Albert Einstein, German-born physicist (article use)

[Alexey86]

Here're a couple of excerpts from Encyclopaedia Britannica:

1) Albert Einstein, (born March 14, 1879, Ulm, Württemberg, Germany—died April 18, 1955, Princeton, New Jersey, U.S.), German-born physicist who developed the special and general theories of relativity and won the Nobel Prize for Physics in 1921 for his explanation of the photoelectric effect. Einstein is generally considered the most influential physicist of the 20th century.

2) Thomas Edison, in full Thomas Alva Edison, (born February 11, 1847, Milan, Ohio, U.S.—died October 18, 1931, West Orange, New Jersey), American inventor who, singly or jointly, held a world record 1,093 patents.

Why is there no article before German-born physicist and American inventor?

[Piscean]

Reference works such as dictionaries and encyclopaedias often leave out articles that would be necessary in normal writing.

[Alexey86]

Reference works such as dictionaries and encyclopaedias often leave out articles that would be necessary in normal writing.

But they never leave out articles in sentences like Albert Einstein was a German-born physicist...

Why does using a comma instead of be let us omit the article?

[Charlie Bernstein]

But they never leave out articles in sentences like Albert Einstein was a German-born physicist...

They don't. Your examples aren't complete sentences. As Piscean said, it's common shorthand in concise references to omit articles and verbs. Another reference might say:

Albert Einstein, German-born, Nobel Prize recipient, twentieth century's most influential physicist.

They're not trying to make sentences. They're trying to tell us who the person was.

Why does using a comma instead of forms of be let us omit the article?

It doesn't. It's not grammatical, just efficient. Pages are expensive.

That makes sense, right?

[Alexey86]

They don't. Your examples aren't complete sentences.

Albert Einstein, a/the German-born physicist who developed the special and general theories of relativity, liked to play the violin.

What article should I use here? On the one hand, he created the special theory of relativity, but on the other hand, he was one of many physicists developing it.

[Piscean]

Einstein is so famous for his work on relativity (and other scientists virtually unknown to most people) that the definite article is the appropriate one.

[Tdol]

This is just a summary. If you look at the rest of the article, it is written with articles, etc.

[Charlie Bernstein]

Albert Einstein, a/the German-born physicist who developed the special and general theories of relativity, liked to play the violin.

What article should I use here? On the one hand, he created the special theory of relativity, but on the other hand, he was one of many physicists developing it.

He's the only one who's widely recognized for those theories, and he led the way, so I'd choose the.