Physics
Gravity Waves
Gravity waves are ripples in the curvature of spacetime caused by accelerating masses, as predicted by Einstein's theory of general relativity. These waves propagate at the speed of light and are generated by cataclysmic events such as the collision of black holes or the merging of neutron stars. They provide a new way to observe and study the universe, offering insights into phenomena that are otherwise invisible.
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11 Key excerpts on "Gravity Waves"
eBook - PDFGravity from the Ground Up
An Introductory Guide to Gravity and General Relativity
- Bernard Schutz(Author)
- 2003(Publication Date)
- Cambridge University Press(Publisher)
Gravitational waves: gravity speaks 22 22 O ne of the most radical changes in the behavior of gravity in going from In this chapter: we meet the dynamical part of gravity. Gravitational waves are generated by mass-energy motions, carry energy, and act transversely as they pass through matter. Binary systems, involving compact stars or black holes, are the most important sources of detectable waves. The first detections are likely to be made by interferometers now under construction. The low-frequency observing window will be opened after 2010 by the planned international space-based lisa detector. Newton’s theory to Einstein’s is that Einstein’s gravity has waves. When two stars orbit one another in a binary system, the gravitational field they create is constantly changing, responding to the changes in the positions of the stars. In any theory of gravity that respects special relativity, the information about these changes cannot reach distant experimenters faster than light. In general relativity, these changes in gravity ripple outwards at exactly the speed of light. These gravitational waves offer a new way of observing astronomical systems whose gravity is changing. They are an attractive form of radiation to observe, because they are not scattered or absorbed by dust or plasma between the radiat- ing system and the Earth: as we saw in Chapter 1, gravity always gets through. Unfortunately, the weakness of gravity, which we also noted in Chapter 1, poses a severe problem. Gravitational waves affect laboratory equipment so little that only recently has it become possible to build instruments sensitive enough to register them. In this chapter we will learn what gravitational waves are, why scientists are confident that general relativity describes them correctly, how they are emitted by astronomical bodies, and what efforts are underway to detect them.
eBook - PDFGravitation
Foundations and Frontiers
- T. Padmanabhan(Author)
- 2010(Publication Date)
- Cambridge University Press(Publisher)
9 Gravitational waves 9.1 Introduction One of the key new phenomena that arises in general relativity is the existence of solutions to Einstein’s equations which represent disturbances in the spacetime that propagate at the speed of light. Such solutions are called gravitational waves and this chapter will explore several features of them. 1 9.2 Propagating modes of gravity Within the context of special relativity, it is easy to identify a wave solution. For example, a propagating, monochromatic spherical wave will be described by an amplitude that varies in space and time as f ( t, r ) ∝ r − 1 exp[ − iω ( t − r )] . This disturbance clearly propagates from the origin with the speed of light (which is unity in our notation) with an amplitude that decreases as (1 /r ) . Since the energy flux of a wave varies as the square of the amplitude, this wave transports a constant amount of energy across every spherical surface. Such a description can be easily made Lorentz covariant in terms of an appropriate wave vector, etc., and has an unambiguous meaning. The situation is somewhat more complicated in the case of gravity for two (closely related) reasons. First, not all the components of the metric g ab enjoy equal status in the dynamics of gravity. We saw in Section 6.3 that the g 00 and g 0 α com-ponents do not propagate in general relativity. The equations governing them are constraint equations involving G 0 0 and G 0 α and are analogous to the equation gov-erning the gauge dependent mode in electrodynamics. Recall that, in the case of electrodynamics without sources , only the two transverse degrees of freedom of the vector potential represent a genuine electromagnetic wave propagating with the speed of light. The scalar potential as well as the longitudinal part of the vector potential can be eliminated by a suitable choice of gauge. The two residual degrees of freedom represent the two physical degrees of freedom of a massless spin-1 399
- Peter R Saulson(Author)
- 1994(Publication Date)
- World Scientific(Publisher)
Chapter 2 T H E N A T U R E O F G R A V I T A T I O N A L WAVES The existence of wave solutions to Einstein's field equations is, arguably, the most relativistic feature of the theory of gravitation known as the General Theory of Relativity. This is true in the sense that it is the instantaneous action-at-a-distance of Newtonian gravity that most offends our notions of causality as understood in the context of the Special Theory of Relativity. Newton's theory, taken literally, would predict that the gravitational field produced by a mass always has the familiar I / r s form, with r referring to its present position, no matter how rapidly it might move (or accelerate), and no matter how far away from it we consider its field. General relativity fixes the problem posed by moving sources of a gravitational field. It proposes that the gravitational field (that is, the curvature of space-time) does not change instantaneously at arbitrary distances from a moving source. Instead, in a manner deeply analogous to electromagnetic waves, the news of the motion of a source of space-time curvature propagates at the speed of light. In this chapter, we wili briefly examine how gravitational waves of finite speed arise in general relativity. Then we will discuss the interaction of gravitational waves with systems of test bodies, and consider how such interactions may be observed. 2.1 Waves in General Relativity One of the most fundamental concepts in the Special Theory of Relativity is that the s p a c e -t i m e i n t e r v a l d s between any two neighboring points is given by the expression d s 2 = ~ c 2 d t 2 + d x 2 + d y 1 + d z 1 (2.1) d s 2 = i f o f r d z W , with the Minkowski metric given, in Cartesian coordinates, by (2.2) / -1 0 0 0 > 0 1 0 0 0 0 1 0 o 0 0 1 i (2.3] 10 The Nature of Gravitational Waves Note that in Eq. 2.1 all of the superscripts indicate raising to the second power, while in E q .
- Peter R Saulson(Author)
- 2017(Publication Date)
- WSPC(Publisher)
The Nature of Gravitational Waves2The existence of wave solutions to Einstein’s field equations is, arguably, the most “relativistic” feature of the theory of gravitation known as the General Theory of Relativity. This is true in the sense that it is the instantaneous action-at-a-distance of Newtonian gravity that most offends our notions of causality as understood in the context of the Special Theory of Relativity. Newton’s theory, taken literally, would predict that the gravitational field produced by a mass always has the familiar 1/r2 form, with r referring to its present position, no matter how rapidly it might move (or accelerate), and no matter how far away from it we consider its field.General relativity fixes the problem posed by moving sources of a gravitational field. It proposes that the gravitational field (that is, the curvature of space-time) does not change instantaneously at arbitrary distances from a moving source. Instead, in a manner deeply analogous to electromagnetic waves, the “news” of the motion of a source of space-time curvature propagates at the speed of light.In this chapter, we will briefly examine how gravitational waves of finite speed arise in general relativity. Then we will discuss the interaction of gravitational waves with systems of test bodies, and consider how such interactions may be observed.2.1Waves in General RelativityOne of the most fundamental concepts in the Special Theory of Relativity is that the space-time interval ds between any two neighboring points is given by the expression
or(2.1) (2.2) with the Minkowski metric ηµνgiven, in Cartesian coordinates, by(2.3) Note that in Eq. 2.1 all of the superscripts indicate raising to the second power, while in Eq. 2.2 the Greek indices range from 0 to 3 to represent t, x, y, and z, respectively. Equation 2.2
eBook - PDF- Hans C. Ohanian, Remo Ruffini(Authors)
- 2013(Publication Date)
- Cambridge University Press(Publisher)
5 Gravitational waves If you ask me whether there are gravitational waves or not, I must answer that I do not know. But it is a highly interesting problem. Albert Einstein Gravitational effects cannot propagate with infinite speed. This is obvious both from the lack of Lorentz invariance of infinite speed and from the causality violations that are associated with signal speeds in excess of the speed of light. Since the speed of light is the only Lorentz-invariant speed, we expect that gravitational effects propagate in the form of waves at the speed of light. As a concrete example, consider an apple that hangs on a tree. At some time, the stem of the apple breaks and the apple falls to the ground, which means there is a sudden change in the terrestrial mass distribution. The gravitational field surrounding the Earth must then adapt itself to this new mass distribution. The change in the field will not occur simultaneously throughout the universe – at any given point of space the change will be delayed by a time equal to the time needed for a light signal to travel from the Earth to that point. Hence the disturbance in the gravitational field propagates outward at the speed of light. Such a propagating disturbance is a gravitational wave. The existence of gravitational waves is an immediate consequence of special relativity, and, to some extent, the experimental discovery of gravitational waves would merely confirm the obvious. Although the existence of waves is ensured by general arguments, the strength and type of wave depend on the details of the gravitational theory, and hence the experimental investigation of the properties of the waves would serve as a test of the theory. Even more important, gravitational-wave astronomy would be a useful adjunct to optical, radio, and X-ray astronomy. Gravitational waves would permit us to “look” into the very cores of quasars and other regions of strong gravitational fields.
eBook - PDF- Bernard Schutz(Author)
- 2009(Publication Date)
- Cambridge University Press(Publisher)
Gravitational waves are hardly disturbed by matter at all. They follow the null geodesics even through matter. The reason is the weakness of their interaction with matter, as we saw in Eq. (9.24) . If the wave amplitudes h TT ij are small, then their effect on any matter they pass through is also small, and the back-effect of the matter on them will be of the same order of smallness. Gravitational waves are therefore highly prized carriers of information from distant regions of the universe: we can in principle use them to ‘see’ into the centers of supernova explosions, through obscuring dust clouds, or right back to the first fractions of a second after the Big Bang. 213 9.2 The detection of gravitational waves 9.2 The detection of gravitational waves General considerations The great progress that astronomy has made since about 1960 is due largely to the fact that technology has permitted astronomers to begin to observe in many different parts of the electromagnetic spectrum. Because they were restricted to observing visible light, the astronomers of the 1940s could have had no inkling of such diverse and exciting phenom-ena as quasars, pulsars, black holes in X-ray binaries, giant black holes in galactic centers, gamma-ray bursts, and the cosmic microwave background radiation. As technology has progressed, each new wavelength region has revealed unexpected and important informa-tion. Most regions of the electromagnetic spectrum have now been explored at some level of sensitivity, but there is another spectrum which is as yet completely untouched: the gravitational wave spectrum. As we shall see in § 9.5 below, nearly all astrophysical phenomena emit gravitational waves, and the most violent ones (which are of course among the most interesting ones!) give off radiation in copious amounts. In some situations, gravitational radiation carries information that no electromagnetic radiation can give us.
eBook - PDF- Charles W. Misner, Kip S. Thorne, John Archibald Wheeler(Authors)
- 2017(Publication Date)
- Princeton University Press(Publisher)
(1) approximate nature of a wave (2) local viewpoint vs. large-scale viewpoint Linearized theory of gravitational waves: (1) Lorentz gauge condition 944 35. PROPAGATION OF GRAVITATIONAL WAVES Ripples of what? Ripples in the shape of the ocean's surface; ripples in the shape (i.e., curvature) of spacetime. Both types of waves are idealizations. One cannot , with infinite accuracy, delineate at any moment which drops of water are in the waves and which are in the underlying ocean: Similarly, one cannot delineate precisely which parts of the spacetime curvature are in the ripples and which are in the cosmological background. But one can almost do so; otherwise one would not speak of "waves"! Look at the ocean from a rowboat. Waves dominate the seascape. Changes in angle and level of the surface occur every 30 feet or less. These changes propagate. They obey a simple wave equation + + L) (height of surface) = O. g at 4 ay2 ax 2 Now get more sophisticated. Notice from a spaceship the large-scale curvature of the ocean's surface-curvature because the Earth is round, curvature because the sun and the moon pull on the water. As waves propagate long distances, this curvature bends their fronts and changes slightly their simple wave equation. Also important over large distance are nonlinear interactions between waves, interaction with the wind, Coriolis forces due to the Earth's rotation, etc. Spacetime is similar. Propagating through the universe, according to Einstein's theory, must be a complex pattern of small-scale ripples in the spacetime curvature, ripples produced by binary stars, by supernovae, by gravitational collapse, by explosions in galactic nuclei. Locally ("rowboat viewpoint") one can ignore the interaction of these ripples with the large-scale curvature of spacetime and their nonlinear interaction with each other. One can pretend the waves propagate in fiat spacetime; and one can write down a simple wave equation for them.
eBook - PDFObservational Astronomy
Techniques and Instrumentation
- Edmund C. Sutton(Author)
- 2011(Publication Date)
- Cambridge University Press(Publisher)
16 Gravitational waves Few physicists today doubt the reality of gravitational radiation. The existence of gravitational waves is a firm prediction of the theory of general relativity, and grav- itational radiation is observed indirectly through the energy loss and decreasing orbital period of the Hulse–Taylor binary pulsar system PSR J1915+1606 (Hulse & Taylor, 1975). Observing gravitational radiation directly would certainly be a further confirmation of general relativity. But more importantly, observations of gravitational radiation will enable us to determine properties of regions and of times for which we otherwise have little information. The pioneering work of Joseph Weber using resonant bar detectors (Weber, 1966) is of great importance in this field and has inspired much of the observa- tional work that followed. Most books and reviews on gravitational wave detection begin with a discussion of Weber bars. In this chapter we concentrate on interfero- metric detectors, which seem at this time to hold the greatest promise for detecting gravitational waves. 16.1 Characteristics of gravitational radiation Gravitation is described in the field equations of general relativity as curvature of space-time. 1 In quantum field theory the mediator of the gravitational interaction is thought to be the massless, spin-2 graviton. In the classical limit these formula- tions are equivalent. Both predict the existence of gravitational radiation which is quadrupolar in nature. In a linearized theory, gravitational waves in free space are described as small perturbations h μν on the Minkowski flat space-time metric. 2 The perturbation 1 Space limitations force us to gloss over many of the subtleties of general relativity. 2 In constructing 4-vectors we let x 0 = ct and employ the Einstein summation convention. Greek indices run from 0 to 3 and Latin indices from 1 to 3.
eBook - ePubTraveling at the Speed of Thought
Einstein and the Quest for Gravitational Waves
- Daniel Kennefick(Author)
- 2016(Publication Date)
- Princeton University Press(Publisher)
µν [the small perturbative quantities] can be calculated in a manner analogous to that of retarded potentials in electrodynamics. From this it follows that gravitational fields propagate with the speed of light. Subsequent to this general solution we shall investigate gravitational waves and how they originate. It turned out that my suggested choice of a system of reference … is not advantageous for the calculation of fields in first approximation. A letter note from the astronomer De Sitter alerted me to his finding that a choice of reference system, different from the one I had previously given [in 1915, p. 833], leads to a simpler expression of the gravitational field of a point mass at rest. (Einstein 1916, p. 688)So the analogy now passed from being merely suggestive to a precise correspondence between two sets of equations, one being the vector equations describing the electromagnetic field, the other being the tensorial equations describing the gravitational field in linearized approximation. Employing the same procedure that one would in the electromagnetic case, it naturally transpires that both sets of equations lead to a wave equation. If the electromagnetic wave equation describes the well-known and experimentally well-understood electromagnetic waves, it seems reasonable to conclude that the gravitational wave equation describes gravitational waves, which propagate at the same speed as light but which consist of oscillations in the gravitational field.Einstein derived solutions to his wave equation that were intended to represent plane gravitational waves, by which we mean waves whose wave front is flat, rather than curved. They can be thought of as waves that are so far from their source their spherical shell, centered on the source, appears flat at any one point, just as the Earth appears flat when one is standing on it. Einstein proceeded to classify the waves into three types representing different symmetries. He called these types longitudinal, transversal (referring to transverse and longitudinal waves familiar from waves in other media), and a “new type of symmetry,” arising from the third set of conditions.Now it would be interesting to know whether the waves carry energy. Employing a pseudo-tensor quantity derived in the first part of the paper, Einstein proceeded to calculate the energy transported by these waves. He found that “only waves of the last named type [the “new type” of wave] do transport energy.” What could this mean? Did it make any kind of sense to speak of a wave that did not actually carry any energy along with it? How would one even know it existed? This obviously puzzled Einstein, and he discussed the problem with de Sitter (continuing the letter quoted above):
eBook - PDF- Bernard Schutz(Author)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
They are essentially omnidirectional, with quadrupolar antenna patterns, which we will discuss in § 12.3. These properties are analogous to sound: microphones record the phase oscillations of incident pressure waves and, because the waves generally have long wavelengths, it is difficult to focus a microphone in any particular direction. If we want to locate the source of a gravitational wave on the sky we need a network where we combine the detector outputs coherently, judging direction from phase delays. This is analogous, for example, to underwater acoustic detection networks, for military or geophysical use. As we shall see in the next section, gravitational waves are generated by the overall motions and mass distributions in their sources, rather than coming from quantum transitions in individual atoms within the source. The reason is that gravity is a field generated by a ‘charge’ of only one sign: masses in different locations are all positive, and they reinforce one another in generating a wave. In electromagnetism there are two charges, which in normal matter never get separated by more than something like a nanometer. This ensures that the radiation generated by one atom is not correlated with that from another. But gravity is similar to sound in this respect as well: sound is generated by local pressure changes, all of which combine coherently to create the radiated sound wave. The propagation of gravitational waves is therefore a kind of cosmic sound, a stress in spacetime that rockets across the Universe at the speed of light. When a detector receives this wave, its one-dimensional time series output can straightforwardly be converted into sound that our ears can hear. Gravitational wave physicists have come to use the language of sound to describe their work: we listen to gravitational waves, the signals from binaries (see the next section) chirp upwards in frequency, radiating binary systems are standard sirens (§ 9.6).
eBook - ePubParticle Physics and Cosmology: the Fabric of Spacetime
Lecture Notes of the Les Houches Summer School 2006
- (Author)
- 2007(Publication Date)
- Elsevier Science(Publisher)
Course 1Gravitational Waves
Alessandra Buonanno, Department of Physics, University of Maryland College Park MD 20742, USA ; AstroParticle and Cosmology, University Paris VII, FranceContents 1. Introduction 7 2. Linearization of Einstein equations 82.1. Einstein equations and gauge symmetry 9 2.2. Wave equation 11 2.3. Transverse-traceless gauge 123. Interaction of gravitational waves with point particles 133.1. Newtonian and relativistic description of tidal gravity 13 3.2. Description in the transverse-traceless gauge 14 3.3. Description in the free-falling frame 15 3.4. Key ideas underlying gravitational-wave detectors 164. Effective stress-energy tensor of gravitational waves 18 5. Generation of gravitational waves 215.1. Sources in slow motion, weak-field and negligible self-gravity 21 5.2. Sources in slow motion and weak-field, but non-negligible self-gravity 23 5.3. Radiated energy, angular momentum and linear momentum 246. Application to binary systems 256.1. Inspiral waveforms at leading Newtonian order 25 6.2. Inspiral waveform including post-Newtonian corrections 28 6.3. Merger and ring-down waveforms 30 6.4. Templates for data analysis 327. Other astrophysical sources 367.1. Pulsars 36 7.2. Supernovae 398. Cosmological sources 398.1. Phenomenological bounds 40 8.2. Gravitational waves produced by causal mechanisms 41 8.3. Gravitational waves produced by cosmic and fundamental strings 44 8.4. Gravitational waves produced during inflation 45References1 Introduction
Gravitational-wave (GW) science has entered a new era. Experimentally,1 several ground-based laser-interferometer GW detectors (10–1 kHz) have been built in the United States (LIGO) [1] , Europe (VIRGO and GEO) [2, 3 ] and Japan (TAMA) [4] , and are now taking data at design sensitivity. Advanced optical configurations capable of reaching sensitivities slightly above and even below the so-called standard-quantum-limit for a free test-particle, have been designed for second [5] and third generation [6] GW detectors (∼2011–2020). A laser interferometer space antenna (LISA) [7] (10−4 –10−2 Hz) might fly within the next decade. Resonant-bar detectors (∼1 kHz) [8] are improving more and more their sensitivity, broadening their frequency band. At much lower frequencies, ∼10−17 Hz, future cosmic microwave background (CMB) probes might detect GWs by measuring the CMB polarization [9] . Millisecond pulsar timing can set interesting upper limits [10] in the frequency range 10−9 –10−8 Hz. At such frequencies, the large number of millisecond pulsars which will be detectable with the square kilometer array [11]
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