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Register a new userLorentz transformations in de Sitter relativity
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Added by
Jose Geraldo Pereira
Publication date
2007
fields
Physics
and research's language is
English
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The properties of Lorentz transformations in de Sitter relativity are studied. It is shown that, in addition to leaving invariant the velocity of light, they also leave invariant the length-scale related to the curvature of the de Sitter spacetime. The basic conclusion is that it is possible to have an invariant length parameter without breaking the Lorentz symmetry. This result may have important implications for the study of quantum kinematics, and in particular for quantum gravity.
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In the presence of a cosmological constant, interpreted as a purely geometric entity, absence of matter is represented by a de Sitter spacetime. As a consequence, ordinary Poincare special relativity is no longer valid and must be replaced by a de Sitter special relativity. By considering the kinematics of a spinless particle in a de Sitter spacetime, we study the geodesics of this spacetime, the ensuing definitions of canonical momenta, and explore possible implications for quantum mechanics.
The dispersion relation of de Sitter special relativity is obtained in a simple and compact form, which is formally similar to the dispersion relation of ordinary special relativity. It is manifestly invariant under change of scale of mass, energy and momentum, and can thus be applied at any energy scale. When applied to the universe as a whole, the de Sitter special relativity is found to provide a natural scenario for the existence of an evolving cosmological term, and agrees in particular with the present-day observed value. It is furthermore consistent with a conformal cyclic view of the universe, in which the transition between two consecutive eras occurs through a conformal invariant spacetime.
We compute the linearized Weyl-Weyl correlator using a new solution for the graviton propagator on de Sitter background in de Donder gauge. The result agrees exactly with a previous computation in a noncovariant gauge. We also use dimensional regularization to compute the one loop expectation value of the square of the Weyl tensor.
We study the dynamics of a spherically symmetric thin shell of perfect fluid embedded in d-dimensional Anti-de Sitter space-time. In global coordinates, besides collapsing solutions, oscillating solutions are found where the shell bounces back and forth between two radii. The parameter space where these oscillating solutions exist is scanned in arbitrary number of dimensions. As expected AdS3 appears to be singled out.
Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordstrom-de Sitter black holes. It was argued that perturbations of such a black hole decay sufficiently rapidly that the perturbed spacetime can be extended across the Cauchy horizon as a weak solution of the equations of motion. In this paper we consider the case of Kerr-de Sitter black holes. We find that, for any non-extremal value of the black hole parameters, there are quasinormal modes which decay sufficiently slowly to ensure that strong cosmic censorship is respected. Our analysis covers both scalar field and linearized gravitational perturbations.
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