# Embeddings for general relativity

@article{Leon2015EmbeddingsFG, title={Embeddings for general relativity}, author={Jaime Ponce de Leon}, journal={Classical and Quantum Gravity}, year={2015}, volume={32}, pages={195018} }

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…

## 5 Citations

### On the Ck-embedding of Lorentzian manifolds in Ricci-flat spaces

- Mathematics
- 2017

In this paper, we investigate the problem of non-analytic embeddings of Lorentzian manifolds in Ricci-flat semi-Riemannian spaces. In order to do this, we first review some relevant results in the…

### A study of anisotropic compact stars based on embedding class 1 condition

- PhysicsInternational Journal of Modern Physics D
- 2019

This paper discusses a generalized model for compact stars, assumed to be anisotropic in nature due to the presence of highly dense and ultra-relativistic matter distribution. After embedding the 4D…

### On the embedding of Weyl manifolds

- Mathematics
- 2017

We discuss the possibility of extending different versions of the Campbell-Magaard theorem, which have already been established in the context of semi-Riemannian geometry, to the context of Weyl’s…

### Exploring physical features of anisotropic strange stars beyond standard maximum mass limit in $f\left(R,\mathcal {T}\right)$ gravity

- PhysicsMonthly Notices of the Royal Astronomical Society
- 2019

We study a specific model of anisotropic strange stars in the modified |$f\left(R,\mathcal {T}\right)$|-type gravity by deriving solutions to the modified Einstein field equations representing a…

### A generalized Finch–Skea class one static solution

- PhysicsThe European Physical Journal C
- 2019

In the present article, we discuss relativistic anisotropic solutions of Einstein field equations for the spherically symmetric line element under the class I condition. To do so we apply the…

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