Embedding theory as new geometrical mimetic gravity

Abstract

It is known that recently proposed model of mimetic gravity can be presented as general relativity with an additional mimetic matter. We discuss a possibility to analogously reformulate the embedding theory, which is the geometrical description of gravity proposed by Regge and Teitelboim, treating it also as general relativity with some additional matter. We propose a form of action which allows to describe this matter in terms of conserved currents. This action turns out to be a generalization of the perfect fluid action, which can be useful in the analysis of the properties of the additional matter. On the other side, the action contains a trace of the root of the matrix product, which is similar to the constructions appearing in bimetric theories of gravity. The action is completely equivalent to the original embedding theory, so it is not just some artificial model, but has a clear geometric sense. We discuss the possible equivalent forms of the theory and ways of study of the appearing equations of motion.

arXiv commentLaTeX, 11 pages

References in corpus (14)

• The Relation between Physical and Gravitational Geometry
• Cosmology with Mimetic Matter
• On the recently proposed Mimetic Dark Matter
• Imperfect Dark Matter
• Geodetic Brane Gravity
• On the quantisation of gravity by embedding spacetime in a higher dimensional space
• Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity
• Healthy imperfect dark matter from effective theory of mimetic cosmological perturbations
• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Λ=0 Cosmology of a Brane-like Universe
• From the Embedding Theory to General Relativity in a result of inflation
• Gravity as a field theory in flat space-time
• Forms of action for perfect fluid in General Relativity and mimetic gravity
• The approach to gravity as a theory of embedded surface

Cited by in corpus (20)

• Non-relativistic limit of embedding gravity as General Relativity with dark matter
• Modifications of gravity via differential transformations of field variables
• Hamiltonian analysis of Mimetic gravity with higher derivatives
• Dark matter from non-relativistic embedding gravity
• Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space
• Dark matter as a gravitational effect in the embedding theory approach
• Analytical analysis of the origin of core-cusp matter density distributions in galaxies
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• Canonical formulation of embedding gravity in a form of General Relativity with dark matter
• Explicit isometric embeddings of collapsing dust ball
• GEMS embeddings of Schwarzschild and RN black holes in Painlevé-Gullstrand spacetimes
• Explicit isometric embeddings of pseudo-Riemannian manifolds: ideas and applications
• Canonical description for formulation of embedding gravity as a field theory in a flat spacetime
• Matter production effects and interacting scenario within a reconstructed mimetic cosmology for late times
• Lovelock type brane gravity from a minimal surface perspective
• Polyakov-like approach to the modified gravity and other geometric theories
• Nontrivial isometric embeddings for flat spaces
• Explicit isometric embeddings of black holes geometry with non-singular matter distribution
• Investigation of Faddeev variant of embedding theory
• GEMS embeddings of Hayward regular black holes in massless and massive gravities