Gravitational radiation with a positive cosmological constant
Open Access
- Author:
- Bonga, Beatrice Philipine
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 05, 2017
- Committee Members:
- Abhay Vasant Ashtekar, Dissertation Advisor/Co-Advisor
Abhay Vasant Ashtekar, Committee Chair/Co-Chair
Eugenio Bianchi, Committee Member
Sarah Elizabeth Shandera, Committee Member
Ping Xu, Outside Member - Keywords:
- gravitational radiation
cosmological constant
dark energy
transverse-traceless modes
asymptotics
quadrupole formula - Abstract:
- Gravitational radiation is well-understood in spacetimes that are asymptotically flat. However, our Universe is currently expanding at an accelerated rate, which is best described by including a positive cosmological constant, $\Lambda$, in Einstein's equations. Consequently, no matter how far one recedes from sources generating gravitational waves, spacetime curvature never dies and is not asymptotically flat. This dissertation provides first steps to incorporate $\Lambda$ in the study of gravitational radiation by analyzing linearized gravitational waves on a de Sitter background. Since the asymptotic structure of de Sitter is very different from that of Minkowski spacetime, many conceptual and technical difficulties arise. The limit $\Lambda \to 0$ can be discontinuous: Although energy carried by gravitational waves is always positive in Minkowski spacetime, it can be arbitrarily negative in de Sitter spacetime. Additionally, many of the standard techniques, including $1/r$ expansions, are no longer applicable. We generalize Einstein's celebrated quadrupole formula describing the power radiated on a flat background to de Sitter spacetime. Even a tiny $\Lambda$ brings in qualitatively new features such as contributions from pressure quadrupole moments. Nonetheless, corrections induced by $\Lambda$ are $\ord (\sqrt{\Lambda} t_c)$ with $t_c$ the characteristic time scale of the source and are negligible for current gravitational wave observatories. We demonstrate this explicitly for a binary system in a circular orbit. Radiative modes are encoded in the transverse-traceless part of the spatial components of a gravitational perturbation. When $\Lambda=0$, one typically extracts these modes in the wave zone by projecting the gravitational perturbation onto the two-sphere orthogonal to the radial direction. We show that this method for waves emitted by spatially compact sources on Minkowski spacetime generically does not yield the transverse-traceless modes; not even infinitely far away. However, the difference between the transverse-traceless and projected modes is non-dynamical and disappears from all physical observables. When one is interested in `Coulombic' information not captured by the radiative modes, the projection method does not suffice. This is, for example, important for angular momentum carried by gravitational waves. This result relies on Bondi-type expansions for asymptotically flat spacetimes. Therefore, the projection method is not applicable to de Sitter spacetimes.