|8 April||Abraham Harte|
Dublin City University
|Does geometric optics depend on geometry?|
An immediate answer to the question in the title might be that of course geometric optics depends on geometry; it’s right there in the name! However, the point of this talk will be to explain that while geometric optics does depend on geometry, it does so only slightly. This can be important because certain astronomical observations attempt to infer the geometry of spacetime (and its matter content) using the properties of electromagnetic or gravitational waves which pass through it. Doing so naturally leads to the question of whether or not such inferences are unique: If a particular field is known to be compatible with a particular background metric, is it compatible with other metrics as well? I will explain that in fact, the number of possibilities is enormous. This is particularly true in the geometric optics approximation, where, for many observables, the class of allowed metrics involves seven free functions. Some of these functions may be identified with conformal and Kerr-Schild transformations, but there is much more besides. Going beyond geometric optics can provide a somewhat more discerning picture of the underlying geometry, but some observables remain invariant with respect to large classes of metric transformations.
|8 April||Scott Hughes|
Massachusetts Institute of Technology
The new astronomy of
Albert Einstein fundamentally changed how we think about space and time. As part of this re-think, he predicted that gravity would radiate: Shake a mass, and a piece of its gravitation field flies off and affects distant objects. One hundred years after this prediction, an international collaboration announced that they had at last measured these waves, discovering the gravitational “chirp” produced when two black holes merge into one. Gravitational-wave astronomy was born, and has now grown into an active field. This lecture will describe the quest for gravitational waves, and will describe what has been found already since that first discovery. I will emphasize that it is best to think of these waves as “sound-like,” and that the antennae which measure these waves are more like ears than eyes. I will play examples of the songs that different astronomical objects can sing as I describe how this new astronomy is now developing.
|19 November||Rodrigo Macedo|
Queen Mary University of London
|Revisiting black-hole perturbation theory: the hyperboloidal slice approach|
After reviewing the well-stablished notion of black-hole perturbation theory and the concept of quasinormal modes, we present a spectral representation of solutions to relativistic wave equations based on a geometrical approach in which the constant-time surfaces extend until future null infinity. Here, we restrict ourselves to an asymptotically flat, spherically symmetric spacetime (with focus on the Reisnner-Nordstrom solution). With the help of a Laplace transformation on the wave equation in question, we provide a geometrical interpretation to known algorithms (i.e. Leaver’s approach) in addition to deriving an algorithm for obtaining all ingredients of the desired spectral decomposition, including quasi-normal modes, quasi-normal mode amplitudes, and the jump of the Laplace transform along the branch cut. The work explains the procedure extensively and includes detailed discussions of the contribution of infinite frequency modes to the early time response of the black hole and its relation to the QNM-amplitude growth rates.
|12 November||Jeremy Wachter|
University of the Basque Country
|Gravitational self-interactions of cosmic string loops|
Gravitational wave signals from cosmic strings are strongly influenced by the presence and character of generic features on string loops known as kinks and cusps. We find analytically the leading-order effect of gravitational self-interactions on strings near kinks and cusps, and discuss how these effects might influence loop evolution. We show the results of numerically evolving particular kinds of loops undergoing self-interactions, and comment on how the gravitational wave spectrum from loops might be affected.