rigor vs asperity

rigor and asperity both are nouns.

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

As nouns, rigor and asperity are synonyms defined as:

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

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