A note on spherically symmetric, static spacetimes in Kanno-Soda on-brane gravity

Understand

Spherically symmetric, static on-brane geometries in the Kanno-Soda (KS) effective scalar-tensor theory of on-brane gravity are discussed.

• In order to avoid brane collisions and/or an infinite inter-brane distance, at finite values of the brane coordinates, it is necessary that the radion scalar be everywhere finite and non-zero.
• This requirement constrains the viability of the standard, well-known solutions in General Relativity (GR), in the context of the KS effective theory.
• The radion for the Schwarzschild solution does not satisfy the above requirement.