New theoretical frameworks for compact objects and their perturbations

The detection of gravitational waves (GW) has revolutionized our way of observing the Universe. Thanks to GW signals, we can now explore features of astrophysical objects which were impossible to detect only a few years ago. In particular, we can probe deeper into the structure of compact relativistic objects and their evolution. Such an advance in detection measurement requires an equal advance in theoretical tools within which such objects can be understood.

This project aims to develop such tools. In particular, the objective will be to use covariant formalisms to construct relativistic models of compact stars and study their properties with particular attention to the interaction that such objects might have with gravitational waves. This work involves the careful study of solutions of the equations of relativistic hydrostatic equilibrium and the determination of the evolution of the perturbations of such solutions.

The project will start with the analysis of compact objects solutions in the context of General Relativity considering several (combinations of) fluid sources. The knowledge acquired by this preliminary activity will be applied to the study of these solutions in the context of extensions of General Relativity. The aim will be to consolidate our lore on the known theoretical models and offer a way to test General Relativity using the new data coming from the present and next generation of gravitational waves detectors.

References:

• The covariant formalisms

1. Ellis, George FR, Roy Maartens, and Malcolm AH MacCallum. Relativistic cosmology. Cambridge University Press, 2012.
2. Clarkson, Chris A., and Richard K. Barrett. „Covariant perturbations of Schwarzschild black holes.“ Classical and Quantum Gravity 20.18 (2003): 3855.

• The theory of compact stars: general

1. Shapiro, Stuart L., et al. „The physics of compact objects.“ Wiley, New York 19832 (1983): 119–123.

• The theory of compact stars: covariant

2. Carloni, Sante, and Daniele Vernieri. „Covariant Tolman-Oppenheimer-Volkoff equations. ii. the anisotropic case.“ Physical Review D 97.12 (2018): 124057.
3. Carloni, Sante, and Daniele Vernieri. „Covariant Tolman-Oppenheimer-Volkoff equations. i. the isotropic case.“ Physical Review D 97.12 (2018): 124056.
4. Luz, Paulo, and Sante Carloni. „Static compact objects in Einstein-Cartan theory.“ Physical Review D 100.8 (2019): 084037.
5. Naidu, Nolene F., Sante Carloni, and Peter Dunsby. „Two-fluid stellar objects in General Relativity: the covariant formulation.“ arXiv preprint arXiv:2102.05693 (2021).