Embeddings for general relativity
Abstract
We present a systematic approach to embed ndimensional vacuum general relativity in an (n+1)dimensional pseudoRiemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally coupled to Einstein gravity. Our approach allows us to generalize a number of results discussed in the literature. We construct all the possible (physically distinct) embeddings in Einstein spaces, including the Ricciflat ones widely discussed in the literature. We examine in detail their generalization, whichin the framework under considerationare higherdimensional spacetimes sourced by a scalar field with flat (constant $\ne $ ≠ <!MPSinvTimes> 0) potential. We use the Kretschmann curvature scalar to show that many embedding spaces have a physical singularity at some finite value of the extra coordinate. We develop several classes of embeddings that are free of singularities, have distinct nonvanishing selfinteracting potentials and are continuously connected (in various limits) to Einstein embeddings. We point out that the induced metric possesses scaling symmetry and, as a consequence, the effective physical parameters (e.g., mass, angular momentum, cosmological constant) can be interpreted as functions of the extra coordinate.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 October 2015
 DOI:
 10.1088/02649381/32/19/195018
 arXiv:
 arXiv:1509.00148
 Bibcode:
 2015CQGra..32s5018P
 Keywords:

 embeddings for general relativity;
 modified general relativity;
 KaluzaKlein Gravity;
 General Relativity and Quantum Cosmology
 EPrint:
 Accepted for publication in Classical and Quantum Gravity