Non-relativistic limit of embedding gravity as General Relativity with dark matter

Abstract

Regge-Teitelboim embedding gravity is the modified gravity based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. This theory is similar to the recently popular theory of mimetic gravity: the modification of gravity appears in both theories as a result of the change of variables in the action of General Relativity. Embedding gravity, as well as mimetic gravity, can be used in explaining the dark matter mystery since, in both cases, the modified theory can be presented as General Relativity with additional fictitious matter (embedding matter or mimetic matter). For the general case, we obtain the equations of motion of embedding matter in terms of embedding function as a set of first-order dynamical equations and constraints consistent with them. Then we construct a non-relativistic limit of these equations, in which the motion of embedding matter turns out to be slow enough so that it can play the role of cold dark matter. The non-relativistic embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the LambdaCDM model.

LaTeX, 19 pages; in v2 some references were added

References in corpus (8)

• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Dark matters on the scale of galaxies
• On the quantisation of gravity by embedding spacetime in a higher dimensional space
• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Forms of action for perfect fluid in General Relativity and mimetic gravity
• Modifications of gravity via differential transformations of field variables
• Dark matter from non-relativistic embedding gravity
• Hamilton-Jacobi approach for Regge-Teitelboim cosmology

Cited by in corpus (18)

• Dark matter from non-relativistic embedding gravity
• Dark matter as a gravitational effect in the embedding theory approach
• Weak field limit for embedding gravity
• Analytical analysis of the origin of core-cusp matter density distributions in galaxies
• Lower-dimensional Regge-Teitelboim gravity
• Canonical formulation of embedding gravity in a form of General Relativity with dark matter
• GEMS embeddings of Schwarzschild and RN black holes in Painlevé-Gullstrand spacetimes
• Possible types of dark matter condensation in embedding gravity
• Equiaffine braneworld
• Classification of ten-dimensional embeddings of spherically symmetric static metrics
• Nontrivial isometric embeddings for flat spaces
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)
• Jacobi equations of geodetic brane gravity
• Explicit isometric embeddings of black holes geometry with non-singular matter distribution
• Analysis of the equations of motion of fictitious matter in embedding theory
• Gravity as embedding theory and the distribution of matter in galaxies
• Investigation of Faddeev variant of embedding theory
• GEMS embeddings of Hayward regular black holes in massless and massive gravities