For the "hearth" aspect:
* Cultural periphery: This suggests a region or group that is less central to a cultural influence.
* Cultural borderland: This suggests a zone where different cultures meet and mix.
* Cultural wasteland: This implies a lack of cultural development or vibrancy.
For the "culture" aspect:
* Cultural stagnation: This suggests a lack of development or change.
* Cultural decline: This suggests a deterioration or loss of cultural values.
* Cultural extinction: This suggests the complete disappearance of a culture.
Other alternatives:
* Cultural backwater: This implies a region or group that is isolated and behind the times.
* Cultural dead end: This implies a lack of potential for further cultural development.
The best antonym for "culture hearth" will depend on the specific meaning you want to convey.