Các Định Lý về Sự Tồn Tại và Động Lực Học Toàn Cầu cho Phương Trình Einstein

Springer Science and Business Media LLC - Tập 8 Số 1 - Trang 1-68 - 2005
Rendall, Alan D.1
1Max-Planck-Institut für Gravitationsphysik, Golm, Germany

Tóm tắt

Bài báo này là một hướng dẫn về các định lý liên quan đến sự tồn tại và động lực học toàn cầu của các nghiệm của phương trình Einstein. Nó thu hút sự chú ý đến các câu hỏi mở trong lĩnh vực này. Vấn đề Cauchy cục bộ theo thời gian, vốn đã tương đối được hiểu rõ, được khảo sát. Các kết quả toàn cầu cho các nghiệm với các loại đối xứng khác nhau được thảo luận. Một sự lựa chọn các kết quả từ lý thuyết Newton và thuyết tương đối đặc biệt cung cấp những so sánh hữu ích được trình bày. Những cách tiếp cận kết quả toàn cầu trong trường hợp dữ liệu nhỏ và các kết quả về việc xây dựng không - thời gian với cấu trúc kỳ dị đã cho hoặc độ lớn suy giảm theo thời gian được đưa ra. Một bức tranh dự đoán về hành vi tiệm cận của các nghiệm vũ trụ tổng quát của phương trình Einstein được xây dựng. Một số chủ đề linh tinh liên quan đến chủ đề chính được thu thập trong một phần riêng.

Từ khóa

#Phương trình Einstein #định lý tồn tại #động lực học toàn cầu #vấn đề Cauchy #đối xứng #lý thuyết Newton #thuyết tương đối đặc biệt #không-thời gian #cấu trúc kỳ dị

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