自廣義相對論的成功之後,我們依舊未完全解決重力領域的問題。雙度規重力 是眾多修改重力嘗試的其中之一。在本文中我們將回顧此理論之發展。另一方 面,超重力及弦論中存在稱做為膜的擴展物件。我們也將回顧其處理之過程。 最後,我們嘗試在雙度規重力框架下搜尋膜存在之可能性。

In this thesis, we reviewed the field of massive gravity. We present the development from linearized Fierz-Pauli theory to massive bi-gravity. Some feature on brane solutions in supergravity theory is also reviewed. We applied the method to search for the possibility of brane in massive bi-gravity theory.

1 Introduction 1

2 Massive Gravity 3
2.1 GeneralRelativityandFierz-PauliTheory . . . . . . . . . . . . . . 3
2.2 vDVZ discontinuity and Vainshtein Mechanism . . . . . . . . . . . 6
2.3 dRGTMassiveGravityandBi-gravity ................ 10
2.4 MaximallySymmetricSolution .................... 17

3 Brane Solution 20
3.1 FormFields............................... 20
3.2 Branes.................................. 22
3.3 Methods................................. 24

4 Brane Solution in Bi-gravity 31
4.1 TheModel................................ 31
4.2 BraneSolutionSearching........................ 33

5 Summary 36

Appendix 38
A.DerivingFieldEquationsindRGTTheory . . . . . . . . . . . . . . . 38 B.DifferentialForms............................. 40

Reference 42

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