Given

<field name="active" type="boolean" indexed="true" stored="true" multiValued="false" docValues="true"/>

I'd like to find docs where field with name active is missing or has active set to false.

fq=((-active:*) OR (active:false)) returns only (active:false) docs, but does not include the ones with missing active field (-active:*).

What is the correct way todo this kind of fq query?