7 pages; contribution to the Special Issue of the International Journal of Geometric Methods in Modern Physics dedicated to the conference Geometric Foundations of Gravity in Tartu 2021
The more precise definition and the more fundamental understanding of the concepts of time, energy, entropy and information are building upon the new, relativistic foundation of gravity. This lecture is an attempt to explain the basic principles that underpin this progress, by focusing on the simple but subtle universal definition of energy. The principles are unearthed from Einstein's theory and Noether's theorems, beneath a century of misconceptions.
We present a method of contraction that can be applied to re-construct the recent extended non-relativistic and ultra-relativistic algebras as well as corresponding action principles. The methodology involves the use of multiple copies of Poincaré algebra. Consequently, the contraction defines non-relativistic or ultra-relativistic limits of multimetric theories of gravity. In particular, we show that the non-relativistic scaling limit of bi-metric gravity corresponds to the recent formulation of an action principle for Newtonian gravity with a constant background mass density.
In this work we present a non-relativistic gravity theory defined in four spacetime dimensions using the MacDowell-Mansouri geometrical formulation. We obtain a Newtonian gravity action which is constructed from the curvature of a Newton-Hooke version of the so-called Newtonian algebra. We show that the non-relativistic gravity theory presented here contains the Poisson equation in presence of a cosmological constant. Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity by considering a particular ansatz for a given gauge field. We extend our results to a g…
The Earth's geoid is one of the most essential and fundamental concepts to provide a gravity field-related height reference in geodesy and associated sciences. To keep up with the ever-increasing experimental capabilities and to consistently interpret high-precision measurements without any doubt, a relativistic treatment of geodetic notions (including the geoid) within Einstein's theory of General Relativity is inevitable. Building on the theoretical construction of isochronometric surfaces and the so-called redshift potential for clock comparison, we define a relativistic gravity potential a…
In this paper, we present novel and known non-relativistic and ultra-relativistic spin-3 algebras, by considering the Lie algebra expansion method. We start by applying the expansion procedure using different semigroups to the spin-3 extension of the AdS algebra, leading to spin-3 extensions of known non-relativistic and ultra-relativistic algebras. We then generalize the procedure considering an infinite-dimensional semigroup, which allows to obtain a spin-3 extension of two new infinite families of the Newton-Hooke type and AdS-Carroll type. We also present the construction of the gravity th…
Gravity gradiometry within the framework of the general theory of relativity involves the measurement of the elements of the relativistic tidal matrix, which is theoretically obtained via the projection of the spacetime curvature tensor upon the nonrotating orthonormal tetrad frame of a geodesic observer. The behavior of the measured components of the curvature tensor under Lorentz boosts is briefly described in connection with the existence of certain special tidal directions. Relativistic gravity gradiometry in the exterior gravitational field of a rotating mass is discussed and a gravitomag…
We provide a constrained Hamiltonian analysis of a non relativistic Schrodinger field in 2+1 dimensions , coupled with Chern - Simons gravity. The coupling is achieved by the recently advanced Galilean gauge theory \cite{BMM1},\cite{ BMM2}, \cite{BM4}. The calculations are repeated with a truncated model to show that deviation from Galilean gauge theory makes the theory untenable. The issue of nonrelativistic spatial diffeomorphism is discussed in this context.
The effects of highly relativistic spin-gravity coupling in the Schwarzschild-de Sitter background which follow from the Mathisson-Papapetrou equations are investigated. The dependence of gravitoelectric and gravitomagnetic components of gravitational field on the velocity of an observer which is moving in Schwarzschild-de Sitter's background is estimated. The action of gravitomagnetic components on a fast moving spinning particle is considered. Different cases of the highly relativistic circular orbits of a spinning particle which essentially differ from the corresponding geodesic orbits are …
We study the possibility to explain the mystery of the dark matter through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a 4-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold dark matter. We prove the stability of such t…
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 …
We present the non-relativistic limit of the stellar structure equations of Ricci-based gravities, a family of metric-affine theories whose Lagrangian is built via contractions of the metric with the Ricci tensor of an a priori independent connection. We find that this limit is characterized by four parameters that arise in the expansion of several geometric quantities in powers of the stress-energy tensor of the matter fields. We discuss the relevance of this result for the phenomenology of non-relativistic stars, such as main-sequence stars as well as several substellar objects.
We study the static and spherical symmetric (SSS) configurations in the non-minimal model of the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a flat reference metric. Considering the modified Tolman-Oppenheimer-Volkoff (TOV) equation, the Bianchi identity, and energy-momentum conservation, we find a new algebraic equation for the radial coordinate of the reference metric. We demonstrate that this equation suggests an absence of the Vainshtein mechanism in the minimal model of the dRGT massive gravity, while it has two branches of solutions where one connects with the Schwarzschild spac…
In this paper, we study the effects of a modified theory of gravity - the rainbow gravity - on the relativistic Bose-Einstein condensate (BEC). We initially discuss some formal aspects of the model in order to compute the corrections to the relevant quantities of the condensate. Following, we evaluate the generating functional from which obtain some thermodynamic parameters. Then we calculate the corrected critical temperature $T_c$ that sets the relativistic Bose-Einstein condensate considering the three principal rainbow functions, finding, in addition, a phenomenological upper bound for the…
