Dott. A.Rocchi, R. Peron
Gravitational Physics
(S3, elective, 6 ECTS)
Learning Outcomes:The class is aimed at providing an advanced preparation on Physics, in particular in the field of experimental gravitation. The educational objectives include knowledge of relativistic physics and experimental methods for the verification of the different metric theories of gravitation.
Knowledge and Understanding:
Students will have to demonstrate a good understanding of the most important theories of gravitation and related experimental problems. The verification of knowledge and understanding is done through an oral test.
Applying Knowledge and Understanding:Students must be able to identify the essential elements of a physical problem (even a complex one) and learn how to create an approximate model. They must be able to update these models by comparing them with existing experimental data.
PrerequisitesBasics of Physics and Mathematical methods for Physics
ProgramNewtonian gravitation (Potential theory, Newtonian fluid dynamics, Conserved quantities – Bodies with spherical/non-spherical symmetry, Geodesy, Tides – Keplerian motion, Perturbative methods – Tests of inverse-square law, Measurements of G). Foundations (Equivalence Principle (WEP, EEP, SEP) and its experimental tests). Post-Newtonian gravitation (PPN formalism, Main PPN effects, Equations of motion, Gravitomagnetism, PPN effects around Earth). Experimental tests of PPN gravitation (Gravitational test mass, Tracking techniques (SLR, radiometric), Geodetic satellites, Satellite dynamics in Earth orbit, Reference frames, POD of geodynamic satellites, GNSS, LLR, Cassini and other deep-space missions, BepiColombo, ISA). Tests of General Relativity with radio observations of binary neutron star systems. Pulsar Timing: relativistic corrections to Time of Arrivals. Post Keplerian parameters in the PPN formalism. Observational results from some peculiar systems: PSR B1913+16; PSR B1534+12; PSR J0737−3039A/B. Basics on gravitational waves. Description of the dynamic evolution of a binary system of compact objects in the PPN formalism. Tests of General Relativity: waveform consistency; massive graviton; speed of GWs; equivalence principle; polarization states.
Description of how the course is conducted
Description of the didactic methods
Description of the evaluation methodsThe student’s assessment includes an oral test in which questions are proposed on the entire program of the class. The student will have to demonstrate to have acquired a sufficient knowledge of the different metric theories of gravity, of their implications and of the actual experimental methodologies used for the verification of the different theories. In particular, the student must be able to discuss the fundamental limits to the accuracy of the measurements.
Adopted TextbooksH.C. Ohanian, R. Ruffini, Gravitation and space-time, Cambridge University Press, 2013 (3) E. Poisson and C.M. Will, Gravity: Newtonian, Post-Newtonian, Relativistic, Cambridge University Press, 2014 M. Maggiore Gravitational Waves Volume 1. Theory and Experiments Oxford University Press
Recommended readingsC.M. Will, The Confrontation between General Relativity and Experiment, Living Rev. Relativity 17, (2014), 4 S.M. Merkowitz, Tests of Gravity Using Lunar Laser Ranging, Living Rev. Relativity 13, (2010), 7 A. G. Lyne et al., A Double-Pulsar System: A Rare Laboratory for Relativistic Gravity and Plasma Physics, Science 303 (2004) M. Kramer et al., Tests of General Relativity from Timing the Double Pulsar, Science 314 (2006) I. Ciufolini and J. A. Wheeler, Gravitation and Inertia, Princeton University Press, 1995 B. Bertotti, P. Farinella, and D. Vokrouhlický, Physics of the Solar System — Dynamics and Evolution, Space Physics, and Spacetime Structure, Kluwer Academic Publishers, 2003 O. Montenbruck and E. Gill, Satellite Orbits — Models, Methods and Applications, Springer, 2000 B. P. Abbott et al., “Observation of Gravitational Waves from a Binary Black Hole Merger”, Phys. Rev. Lett. 116, 061102 (2016) B. P. Abbott et al., “Tests of General Relativity with GW150914”,Phys. Rev. Lett. 116, 221101 (2016) B. P. Abbott et al., “GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence”, Phys. Rev. Lett. 119, 141101 (2017) B. P. Abbott et al., “Tests of General Relativity with the Binary Black Hole Signals from the LIGO-Virgo Catalog GWTC-1”, arXiv:1903.04467v2