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

TL;DR

This paper introduces a unified brane theory by relaxing Israel junction conditions through Dirac's brane variation, connecting Randall-Sundrum and Regge-Teitelboim models and exploring implications for dark matter and energy.

Contribution

It develops a novel approach to brane variation that unifies different brane models and relaxes junction conditions while preserving original solutions.

Findings

Generalized Randall-Sundrum models within the unified framework

Reformulation of Israel junction conditions as Regge-Teitelboim equations

Implications for dark matter/energy in brane cosmology

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.