We consider a point particle coupled to 2+1 gravity, with de Sitter gauge group SO(3,1). We observe that there are two contraction limits of the gauge group: one resulting in the Poincare group, and the second with the gauge group having the form AN(
2) ltimes an(2)^*. The former case was thoroughly discussed in the literature, while the latter leads to the deformed particle action with de Sitter momentum space, like in the case of kappa-Poincare particle. However, the construction forces the mass shell constraint to have the form p_0^2 = m^2, so that the effective particle action describes the deformed Carroll particle.
We study the variability mechanism of active galactic nuclei (AGN) within the framework of the flare model. To this end we examine the case of Seyfert/LINER galaxy NGC 4258, which is observed at high inclination angle and exhibits rapid fluctuations
of the X-ray light curve. We construct a model light curve based on the assumption of magnetic flares localized in the equatorial plane and orbiting with Keplerian speed at each given radius. We calculate the level of variability as a function of the inclination of an observer, taking into account all effects of general relativity near a rotating supermassive black hole. The variability level is a monotonic function of the source inclination. It rises more rapidly for larger values of the black hole spin (Kerr parameter) and for steeper emissivity (index beta of the radial profile). We compare the expected level of variability for the viewing angle 81.6 deg, as inferred for NGC 4258, with the case of moderate viewing angles about 30 deg, typical for Seyfert type-1 galaxies. Highly inclined sources such as this one are particularly suitable to test the flare model because the effects of orbital motion, Doppler boosting and light bending are all expected to have maximum when the accretion disk is seen almost edge-on. The model is consistent with the NGC 4258 variability, where the obscuring material is thought to be localized mainly towards the equatorial plane rather than forming a geometrically thick torus. Once the intrinsic time-scales of the flare duration are determined to better precision, this kind of highly inclined objects with a precisely known mass of the black hole can be used to set independent constraints on the spin parameter.
Causal dynamical triangulations (CDT) constitute a background independent, nonperturbative approach to quantum gravity, in which the gravitational path integral is approximated by the weighted sum over causally well-behaving simplicial manifolds i.e.
causal triangulations. This thesis is an analysis of the data from the Monte Carlo computer simulations of CDT in 3+1 dimensions. It is confirmed here that there exist the semiclassical limit of CDT for so-called (4,1) (or equivalent (1,4)) simplices, being a discrete version of the mini-superspace model. Next, the form of the corresponding discrete action is investigated. Furthermore, it is demonstrated that the effective, semiclassical solution works also after the inclusion of remaining (3,2) and (2,3) simplices, treated collectively. A specific form of the resulting extended discrete action is examined and a transition from the broader framework to the former narrower one is shown.
