我们考虑在Einstein & de Sitter时空中传播的波。Einstein & de Sitter时空中的协变d'Alembert算子属于非Fuchsian偏微分算子族。引入了该方程的初值问题，并给出了解的显式表示公式。我们还展示了解的$L^p - L^q$估计。
英文摘要：
We consider the wave propagating in the Einstein & de Sitter spacetime. The covariant d'Alembert's operator in the Einstein & de Sitter spacetime belongs to the family of the non-Fuchsian partial differential operators. We introduce the initial value problem for this equation and give the explicit representation formulas for the solutions. We also show the $L^p - L^q$ estimates for solutions.
We propose a new deformed Rieffel product for functions in de Sitter spacetime, and study the resulting deformation of quantum field theory in de Sitter using warped convolutions. This deformation is obtained by embedding de Sitter in a higher-dimensional Minkowski spacetime, deforming there using the action of translations and subsequently projecting back to de Sitter. We determine the two-point function of a deformed free scalar quantum field, which differs from the undeformed one, in contrast to the results in deformed Minkowski spacetime where they coincide. Nevertheless, we show that in t…
Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat $\mathscr{I}$. Kerr-Schild-de Sitter are spacetimes of Kerr-Schild form with de Sitter background that solve the $(Λ>0)$-vacuum Einstein equations and admit a smooth conformal compactification sharing $\mathscr{I}$ with the background metric. Kerr-de Sitter-like metrics with conformally flat $\mathscr{I}$ are a generalization of the Kerr-de Sitter metrics, defined ori…
In this paper, we propose a survey of the basic geometric properties of Carters Kerr-de Sitter solution to Einsteins equation with positive cosmological constant. In particular, we give simple characterisations of the Kerr-de Sitter analogs of fast, slow and extreme Kerr spacetime and conclude with a discussion on maximal analytical extensions in each of these cases.
