Seminar is held on Tuesdays at 13:10 pm in the lecture room of the Institute
on the 10th floor of the department building at Trója, V Holešovičkách 2, Prague 8
In 1975, in a short paper named "A toroidal solution of the vacuum Einstein field equations", Kip S. Thorne suggested that an external field of gravitating toroidal source requires introducing cuts and identifications in order to be expressed in Weyl coordinates with their attractively simple form of field equations. Since then only 10 papers seem to have this result in their references and only one actually uses Thorne's result. Among others, I will show how these cuts and identifications necessarily arise from the analytic properties of transformations leading to Weyl metric, what coordinates should be used to get smooth metric, and how one can find metric of this spacetime numerically.
The main observable for the detection of gravitational waves in general relativity generated by compact binary systems is the phase of the wave. Within the post-Newtonian approximation, where the objects are assumed to be well-separated and to have small velocities, one can obtain analytical expressions for the phase as a series in $(v/c)^2$. Before this work, the phase (as well as the complete waveform) was known up to 3.5 post-Newtonian (PN) order. In this talk, I will discuss our recent computation of the flux and phase at 4.5PN order, as well as the $(\ell,m)=(2,2)$ mode at 4PN order. I will give a brief overview of the different steps leading to this results, then will discuss more in detail my work on the tails of memory. Finally, I will discuss what is needed to obtain all the $(\ell,m)$ modes entering the 4PN waveform, and how the tail-of-memory methodology will be central to it.
It is commonly held that the propagator for the massless vector field in de Sitter in the general covariant gauge has to respect all the symmetries of the maximally symmetric background. However, this is precluded by the Ward-Takahashi identity that has gone unnoticed thus far. I will present the recent construction of the photon propagator that satisfies all the conditions of a consistently quantized theory, and that maintains all de Sitter symmetries except spatial special conformal transformations. This propagator vanishes in the infrared, opposed to previously reported solutions that satisfied just the propagator equation of motion. Even though the de Sitter breaking pertains to the gauge sector, it is important when interactions are considered. I will discuss the energy-momentum tensor as the simplest one-loop observable to demonstrate further problems arising from failing to account for the Ward-Takahashi identity and the de Sitter breaking it requires.
It is a well-known fact that light is bent around strongly gravitating objects, such as black holes or neutron stars. However, not only gravitation itself, but also plasma surrounding the relativistic object affects the light rays. Both factors need to be considered when dealing with realistic estimates of light trajectories in astrophysical situations. We obtained a general formula for deflection angle in an axially symmetric spacetime surrounded by a dispersive and refractive medium. We studied in particular the Hartle-Thorne metric – an axially symmetric spacetime with an arbitrary quadrupole moment which is known to describe appropriately spacetimes outside rapidly rotating neutron stars. We compared the results with those obtained for other spacetimes (Kerr, Schwarzschild, etc.) where the quadrupole moment is fixed by mass and angular momentum. The calculations were performed in the weak field limit and illustrated graphically. Moreover, some preliminary results of my other project related with gravitational lensing will be sketched.
I discuss sensitivity of black hole thermodynamics to certain boundary terms in the gravitational action. In some cases, boundary terms can alter both the black hole entropy and temperature. Remarkably, this behaviour is confirmed by both covariant phase space (Iyer-Wald) and Euclidean (Brown-York) methods. I demonstrate our results on the example of the Gauss-Bonnet boundary term in 4D, both in purely metric and scalar-tensor theories.
Non-linear memory is one of the most intriguing predictions of general relativity which is generated by the passage of gravitational waves (GWs) leaving the spacetime permanently deformed. For example a GW signal from binary black hole (BBH) will have two parts the oscillatory part which is known as the “chirp” and a much fainter non-oscillatory (DC like) part which is non-linear memory. A non-linear memory is produced by all the sources of GWs and has the peculiarity that even if the oscillatory part of the source lies at high frequency the non-linear memory will be available at low frequency. This property of non-linear memory makes it a valuable resource for GW astronomy.
In this talk I will provide and introduction to how we can use gravitational waves memory as a resource for the current and future ground based detectors. To do this I will motivate how we can creatively use the non-linear memory to probe seemingly inaccessible sources of GWs like ultra low mass compact binary mergers where the oscillatory part lies at outside the reach of any current detectors and only non-linear memory could be detected if these sources exist. And the matter effects from neutron stars which are at high frequency but non-linear memory is accessible.
The non-linear memory effect perfectly exemplifies the current times in gravitational waves physics, as this is a subtle effect but since we are now in the era of multiple detections of GW we can afford to think about subtle effects and rare events.
I will present an extension of Misner's periodic time identification of Taub-NUT spacetime to a general family of Plebański-Demiański black holes (mass, acceleration, cosmological constant, Kerr and NUT parameters), including toroidal and higher genus black holes. This allows for regularization of the axis of rotation and in some cases a completely non-singular spacetime. The approach is based on imposing a structure of a suitable U(1)-bundle, corollary of which is an interpretation of the NUT parameter as a topological invariant.
Relation to classification of Isolated Horizons, as well as global structure of the spacetimes will be discussed.
Jiří Bičák Oldřich Semerák