Dirac Relaxation of the Israel Junction Conditions: Unified Randall-Sundrum Brane Theory

Abstract

Following Dirac's brane variation prescription, the brane must not be deformed during the variation process, or else the linearity of the variation may be lost. Alternatively, the variation of the brane is done, in a special Dirac frame, by varying the bulk coordinate system itself. Imposing appropriate Dirac style boundary conditions on the constrained 'sandwiched' gravitational action, we show how Israel junction conditions get relaxed, but remarkably, all solutions of the original Israel equations are still respected. The Israel junction conditions are traded, in the $Z_2$-symmetric case, for a generalized Regge-Teitelboim type equation (plus a local conservation law), and in the generic $Z_2$-asymmetric case, for a pair of coupled Regge-Teitelboim equations. The Randall-Sundrum model and its derivatives, such as the Dvali-Gabadadze-Porrati and the Collins-Holdom models, get generalized accordingly. Furthermore, Randall-Sundrum and Regge-Teitelboim brane theories appear now to be two different faces of the one and the same unified brane theory. Within the framework of unified brane cosmology, we examine the dark matter/energy interpretation of the effective energy/momentum deviations from General Relativity.

11 PRD pages, 1 figure

Cited by in corpus (8)

• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Wormholes and solitonic shells in five-dimensional DGP theory
• Cosmic acceleration in Regge-Teitelboim gravity
• Gravitating defects of codimension-two
• Unified Brane Gravity: Cosmological Dark Matter from Scale Dependent Newton Constant
• Radiation Driven Inflation
• Lovelock type brane gravity from a minimal surface perspective
• Loop Special Relativity: Kaluza-Klein area metric as a line element for stringy events