Brane Gravity from Bulk Vector Field

TL;DR

This paper demonstrates that Einstein's equations on a brane can be derived from multi-dimensional vector field equations in a pseudo-Euclidean space, establishing a link between brane geometry and bulk vector fields.

Contribution

It introduces a novel approach to derive brane gravity equations from bulk vector field equations, connecting intrinsic geometry with vector field components.

Findings

Einstein's equations on the brane can be obtained from bulk vector field equations.

The effective 4D gravity action is consistent whether described by the brane's intrinsic metric or its normal derivatives.

The approach provides a new perspective on the geometric origin of gravity in brane-world scenarios.

Abstract

It is shown that Einstein's equations on the brane can be received from the multi-dimensional vector field equations in pseudo-Euclidean space. The idea is based on the observation that the brane geometry can be equivalently described by the intrinsic metric or by the derivatives of its normal. From the other hand the normal to the brane can be constructed with the components of some multi-dimensional vector fields. For the both cases 4-dimensional effective action for gravity appears to be the same.