Seminář se koná v úterý ve 13:10 v posluchárně ÚTF MFF UK
v 10. patře katedrové budovy v Tróji, V Holešovičkách 2, Praha 8
We construct a position-space cosmological perturbation theory around spatially flat Friedmann-Lemaître-Robertson-Walker geometries that allows us to model localized sources of gravitational waves. The equations of motion are decoupled using a generalized harmonic gauge, which avoids the use of a scalar-vector-tensor decomposition. To begin with, we discuss linearized gravitational waves from compact sources on de Sitter background. We obtain the closed form expression for the metric perturbation around de Sitter spacetime up to quadrupolar order in the multipolar expansion. We emphasize that a consistent quadrupolar truncation is needed for conservation of stress-energy tensor. In the later part of my talk, we will generalize this idea for power-law cosmologies.
The Vaidya spacetime is a spherically symmetric solution of the Einstein equations with a null dust source. This can be used to model the gravitational collapse of a thick shell of radiation: a flat interior region is matched at an inner boundary to the null dust filled region, which is then matched at an outer boundary to Schwazschild spacetime. A central singularity inevitably forms, and depending on the profile of the energy density of the null dust, this singularity can be globally naked. Motivated by the cosmic censorship hypothesis, we consider perturbations of this configuration. We review previous work, and describe recent work where the perturbation of the inner boundary - the past null cone of the central singularity - is analysed using a framework for studying perturbations of general hypersurfaces. This sets boundary conditions for perturbations at the past null cone, and we then consider the evolutionary problem, focussing on the question of the stability of the Cauchy horizon of the naked singularity.
I will describe a new construction of Ricci flat metrics using gauged linear sigma models satisfying the Calabi-Yau condition. The approach will be introductory using elementary examples to illustrate the main points and to underline the connection between physical and mathematical concepts.
David Kubizňák Oldřich Semerák