Parameters
RS1 model:
Two 3-branes at y=0 and y=πr_c in AdS₅. Metric: ds²=e^{−2ky}η_μν dx²+dy²
Warp factor:
Effective Planck scale: M_Pl² = M₅³(1−e^{−2kπr_c})/k
Hierarchy: m_EW ~ M_Pl e^{−kπr_c}
KK modes:
Graviton tower: m_n ~ k e^{−kπr_c} × zeros of Bessel functions
RS2:
One brane, infinite extra dim — gravity localized by warp factor.
Two 3-branes at y=0 and y=πr_c in AdS₅. Metric: ds²=e^{−2ky}η_μν dx²+dy²
Warp factor:
Effective Planck scale: M_Pl² = M₅³(1−e^{−2kπr_c})/k
Hierarchy: m_EW ~ M_Pl e^{−kπr_c}
KK modes:
Graviton tower: m_n ~ k e^{−kπr_c} × zeros of Bessel functions
RS2:
One brane, infinite extra dim — gravity localized by warp factor.