asperity vs rigor

asperity and rigor both are nouns.

Word	Noun	Adjective	Verb	Adverb
asperity	Yes	No	No	No
rigor	Yes	No	No	No

As nouns, asperity and rigor are synonyms defined as:

Other synonyms of asperity include grimness, hardship, rigorousness, rigour, rigourousness, severeness, severity.

asperity (noun)	rigor (noun)
something hard to endure	something hard to endure
harshness of manner	the quality of being valid and rigorous
	excessive sternness