It is a matter of opinion, hence the answer to this question cannot be precisely answered. But if when talking about the playwriting, for the fact that if there is a proper inspiration and determination and proper research work done to do the work, any work is possible.
Therefore, a white playwriter can obviously write about the black experience but definitely with the proper amount of research work done in that field and with the proper and authenticated source or with the help of the experience of any person who have been through the same situation.
The most important part will be played by your determination to know the characterization of your character in your play focusing on your playwriting skills.
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