Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the semiduals of local isometry groups in 3d gravity
277
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this way we obtain quantum doubles of the Lorentz and rotation groups in 3d, as well as kappa-Poincare algebras whose associated r-matrices have spacelike, timelike and lightlike deformation parameters. We confirm and elaborate the interpretation of semiduality proposed in [13] as the exchange of the cosmological length scale and the Planck mass in the context of 3d quantum gravity. In particular, semiduality gives a simple understanding of why the quantum double of the Lorentz group and the kappa-Poincare algebra with spacelike deformation parameter are both associated to 3d gravity with vanishing cosmological constant, while the kappa-Poincare algebra with a timelike deformation parameter can only be associated to 3d gravity if one takes the Planck mass to be imaginary.
rate research
Read More
A solution of the old problem raised by Tolman, Ehrenfest, Podolsky and Wheeler, concerning the lack of attraction of two light pencils moving parallel, is proposed, considering that the light can be source of nonlinear gravitational waves corresponding (in the would be quantum theory of gravity) to spin-1 massless particles.
We study the entropy of the black hole with torsion using the covariant form of the partition function. The regularization of infinities appearing in the semiclassical calculation is shown to be consistent with the grand canonical boundary conditions. The correct value for the black hole entropy is obtained provided the black hole manifold has two boundaries, one at infinity and one at the horizon. However, one can construct special coordinate systems, in which the entropy is effectively associated with only one of these boundaries.
We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+epsilon dimensions as epsilon goes to zero, provided Newtons constant scales with epsilon. Our procedure - spherical reduction, dualization, limit, dualizing back - passes several consistency tests: geometric properties, interactions with matter and the Bekenstein-Hawking entropy are as expected from Einstein gravity.
This Thesis is devoted to the study of Metric-Affine Theories of Gravity and Applications to Cosmology. The thesis is organized as follows. In the first Chapter we define the various geometrical quantities that characterize a non-Riemannian geometry. In the second Chapter we explore the MAG model building. In Chapter 3 we use a well known procedure to excite torsional degrees of freedom by coupling surface terms to scalars. Then, in Chapter 4 which seems to be the most important Chapter of the thesis, at least with regards to its use in applications, we present a step by step way to solve for the affine connection in non-Riemannian geometries, for the first time in the literature. A peculiar f(R) case is studied in Chapter 5. This is the conformally (as well as projective invariant) invariant theory f(R)=a R^{2} which contains an undetermined scalar degree of freedom. We then turn our attention to Cosmology with torsion and non-metricity (Chapter 6). In Chapter 7, we formulate the necessary setup for the $1+3$ splitting of the generalized spacetime. Having clarified the subtle points (that generally stem from non-metricity) in the aforementioned formulation we carefully derive the generalized Raychaudhuri equation in the presence of both torsion and non-metricity (along with curvature). This, as it stands, is the most general form of the Raychaudhuri equation that exists in the literature. We close this Thesis by considering three possible scale transformations that one can consider in Metric-Affine Geometry.
We present a new regularisation of Euclidean Einstein gravity in terms of (sequences of) graphs. In particular, we define a discrete Einstein-Hilbert action that converges to its manifold counterpart on sufficiently dense random geometric graphs (more generally on any sequence of graphs that converges to the manifold in the sense of Gromov-Hausdorff). Our construction relies crucially on the Ollivier curvature of optimal transport theory. Our methods also allow us to define an analogous discrete action for Klein-Gordon fields. These results may be taken as the basis for a combinatorial approach to quantum gravity where we seek to generate graphs that approximate manifolds as metric-measure structures.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
