waiting for refusal under certain circumstances. It must be a situation where people are in imminent danger, evidence faces imminent destruction or a suspect will escape.
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Adjective
1. demanding attention; "clamant needs"; "a crying need"; "regarded literary questions as exigent and momentous"- H.L.Mencken; "insistent hunger"; "an instant need"
(synonym) clamant, crying, insistent, instant
(similar) imperative
2. requiring precise accuracy; "an exacting job"; "became more exigent over his pronunciation"
(synonym) exacting
(similar) demanding

v. demand, require; exact, call for

(n.)
The name of a writ in proceedings before outlawry.
  

(n.)
Exigency; pressing necessity; decisive moment.
  

(a.)
Exacting or requiring immediate aid or action; pressing; critical.