Kip S. Thorne

LIGO: The Laser Interferometer Gravitational-Wave Observatory

The goal of the Laser Interferometer Gravitational-Wave Observatory (LIGO) Project is to detect and study astrophysical gravitational waves and use data from them for research in physics and astronomy. LIGO will support studies concerning the nature and nonlinear dynamics of gravity, the structures of black holes, and the equation of state of nuclear matter. It will also measure the masses, birth rates, collisions, and distributions of black holes and neutron stars in the universe and probe the cores of supernovae and the very early universe. The technology for LIGO has been developed during the past 20 years. Construction will begin in 1992, and under the present schedule, LIGOs gravitational-wave searches will begin in 1998.

Black Holes: The Membrane Paradigm

The physics of black holes is explored in terms of a membrane paradigm which treats the event horizon as a two-dimensional membrane embedded in three-dimensional space. A 3+1 formalism is used to split Schwarzschild space-time and the laws of physics outside a nonrotating hole, which permits treatment of the atmosphere in terms of the physical properties of thin slices. The model is applied to perturbed slowly or rapidly rotating and nonrotating holes, and to quantify the electric and magnetic fields and eddy currents passing through a membrane surface which represents a stretched horizon. Features of tidal gravitational fields in the vicinity of the horizon, quasars and active galalctic nuclei, the alignment of jets perpendicular to accretion disks, and the effects of black holes at the center of ellipsoidal star clusters are investigated. Attention is also given to a black hole in a binary system and the interactions of black holes with matter that is either near or very far from the event horizon. Finally, a statistical mechanics treatment is used to derive a second law of thermodynamics for a perfectly thermal atmosphere of a black hole.

Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity

Rapid interstellar travel by means of spacetime wormholes is described in a way that is useful for teaching elementary general relativity. The description touches base with Carl Sagan’s novel Contact, which, unlike most science fiction novels, treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Many objections are given against the use of black holes or Schwarzschild wormholes for rapid interstellar travel. A new class of solutions of the Einstein field equations is presented, which describe wormholes that, in principle, could be traversed by human beings. It is essential in these solutions that the wormhole possess a throat at which there is no horizon; and this property, together with the Einstein field equations, places an extreme constraint on the material that generates the wormhole’s spacetime curvature: In the wormhole’s throat that material must possess a radial tension τ0 with the enormous magnitude τ0∼ (pressure at the center of the most massive of ne...

Quantum nondemolition measurements

Some future gravitational-wave antennas will be cylinders of mass ∼100 kilograms, whose end-to-end vibrations must be measured so accurately (10–19 centimeter) that they behave quantum mechanically. Moreover, the vibration amplitude must be measured over and over again without perturbing it (quantum nondemolition measurement). This contrasts with quantum chemistry, quantum optics, or atomic, nuclear, and elementary particle physics, where one usually makes measurements on an ensemble of identical objects and does not care whether any single object is perturbed or destroyed by the measurement. This article describes the new electronic techniques required for quantum nondemolition measurements and the theory underlying them. Quantum nondemolition measurements may find application elsewhere in science and technology.

Conversion of conventional gravitational-wave interferometers into quantum nondemolition interferometers by modifying their input and/or output optics

The LIGO-II gravitational-wave interferometers (ca. 2006–2008) are designed to have sensitivities near the standard quantum limit (SQL) in the vicinity of 100 Hz. This paper describes and analyzes possible designs for subsequent LIGO-III interferometers that can beat the SQL. These designs are identical to a conventional broad band interferometer (without signal recycling), except for new input and/or output optics. Three designs are analyzed: (i) a squeezed-input interferometer (conceived by Unruh based on earlier work of Caves) in which squeezed vacuum with frequency-dependent (FD) squeeze angle is injected into the interferometer’s dark port; (ii) a variational-output interferometer (conceived in a different form by Vyatchanin, Matsko and Zubova), in which homodyne detection with FD homodyne phase is performed on the output light; and (iii) a squeezed-variational interferometer with squeezed input and FD-homodyne output. It is shown that the FD squeezed-input light can be produced by sending ordinary squeezed light through two successive Fabry-Perot filter cavities before injection into the interferometer, and FD-homodyne detection can be achieved by sending the output light through two filter cavities before ordinary homodyne detection. With anticipated technology (power squeeze factor e-2R=0.1 for input squeezed vacuum and net fractional loss of signal power in arm cavities and output optical train e*=0.01) and using an input laser power Io in units of that required to reach the SQL (the planned LIGO-II power, ISQL), the three types of interferometer could beat the amplitude SQL at 100 Hz by the following amounts μ≡sqrt[Sh]/sqrt[ShSQL] and with the following corresponding increase V=1/μ3 in the volume of the universe that can be searched for a given noncosmological source: Squeezed input —μ≃sqrt[e-2R]≃0.3 and V≃1/0.33≃30 using Io/ISQL=1. Variational-output—μ≃e*1/4≃0.3 and V≃30 but only if the optics can handle a ten times larger power: Io/ISQL≃1/sqrt[e*]=10. Squeezed varational —μ=1.3(e-2Re*)1/4≃0.24 and V≃80 using Io/ISQL=1; and μ≃(e-2Re*)1/4≃0.18 and V≃180 using Io/ISQL=sqrt[e-2R/e*]≃3.2.

The last three minutes: Issues in gravitational-wave measurements of coalescing compact binaries

Gravitational-wave interferometers are expected to monitor the last three minutes of inspiral and final coalescence of neutron star and black hole binaries at distances approaching cosmological, where the event rate may be many per year. Because the binary’s accumulated orbital phase can be measured to a fractional accuracy ≪10^-3 and relativistic effects are large, the wave forms will be far more complex and carry more information than has been expected. Improved wave form modeling is needed as a foundation for extracting the waves’ information, but is not necessary for wave detection.

An Overview of Gravitational-Wave Sources

Major relativity conferences such as GR16 traditionally include an overview talk on gravitational wave (GW) sources. Some excellent recent ones include those by Flanagan , Finn , and Bender et al. . Such talks are always by theorists, and can be described as basically informed speculation, since until now detectors sufficiently sensitive to detect GW’s have not existed. But km-scale laser interferometers (IFO’s) are now coming on-line, and it seems very likely these will detect mergers of compact binaries within the next seven years, and possibly much sooner. There are several other classes of sources that the ground-based IFO’s might well detect: massive star collapse (supernovae and hypernovae), rapidly rotating neutron stars, and possibly a GW stochastic background created in the early universe. A space-based interferometer, LISA, is also planned (though not yet fully funded), and could fly in ∼ 2011. There is one type of source — short-period galactic binaries — that LISA is guaranteed to observe (at its planned sensitivity), plus a list of very promising candidates: the inspiral and merger of supermassive black holes (SMBH’s), the inspiral and capture of compact objects by SMBH’s, and sources in the very early universe. In this article we review the various GW sources that have been studied, for both ground and space-based detectors, summarizing the best available

The relativistic equations of stellar structure and evolution

The general-relativistic equations of stellar structure and evolution are reformulated in a notation which makes easy contact with Newtonian theory. Also, a general-relativistic version of the mixing-length formalism for convection is presented.

Thermoelastic noise and homogeneous thermal noise in finite sized gravitational-wave test masses

An analysis is given of thermoelastic noise (thermal noise due to thermoelastic dissipation) in finite sized test masses of laser interferometer gravitational-wave detectors. Finite-size effects increase the thermoelastic noise by a modest amount; for example, for the sapphire test masses tentatively planned for LIGO-II and plausible beam-spot radii, the increase is ≲10 percent. As a side issue, errors are pointed out in the currently used formulas for conventional, homogeneous thermal noise (noise associated with dissipation which is homogeneous and described by an imaginary part of the Young’s modulus) in finite sized test masses. Correction of these errors increases the homogeneous thermal noise by ≲5 percent for LIGO-II-type configurations.

Gravitational waves from coalescing black hole MACHO binaries

If MACHOs are black holes of mass ~0.5 M☉, they must have been formed in the early universe when the temperature was ~1 GeV. We estimate that in this case in our Galaxys halo out to ~ 50 kpc there exist ~5×108 black hole binaries the coalescence times of which are comparable to the age of the universe, so that the coalescence rate will be ~5×10−2 events yr-1 per galaxy. This suggests that we can expect a few events per year within 15 Mpc. The gravitational waves from such coalescing black hole MACHOs can be detected by the first generation of interferometers in the LIGO/VIRGO/TAMA/GEO network. Therefore, the existence of black hole MACHOs can be tested within the next 5 yr by gravitational waves.