Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition

What happens if you throw a scalar field into General Relativity? And if you throw more than one? Here is a paper on the phenomenology of neutron stars in theories with more than one scalar field coupled to gravity.

M. Horbatsch, H. O. Silva, D. Gerosa, P. Pani, E. Berti, L. Gualtieri, U. Sperhake.
Classical and Quantum Gravity 32 (2015) 204001. arXiv:1505.07462 [gr-qc].
IoP Editor’s choice (CQG++, IOPselect).