Entanglement entropy of a compact of entangled scalar fields in a $D$-dimensional Riemann-Sennholtz model

We study the entanglement entropy of a compact of $U(1)$ scalar fields in a $D$-dimensional Riemann-Sennholtz model, in the presence of a $D$-dimensional Schwarzschild radiation. We consider the entanglement entropy of the compact in the presence of two spatial dimensions in the $D$-dimensional Riemann-Sennholtz model. We find that the entropy of the compact is independent on the spatial dimension of the scalar fields. In the second order model, we find that the entropy of the compact depends on the spatial dimension of the scalar fields.