Embeddings for general relativity
Abstract
We present a systematic approach to embed n-dimensional vacuum general relativity in an (n+1)-dimensional pseudo-Riemannian 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 Ricci-flat ones widely discussed in the literature. We examine in detail their generalization, which-in the framework under consideration-are higher-dimensional 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 non-vanishing self-interacting 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:
- 10.1088/0264-9381/32/19/195018
- arXiv:
- arXiv:1509.00148
- Bibcode:
- 2015CQGra..32s5018P
- Keywords:
-
- embeddings for general relativity;
- modified general relativity;
- Kaluza-Klein Gravity;
- General Relativity and Quantum Cosmology
- E-Print:
- Accepted for publication in Classical and Quantum Gravity