authority vs certainty

authority and certainty both are nouns.

Word	Noun	Adjective	Verb	Adverb
authority	Yes	No	No	No
certainty	Yes	No	No	No

As nouns, certainty is a hypernym of authority; that is, certainty is a word with a broader meaning than authority:

authority (noun)	certainty (noun)
the power or right to give orders or make decisions	something that is certain
official permission or approval	the state of being certain
freedom from doubt; belief in yourself and your abilities
an authoritative written work
an administrative unit of government
an expert whose views are taken as definitive
(usually plural) persons who exercise (administrative) control over others