Recent observations of the luminosity-red shift relation of distant type Ia supernovae established the fact that the expansion of the universe is accelerated. This is interpreted by saying that there exists some kind of agent (called dark energy), which exerts an overall repulsive effect on ordinary matter. Dark energy contributes today in the amount of about 73 % to the total energy content of the universe, and its spatial distribution is compatible with perfect uniformity. The simplest possible explanation for dark energy is to assume that it is just a universal constant, the so called cosmological constant. This would mean that the background arena for all natural phenomena, once all physical matter-energy has been ideally removed, is the de Sitter space time. Thus, the Poincaré group should be replaced by the de Sitter group, and one is naturally led to a reformulation of the theory of special relativity on these grounds. The absence of a privileged class of equivalent frames (inertial frames) suggests that, in de Sitter relativity it would be desirable, to characterize significant physical quantities in an intrinsic way, namely in a manner independent of the choice of any particular coordinate patch. In this talk we would like to show how this can be accomplished for any set of independent conserved quantities along the geodesic motion of a free de Sitter particle. These quantities allow for a natural discussion of classical pointlike scattering and decay processes.
In General Relativity, finding out the geodesics of a given spacetime manifold is an important task because it determines which classical processes are dynamically forbidden. Conserved quantities play an important role in solving geodesic equations of a general spacetime manifold. Furthermore, knowing all possible conserved quantities of a system tells about the hidden symmetries of that system since, conserved quantities are deeply connected with the symmetries of the system, which are very important in their own right. Conserved quantities are also useful to capture certain features of space…
We revisit the conserved quantities of the Mathisson-Papapetrou-Tulczyjew equations describing the motion of spinning particles on a fixed background. Assuming Ricci-flatness and the existence of a Killing-Yano tensor, we demonstrate that besides the two non-trivial quasi-conserved quantities, i.e. conserved at linear order in the spin, found by Rüdiger, non-trivial quasi-conserved quantities are in one-to-one correspondence with non-trivial mixed-symmetry Killing tensors. We prove that no such stationary and axisymmetric mixed-symmetry Killing tensor exists on the Kerr geometry. We discuss th…
We construct conserved quantities in pure Lovelock gravity for both static and dynamic Vaydia-type black holes with AdS, dS and flat asymptotics, applying field-theoretical formalism developed earlier. Global energy (where applicable), quasi-local energy together with fluxes of these quantities are presented for both types of black holes, considering asymptotic spacetime as background. The same quantities are constructed for dynamic black holes on the background of the related static black holes. Besides, for the dynamic black holes, energy densities and densities of energy flux are calculated…
We discuss the definition of conserved quantities in asymptotically locally de Sitter spacetimes. One may define an analogue of holographic charges at future and past infinity and at other Cauchy surfaces $I_t$ as integrals over the intersection of timelike surfaces $C$ and the Cauchy surface $I_t$. In general, the charges $Q^t$ defined on the Cauchy surface $I_t$ depend on $C$, but if gravitational flux is absent the charges are independent of $C$. On the other hand, if there is a net gravitational flux entering or leaving the spacetime region bounded by $C_1, C_2$ and two Cauchy surfaces the…
The article considers a new mechanism of charge accumulation in the early Universe in theories with compact extra dimensions. The relaxation processes in the extra space metric that take place during its formation lead to the establishment of symmetrical extra space configuration. As a result, the initial accumulation of the number associated with the symmetry occurs. We demonstrate this mechanism using a simple example of a two-dimensional apple-like extra space metric with $U(1)$-symmetry. The conceptual idea of the mechanism can be used to develop a model for the production of the baryon or…
We examine various methods of constructing conserved quantities in the Teleparallel Equivalent of General Relativity (TEGR). We demonstrate that in the covariant formulation the preferred method are the Noether charges that are true invariant quantities. The Noether charges depend on the vector field $ξ$ and we consider two different options where $ξ$ is chosen as either a Killing vector or a four-velocity of the observer. We discuss the physical meaning of each choice on the example of the Schwarzschild solution in different frames: static, freely falling Lemaitre frame, and a newly obtained …
The identification between the bulk and boundary conserved quantities
Central South University of Forestry and Technology（中南林业科技大学）；Beijing Normal University（北京师范大学）；Chinese Academy of Sciences（中国科学院）；University of Chinese Academy of Sciences（中国科学院大学）
