Yes. Grammatically it's acceptable. It usually means it's not yet published, printed or distributed, but this is not explicitly stated - all that's clear is it's somewhere in the production process - anywhere from being just an idea, to being fully written and ready for printing & publishing.

The phrase "this book is currently under production" is understandable but not the most natural way to say it. A more common and natural phrase would be: "This book is currently in production." The phrase "under production" is rarely used in English. We typically say something is "in production" when referring to books, movies, or products being made.

Yes, you can say "this book is currently under production." It's a clear way to indicate that the book is in the process of being created or published. However, it sounds a bit formal or technical. If you're looking for a more casual phrasing, you could say: * "This book is currently being worked on." * "This book is in the works right now." Both of these sound a bit more conversational. Does that help?

Or you can use one of these: “This book is in the works.” “This book is a work in progress.”

By itself, it’s unclear. It could mean, for example, ‘I’m working on a book.’ , ‘The book is in the process of being published.’, or ‘The book is in print.’ The phrase ‘in production’ (generally not ‘under’) is often used for a new product that has been designed but not yet on the market, or a movie that is in the process of being made. With books it’s more common to talk about ‘publishing’ or ‘printing’ than ‘production’.