Clifford M. Will

The Confrontation between General Relativity and Experiment

The status of experimental tests of general relativity and of theoretical frameworks for analyzing them is reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the Eötvös experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse-Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves.

CONSERVATION LAWS AND PREFERRED FRAMES IN RELATIVISTIC GRAVITY. I. PREFERRED-FRAME THEORIES AND AN EXTENDED PPN FORMALISM.

PREFERRED FRAMES IN RELATIVISTIC GRAVITY { C A .thru C. M Will, et al (Jet Propulsion Lab.) May / N72-2736

The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement

We discuss the IAU resolutions B1.3, B1.4, B1.5, and B1.9 that were adopted during the 24th General Assembly in Manchester, 2000, and provides details on and explanations for these resolutions. It is explained why they present significant progress over the corresponding IAU 1991 resolutions and why they are necessary in the light of present accuracies in astrometry, celestial mechanics, and metrology. In fact, most of these resolutions are consistent with astronomical models and software already in use. The metric tensors and gravitational potentials of both the Barycentric Celestial Reference System and the Geocentric Celestial Reference System are defined and discussed. The necessity and relevance of the two celestial reference systems are explained. The transformations of coordinates and gravitational potentials are discussed. Potential coefficients parameterizing the post-Newtonian gravitational potentials are expounded. Simplified versions of the time transformations suitable for modern clock accuracies are elucidated. Various approximations used in the resolutions are explicated and justified. Some models (e.g., for higher spin moments) that serve the purpose of estimating orders of magnitude have actually never been published before.

Black Hole Normal Modes: A Semianalytic Approach

A new semianalytic technique for determining the complex normal mode frequencies of black holes is presented. The method is based on the WKB approximation. It yields a simple analytic formula that gives the real and imaginary parts of the frequency in terms of the parameters of the black hole and of the field whose perturbation is under study, and in terms of the quantity (n + 1/2), where n = 0, 1, 2,... and labels the fundamental mode, first overtone mode, and so on. In the case of the fundamental gravitational normal modes of the Schwarzschild black hole, the WKB estimates agree with numerical results to better than 7 percent in the real part of the frequency and 0.7 percent in the imaginary part, with the relative agreement improving with increasing angular harmonic. Carried to higher order the method may provide an accurate and systematic means to study black hole normal modes.

Gravitational-wave spectroscopy of massive black holes with the space interferometer LISA

Newly formed black holes are expected to emit characteristic radiation in the form of quasinormal modes, called ringdown waves, with discrete frequencies. LISA should be able to detect the ringdown waves emitted by oscillating supermassive black holes throughout the observable Universe. We develop a multimode formalism, applicable to any interferometric detectors, for detecting ringdown signals, for estimating black-hole parameters from those signals, and for testing the no-hair theorem of general relativity. Focusing on LISA, we use current models of its sensitivity to compute the expected signal-to-noise ratio for ringdown events, the relative parameter estimation accuracy, and the resolvability of different modes. We also discuss the extent to which uncertainties on physical parameters, such as the black-hole spin and the energy emitted in each mode, will affect our ability to do black-hole spectroscopy.

Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order

The rate of gravitational-wave energy loss from inspiralling binary systems of compact objects of arbitrary mass is derived through second post-Newtonian (2PN) order O[(Gm/rc 2 ) 2 ] beyond the quadrupole approximation. The result has been derived by two independent calculations of the (source) multipole moments. The 2PN terms, and in particular the finite mass contribution therein (which cannot be obtained in perturbation calculations of black hole spacetimes), are shown to make a significant contribution to the accumulated phase of theoretical templates to be used in matched filtering of the data from future gravitational-wave detectors.

Bounding the mass of the graviton using gravitational wave observations of inspiralling compact binaries

If gravitation is propagated by a massive field, then the velocity of gravitational waves (gravitons) will depend upon their frequency as

Estimating spinning binary parameters and testing alternative theories of gravity with LISA

{(v}_{g}{/c)}^{2}=1\ensuremath{-}(c/f{\ensuremath{\lambda}}_{g}{)}^{2}

Testing the General Relativistic “No-Hair” Theorems Using the Galactic Center Black Hole Sagittarius A*

, and the effective Newtonian potential will have a Yukawa form

Was Einstein right? : putting general relativity to the test

\ensuremath{\propto}{r}^{\ensuremath{-}1}\mathrm{exp}(\ensuremath{-}r/{\ensuremath{\lambda}}_{g})