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Gravitational waves

Alessandra Buonanno

TL;DR

These lectures present a comprehensive introduction to gravitational-wave theory and sources, spanning linearized gravity, GW generation, interaction with matter, and detection. The approach combines analytic methods, post-Newtonian expansions, effective-field theory perspectives, and numerical relativity results to build accurate inspiral–merger–ring-down templates. Key contributions include a clear derivation of the quadrupole emission, treatment of GW energy flux via the effective stress-energy tensor, and practical data-analysis templates for binaries, pulsars, and cosmological backgrounds. The work emphasizes the interplay between theory and experiment across ground- and space-based detectors and outlines cosmological sources such as phase transitions and cosmic strings, highlighting their detectability prospects and current bounds.

Abstract

These lectures are envisioned to be an introductory, basic course in gravitational-wave physics.

Gravitational waves

TL;DR

These lectures present a comprehensive introduction to gravitational-wave theory and sources, spanning linearized gravity, GW generation, interaction with matter, and detection. The approach combines analytic methods, post-Newtonian expansions, effective-field theory perspectives, and numerical relativity results to build accurate inspiral–merger–ring-down templates. Key contributions include a clear derivation of the quadrupole emission, treatment of GW energy flux via the effective stress-energy tensor, and practical data-analysis templates for binaries, pulsars, and cosmological backgrounds. The work emphasizes the interplay between theory and experiment across ground- and space-based detectors and outlines cosmological sources such as phase transitions and cosmic strings, highlighting their detectability prospects and current bounds.

Abstract

These lectures are envisioned to be an introductory, basic course in gravitational-wave physics.

Paper Structure

This paper contains 29 sections, 152 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Linearization of Einstein equations
  3. Einstein equations and gauge symmetry
  4. Wave equation
  5. Transverse-traceless gauge
  6. Interaction of gravitational waves with point particles
  7. Newtonian and relativistic description of tidal gravity
  8. Description in the transverse-traceless gauge
  9. Description in the free-falling frame
  10. Key ideas underlying gravitational-wave detectors
  11. Effective stress-energy tensor of gravitational waves
  12. Generation of gravitational waves
  13. Sources in slow motion, weak-field and negligible self-gravity
  14. Sources in slow motion and weak-field, but non-negligible self-gravity
  15. Radiated energy, angular momentum and linear momentum
  16. ...and 14 more sections

Figures (7)

  • Figure 1: We show how point particles along a ring move as a result of the interaction with a GW propagating in the direction perpendicular to the plane of the ring. The left panel refers to a wave with $+$ polarization, the right panel with $\times$ polarization.
  • Figure 2: Lines of force associated to the $+$ (left panel) and $\times$ (right panel) polarizations.
  • Figure 3: We plot the square root of the noise spectral density versus frequency for the three LIGO detectors together with the LIGO noise curve at designed sensitivity . The noise curves refer to June 2006, during the fifth scientific run.
  • Figure 4: We sketch the curvature potential as function of the tortoise coordinate $r^*$ associated to metric perturbations of a Schwarzschild BH. The potential peaks at the last unstable orbit for a massless particle (the light ring). Ingoing modes propagate toward the BH horizon, whereas outgoing modes propagate away from the source.
  • Figure 5: On the left panel we show the GW signal from an equal-mass nonspinning BH binary as predicted at 2.5PN order by Buonanno and Damour (2000) in Ref. EOB. The merger is assumed almost instantaneous and one QNM is included. On the right panel we show the GW signal from an equal-mass BH binary with a small spin $\chi_1=\chi_2 = 0.06$ obtained in full general relativity by Pretorius BCP
  • ...and 2 more figures