《力学改变生活》课程教学资源（文献资料）The First Sounds of Merging Black Holes

Physics VIEWPOINT The First Sounds of Merging Black Holes Gravitational waves emitted by the merger of two black holes have been detected,setting the course for a new era of observational astrophysics. by Emanuele Berti*.t or decades,scientists have hoped they could "lis- ten in"on violent astrophysical events by detecting their emission of gravitational waves.The waves, which can be described as oscillating distortions in the geometry of spacetime,were first predicted to exist by Einstein in 1916,but they have never been observed di- rectly.Now,in an extraordinary paper,scientists report that they have detected the waves at the Laser Interferometer Gravitational-wave Observatory (LIGO)[1].From an analy- sis of the signal,researchers from LIGO in the US,and their collaborators from the Virgo interferometer in Italy,infer that the gravitational waves were produced by the inspiral and merger of two black holes(Fig.1),each with a mass that is more than 25 times greater than that of our Sun.Their find- ing provides the first observational evidence that black hole binary systems can form and merge in the Universe. Gravitational waves are produced by moving masses,and Figure 1:Numerical simulations of the gravitational waves emitted like electromagnetic waves,they travel at the speed of light. by the inspiral and merger of two black holes.The colored As they travel,the waves squash and stretch spacetime in the contours around each black hole represent the amplitude of the plane perpendicular to their direction of propagation(see gravitational radiation;the blue lines represent the orbits of the black holes and the green arrows represent their spins.(C. inset,Video 1).Detecting them,however,is exceptionally Henze/NASA Ames Research Center) hard because they induce very small distortions:even the strongest gravitational waves from astrophysical events are only expected to produce relative length variations of order 10-21 phase,yielding no signal.A gravitational wave propagat- ing perpendicular to the detector plane disrupts this perfect "Advanced"LIGO,as the recently upgraded version of destructive interference.During its first half-cycle,the wave the experiment is called,consists of two detectors,one in will lengthen one arm and shorten the other;during its sec- Hanford,Washington,and one in Livingston,Louisiana. ond half-cycle,these changes are reversed (see Video 1). Each detector is a Michelson interferometer,consisting of These length variations alter the phase difference between two 4-km-long optical cavities,or "arms,"that are arranged the laser beams,allowing optical power-a signal-to reach in an L shape.The interferometer is designed so that,in the photodetector.With two such interferometers,LIGOcan the absence of gravitational waves,laser beams traveling in rule out spurious signals (from,say,a local seismic wave) the two arms arrive at a photodetector exactly 180 out of that appear in one detector but not in the other. LIGO's sensitivity is exceptional:it can detect length dif- .Department of Physics and Astronomy,The University of Missis- ferences between the arms that are smaller than the size sippi,University,Mississippi 38677,USA of an atomic nucleus.The biggest challenge for LIGO is tCENTRA,Departamento de Fisica,Instituto Superior Tecnico, detector noise,primarily from seismic waves,thermal mo- Universidade de Lisboa,Avenida Rovisco Pais 1,1049 Lisboa,Por- tion,and photon shot noise.These disturbances can easily tugal mask the small signal expected from gravitational waves. physics.aps.org C2016 American Physical Society 11 February 2016 Physics 9,17

VIEWPOINT The First Sounds of Merging Black Holes Gravitational waves emitted by the merger of two black holes have been detected, setting the course for a new era of observational astrophysics. by Emanuele Berti∗,† F or decades, scientists have hoped they could “lis￾ten in” on violent astrophysical events by detecting their emission of gravitational waves. The waves, which can be described as oscillating distortions in the geometry of spacetime, were first predicted to exist by Einstein in 1916, but they have never been observed di￾rectly. Now, in an extraordinary paper, scientists report that they have detected the waves at the Laser Interferometer Gravitational-wave Observatory (LIGO) [1]. From an analy￾sis of the signal, researchers from LIGO in the US, and their collaborators from the Virgo interferometer in Italy, infer that the gravitational waves were produced by the inspiral and merger of two black holes (Fig. 1), each with a mass that is more than 25 times greater than that of our Sun. Their find￾ing provides the first observational evidence that black hole binary systems can form and merge in the Universe. Gravitational waves are produced by moving masses, and like electromagnetic waves, they travel at the speed of light. As they travel, the waves squash and stretch spacetime in the plane perpendicular to their direction of propagation (see inset, Video 1). Detecting them, however, is exceptionally hard because they induce very small distortions: even the strongest gravitational waves from astrophysical events are only expected to produce relative length variations of order 10−21 . “Advanced” LIGO, as the recently upgraded version of the experiment is called, consists of two detectors, one in Hanford, Washington, and one in Livingston, Louisiana. Each detector is a Michelson interferometer, consisting of two 4-km-long optical cavities, or “arms,” that are arranged in an L shape. The interferometer is designed so that, in the absence of gravitational waves, laser beams traveling in the two arms arrive at a photodetector exactly 180◦ out of ∗Department of Physics and Astronomy, The University of Missis￾sippi, University, Mississippi 38677, USA †CENTRA, Departamento de Física, Instituto Superior Técnico, Universidade de Lisboa, Avenida Rovisco Pais 1, 1049 Lisboa, Por￾tugal Figure 1: Numerical simulations of the gravitational waves emitted by the inspiral and merger of two black holes. The colored contours around each black hole represent the amplitude of the gravitational radiation; the blue lines represent the orbits of the black holes and the green arrows represent their spins. (C. Henze/NASA Ames Research Center) phase, yielding no signal. A gravitational wave propagat￾ing perpendicular to the detector plane disrupts this perfect destructive interference. During its first half-cycle, the wave will lengthen one arm and shorten the other; during its sec￾ond half-cycle, these changes are reversed (see Video 1). These length variations alter the phase difference between the laser beams, allowing optical power—a signal—to reach the photodetector. With two such interferometers, LIGO can rule out spurious signals (from, say, a local seismic wave) that appear in one detector but not in the other. LIGO’s sensitivity is exceptional: it can detect length dif￾ferences between the arms that are smaller than the size of an atomic nucleus. The biggest challenge for LIGO is detector noise, primarily from seismic waves, thermal mo￾tion, and photon shot noise. These disturbances can easily mask the small signal expected from gravitational waves. physics.aps.org c 2016 American Physical Society 11 February 2016 Physics 9, 17

Physics Hanford,Washington Livingston,Louisiana 1.0 0.0 1.0 berv回 1.0 0.0 1.0 0.30 0.35、 0.40 0.45 0.300.35 0.40 0.45 Time(s) Time(s) Video 1:(Animation appears online only.)A schematic depiction Figure 2:On September 14,2015,similar signals were observed of LIGO's interferometric gravitational wave detector.Light from a in both of LIGO's interferometers.The top panels show the laser is split in two by a beam splitter;one half travels down the measured signal in the Hanford(top left)and Livingston(top right) vertical arm of the interferometer,the other half travels down the detectors.The bottom panels show the expected signal produced horizontal arm.The detector is designed so that in the absence of by the merger of two black holes,based on numerical simulations gravitational waves(top left)the light takes the same time to travel (B.P.Abbott et al.[1].) back and forth along the two arms and interferes destructively at the photodetector,producing no signal.As the wave passes (moving clockwise from top right)the travel times for the lasers change,and a signal appears in the photodetector.(The actual provide a physically meaningful-and measurable-way to distortions are extremely small,but are exaggerated here for observe it.Sadly,Pirani,who laid the groundwork for our easier viewing.)Inset:The elongations in a ring of particles show modern thinking about gravitational waves and how to de- the effects of a gravitational wave on spacetime.(APS/Alan tect them,passed away on December 31,2015,just weeks Stonebraker) before the LIGO scientists announced their discovery. Other prominent physicists at the meeting,including Joseph Weber,Richard Feynman,and Hermann Bondi,were The upgrade,completed in 2015,improved the detector's instrumental in pushing Pirani's ideas forward.Feynman sensitivity by a factor of 3-5 for waves in the 100-300 Hz fre- and Bondi,in particular,developed Pirani's observation into quency band and by more than a factor of 10 below 60 Hz. what is now known as the "sticky bead"thought experi- These improvements have enhanced the detector's sensitiv- ment.They argued that if beads sliding on a sticky rod ity to more distant sources and were crucial to the discovery accelerated under the effect of a passing gravitational wave, of gravitational waves. then they must surely also transfer heat to the rod by friction. On September 14,2015,within the first two days of Ad- This heat transfer is proof that gravitational waves must in- vanced LIGO's operation,the researchers detected a signal deed carry energy,and are therefore,in principle,detectable. so strong that it could be seen by eye(Fig.2).The most Interest in carrying out such experiments wasn't imme- intense portion of the signal lasted for about 0.2 s and was diate.As Pirani noted in his 1964 lectures on gravitational observed in both detectors,with a combined signal-to-noise radiation [4],Weber thought that meaningful laboratory ratio of 24.Fittingly,this first gravitational wave signal, experiments were "impossible by several orders of magni- dubbed GW150914,arrived less than two months before the tude."At about the same time,William Fowler (the future 100-year anniversary of the publication of Einstein's general Nobel laureate)suggested that a large fraction of the en- relativity theory. ergy emitted by so-called massive double quasars-what we Up until a few decades ago,detecting gravitational waves now know as black hole binaries-might be in the form of was considered an impossible task.In fact,in the 1950s, gravitational radiation.Pirani,however,felt that the direct physicists were still heatedly debating whether the waves observation of gravitational waves was not "necessary or were actual physical entities and whether they could carry sufficient"to justify a corresponding theory,arguing that un- energy.The turning point was a 1957 conference in Chapel less physicists figured out a way to quantize gravity,such a Hill,North Carolina [2,3].There,the theorist Felix Pi- theory would not"have much to do with physics"[4]. rani pointed out a connection between Newton's second What galvanized the field was a 1969 paper from We- law and the equation of geodesic deviation,which describes ber,who claimed he had detected gravitational radiation the effect of tidal forces in general relativity.This connec-with a resonant bar detector(see 22 December 2005 Focus tion allowed him to show that the relative accelerations of story).The finding was controversial-physicists could not neighboring particles in the presence of a gravitational wave duplicate it and by the mid-1970s,most agreed that We- physics.aps.org C2016 American Physical Society 11 February 2016 Physics 9,17

Video 1: (Animation appears online only.) A schematic depiction of LIGO’s interferometric gravitational wave detector. Light from a laser is split in two by a beam splitter; one half travels down the vertical arm of the interferometer, the other half travels down the horizontal arm. The detector is designed so that in the absence of gravitational waves (top left) the light takes the same time to travel back and forth along the two arms and interferes destructively at the photodetector, producing no signal. As the wave passes (moving clockwise from top right) the travel times for the lasers change, and a signal appears in the photodetector. (The actual distortions are extremely small, but are exaggerated here for easier viewing.) Inset: The elongations in a ring of particles show the effects of a gravitational wave on spacetime. (APS/Alan Stonebraker) The upgrade, completed in 2015, improved the detector’s sensitivity by a factor of 3–5 for waves in the 100–300 Hz fre￾quency band and by more than a factor of 10 below 60 Hz. These improvements have enhanced the detector’s sensitiv￾ity to more distant sources and were crucial to the discovery of gravitational waves. On September 14, 2015, within the first two days of Ad￾vanced LIGO’s operation, the researchers detected a signal so strong that it could be seen by eye (Fig. 2). The most intense portion of the signal lasted for about 0.2 s and was observed in both detectors, with a combined signal-to-noise ratio of 24. Fittingly, this first gravitational wave signal, dubbed GW150914, arrived less than two months before the 100-year anniversary of the publication of Einstein’s general relativity theory. Up until a few decades ago, detecting gravitational waves was considered an impossible task. In fact, in the 1950s, physicists were still heatedly debating whether the waves were actual physical entities and whether they could carry energy. The turning point was a 1957 conference in Chapel Hill, North Carolina [2, 3]. There, the theorist Felix Pi￾rani pointed out a connection between Newton’s second law and the equation of geodesic deviation, which describes the effect of tidal forces in general relativity. This connec￾tion allowed him to show that the relative accelerations of neighboring particles in the presence of a gravitational wave Figure 2: On September 14, 2015, similar signals were observed in both of LIGO’s interferometers. The top panels show the measured signal in the Hanford (top left) and Livingston (top right) detectors. The bottom panels show the expected signal produced by the merger of two black holes, based on numerical simulations. (B. P. Abbott et al. [1].) provide a physically meaningful—and measurable—way to observe it. Sadly, Pirani, who laid the groundwork for our modern thinking about gravitational waves and how to de￾tect them, passed away on December 31, 2015, just weeks before the LIGO scientists announced their discovery. Other prominent physicists at the meeting, including Joseph Weber, Richard Feynman, and Hermann Bondi, were instrumental in pushing Pirani’s ideas forward. Feynman and Bondi, in particular, developed Pirani’s observation into what is now known as the “sticky bead” thought experi￾ment. They argued that if beads sliding on a sticky rod accelerated under the effect of a passing gravitational wave, then they must surely also transfer heat to the rod by friction. This heat transfer is proof that gravitational waves must in￾deed carry energy, and are therefore, in principle, detectable. Interest in carrying out such experiments wasn’t imme￾diate. As Pirani noted in his 1964 lectures on gravitational radiation [4], Weber thought that meaningful laboratory experiments were “impossible by several orders of magni￾tude.” At about the same time, William Fowler (the future Nobel laureate) suggested that a large fraction of the en￾ergy emitted by so-called massive double quasars—what we now know as black hole binaries—might be in the form of gravitational radiation. Pirani, however, felt that the direct observation of gravitational waves was not “necessary or sufficient” to justify a corresponding theory, arguing that un￾less physicists figured out a way to quantize gravity, such a theory would not “have much to do with physics” [4]. What galvanized the field was a 1969 paper from We￾ber, who claimed he had detected gravitational radiation with a resonant bar detector (see 22 December 2005 Focus story). The finding was controversial—physicists could not duplicate it and by the mid-1970s, most agreed that We￾physics.aps.org c 2016 American Physical Society 11 February 2016 Physics 9, 17

Physics ber had likely been incorrect.However,a few years later a wave produced by the final black hole [6].They found that young professor at the Massachusetts Institute of Technol- the values inferred from these oscillations agreed with those ogy named Rainer Weiss was preparing for his course on they had calculated.The second test was to analyze the relativity when he came across a proposal by Pirani for de- phase of the wave generated by the black holes as they spi- tecting gravitational waves.Pirani had suggested using light raled inward towards one another.This phase can be written signals to see the variations in the positions of neighboring as a series expansion in v/c,where v is the speed of the particles when a wave passed.His idea,with one key mod- orbiting black holes,and the authors verified that the coeffi- ification,led to the genesis of LIGO:rather than using the cients of this expansion were consistent with the predictions timing of short light pulses,Weiss proposed to make phase of general relativity.By assuming that a graviton with mass measurements in a Michelson interferometer [5].Ronald would modify the phase of the waves,they determined an Drever,Kip Thorne,and many others made crucial contribu- upper bound on the particle's mass of 1.2 x 10-22 ev/c2 im- tions to developing this idea into what LIGO is today.(See proving the bounds from measurements in our Solar System Ref.2]for a historical account. and from observations of binary pulsars.These findings will Now,what was once considered "impossible by sev- be discussed in detail in later papers. eral orders of magnitude"is a reality.To confirm the In physics,we live and breathe for discoveries like the one gravitational-wave nature of their signal,the researchers reported by LIGO,but the best is yet to come.As Kip Thorne used two different data analysis methods.The first was to recently said in a BBC interview,recording a gravitational determine whether the excess power in the photodetector wave for the first time was never LIGO's main goal.The could be caused by a signal,given their best estimate of the motivation was always to open a new window onto the Uni- noise,but without any assumptions about the origin of the verse. signal itself.From this analysis,they could say that a tran- Gravitational wave detection will allow new and more sient,"unmodeled"signal was observed with a statistical precise measurements of astrophysical sources.For ex- significance greater than 4.60.The second method involved ample,the spins of two merging black holes hold clues comparing the instrumental output(signal plus noise)with to their formation mechanism.Although Advanced LIGO a theoretical signal from numerical simulations of merg- wasn't able to measure the magnitude of these spins very ing black holes using general relativity.From this so-called accurately,better measurements might be possible with im- matched-filtering search,the researchers concluded that the proved models of the signal,better data analysis techniques, significance of the observation was greater than 5.10. or more sensitive detectors.Once Advanced LIGO reaches The most exciting conclusions come from comparing the design sensitivity,it should be capable of detecting binaries observed signal's amplitude and phase with numerical rela- like the one that produced GW150914 with 3 times its current tivity predictions,which allows the LIGO researchers to es- signal-to-noise ratio,allowing more accurate determinations timate parameters describing the gravitational-wave source. of source parameters such as mass and spin. The waveform is consistent with a black hole binary system The upcoming network of Earth-based detectors,compris- whose component masses are 36 and 29 times the mass of ing Advanced Virgo,KAGRA in Japan,and possibly a third the Sun.These stellar-mass black holes-so named because LIGO detector in India,will help scientists determine the they likely formed from collapsing stars-are the largest of locations of sources in the sky.This would tell us where their kind to have been observed.Moreover,no binary sys- to aim "traditional"telescopes that collect electromagnetic tem other than black holes can have component masses large radiation or neutrinos.Combining observational tools in enough to explain the observed signal.(The most plausible this way would be the basis for a new research field,some- competitors would be two neutron stars,or a black hole and times referred to as "multimessenger astronomy"[7].Soon a neutron star.)The binary is approximately 1.3 billion light we will also collect the first results from LISA Pathfinder, years from Earth,or equivalently,at a luminosity distance of a spacecraft experiment serving as a testbed for eLISA,a 400 megaparsecs(redshift of z~0.1).The researchers esti- space-based interferometer.eLISA will enable us to peer mate that about 4.6%of the binary's energy was radiated in deeper into the cosmos than ground-based detectors,allow- gravitational waves,leading to a rotating black hole remnant ing studies of the formation of more massive black holes and with mass 62 times the mass of the Sun and dimensionless investigations of the strong-field behavior of gravity at cos- spin of 0.67. mological distances [8]. From the signal,the researchers were also able to perform With Advanced LIGO's result,we are entering the dawn two consistency tests of general relativity and put a bound of the age of gravitational wave astronomy:with this new on the mass of the graviton-the hypothetical quantum par- tool,it is as though we are able to hear,when before we could ticle that mediates gravity.In the first test,they used general only see.It is very significant that the first "sound"picked relativity to estimate the black hole remnant's mass and spin up by Advanced LIGO came from the merger of two black from the pre-merger parameters.They then also determined holes.These are objects we can't see with electromagnetic ra- the remnant's mass and spin from the oscillations in the diation.The implications of gravitational-wave astronomy physics.aps.org 2016 American Physical Society 11 February 2016 Physics 9,17

ber had likely been incorrect. However, a few years later a young professor at the Massachusetts Institute of Technol￾ogy named Rainer Weiss was preparing for his course on relativity when he came across a proposal by Pirani for de￾tecting gravitational waves. Pirani had suggested using light signals to see the variations in the positions of neighboring particles when a wave passed. His idea, with one key mod￾ification, led to the genesis of LIGO: rather than using the timing of short light pulses, Weiss proposed to make phase measurements in a Michelson interferometer [5]. Ronald Drever, Kip Thorne, and many others made crucial contribu￾tions to developing this idea into what LIGO is today. (See Ref. [2] for a historical account.) Now, what was once considered “impossible by sev￾eral orders of magnitude” is a reality. To confirm the gravitational-wave nature of their signal, the researchers used two different data analysis methods. The first was to determine whether the excess power in the photodetector could be caused by a signal, given their best estimate of the noise, but without any assumptions about the origin of the signal itself. From this analysis, they could say that a tran￾sient, “unmodeled” signal was observed with a statistical significance greater than 4.6σ. The second method involved comparing the instrumental output (signal plus noise) with a theoretical signal from numerical simulations of merg￾ing black holes using general relativity. From this so-called matched-filtering search, the researchers concluded that the significance of the observation was greater than 5.1σ. The most exciting conclusions come from comparing the observed signal’s amplitude and phase with numerical rela￾tivity predictions, which allows the LIGO researchers to es￾timate parameters describing the gravitational-wave source. The waveform is consistent with a black hole binary system whose component masses are 36 and 29 times the mass of the Sun. These stellar-mass black holes—so named because they likely formed from collapsing stars—are the largest of their kind to have been observed. Moreover, no binary sys￾tem other than black holes can have component masses large enough to explain the observed signal. (The most plausible competitors would be two neutron stars, or a black hole and a neutron star.) The binary is approximately 1.3 billion light years from Earth, or equivalently, at a luminosity distance of 400 megaparsecs (redshift of z ∼ 0.1). The researchers esti￾mate that about 4.6% of the binary’s energy was radiated in gravitational waves, leading to a rotating black hole remnant with mass 62 times the mass of the Sun and dimensionless spin of 0.67. From the signal, the researchers were also able to perform two consistency tests of general relativity and put a bound on the mass of the graviton—the hypothetical quantum par￾ticle that mediates gravity. In the first test, they used general relativity to estimate the black hole remnant’s mass and spin from the pre-merger parameters. They then also determined the remnant’s mass and spin from the oscillations in the wave produced by the final black hole [6]. They found that the values inferred from these oscillations agreed with those they had calculated. The second test was to analyze the phase of the wave generated by the black holes as they spi￾raled inward towards one another. This phase can be written as a series expansion in v/c, where v is the speed of the orbiting black holes, and the authors verified that the coeffi- cients of this expansion were consistent with the predictions of general relativity. By assuming that a graviton with mass would modify the phase of the waves, they determined an upper bound on the particle’s mass of 1.2 × 10−22 eV/c 2 , im￾proving the bounds from measurements in our Solar System and from observations of binary pulsars. These findings will be discussed in detail in later papers. In physics, we live and breathe for discoveries like the one reported by LIGO, but the best is yet to come. As Kip Thorne recently said in a BBC interview, recording a gravitational wave for the first time was never LIGO’s main goal. The motivation was always to open a new window onto the Uni￾verse. Gravitational wave detection will allow new and more precise measurements of astrophysical sources. For ex￾ample, the spins of two merging black holes hold clues to their formation mechanism. Although Advanced LIGO wasn’t able to measure the magnitude of these spins very accurately, better measurements might be possible with im￾proved models of the signal, better data analysis techniques, or more sensitive detectors. Once Advanced LIGO reaches design sensitivity, it should be capable of detecting binaries like the one that produced GW150914 with 3 times its current signal-to-noise ratio, allowing more accurate determinations of source parameters such as mass and spin. The upcoming network of Earth-based detectors, compris￾ing Advanced Virgo, KAGRA in Japan, and possibly a third LIGO detector in India, will help scientists determine the locations of sources in the sky. This would tell us where to aim “traditional” telescopes that collect electromagnetic radiation or neutrinos. Combining observational tools in this way would be the basis for a new research field, some￾times referred to as “multimessenger astronomy” [7]. Soon we will also collect the first results from LISA Pathfinder, a spacecraft experiment serving as a testbed for eLISA, a space-based interferometer. eLISA will enable us to peer deeper into the cosmos than ground-based detectors, allow￾ing studies of the formation of more massive black holes and investigations of the strong-field behavior of gravity at cos￾mological distances [8]. With Advanced LIGO’s result, we are entering the dawn of the age of gravitational wave astronomy: with this new tool, it is as though we are able to hear, when before we could only see. It is very significant that the first “sound” picked up by Advanced LIGO came from the merger of two black holes. These are objects we can’t see with electromagnetic ra￾diation. The implications of gravitational-wave astronomy physics.aps.org c 2016 American Physical Society 11 February 2016 Physics 9, 17

Physics for astrophysics in the near future are dazzling.Multiple de- Summer Institute of Theoretical Physics,edited by A.Traut- tections will allow us to study how often black holes merge man,F.A.E.Pirani,and H.Bondi(Prentice-Hall,Englewood, in the cosmos and to test astrophysical models that describe NJ,1965),p.249-273. the formation of binary systems [9,10].In this respect,it's [5]R.Weiss,"Electromagnetically Coupled Broadband Gravita- encouraging to note that LIGO may have already detected tional Antenna,"Quarterly Progress Report of the MIT Re- a second event;a very preliminary analysis suggests that search Laboratory of Electronics,No.105,54(1972),available online at http://dspace.mit.edu/bitstream/handle/1721.1/56271 if this event proves to have an astrophysical origin,then it /RLE QPR 105 V.pdf. is likely to also be from a black hole binary system.The [6]E.Berti,V.Cardoso,and A.O.Starinets,"Quasinormal Modes detection of strong signals will also allow physicists to test of Black Holes and Black Branes,"Class.Quantum Grav.26, the so-called no-hair theorem,which says that a black hole's 163001(2009). structure and dynamics depend only on its mass and spin. [7]B.P.Abbott et al.,"Prospects for Observing and Localizing Observing gravitational waves from black holes might also Gravitational-Wave Transients with Advanced LIGO and Ad- tell us about the nature of gravity.Does gravity really be- vanced Virgo,"Living Rev.Relativity 19,1(2016). have as predicted by Einstein in the vicinity of black holes, [8]P.Amaro-Seoane et al.,"eLISA:Astrophysics and Cosmology where the fields are very strong?Can dark energy and the in the Millihertz Regime,"arXiv:1201.3621. acceleration of the Universe be explained if we modify Ein- [9]M.Dominik,E.Berti,R.O'Shaughnessy,I.Mandel,K.Belczyn- stein's gravity?We are only just beginning to answer these ski,C.Fryer,D.E.Holz,T.Bulik,and F.Pannarale,"Double Compact Objects.Ill.Gravitational-Wave Detection Rates," questions [11,12]. Astrophys..J.806,263(2015). [10]S.Stevenson,F.Ohme,and S.Fairhurst,"Distinguishing Com- REFERENCES pact Binary Population Synthesis Models Using Gravitational Wave Observations of Coalescing Binary Black Holes,Astro- [1]B.P.Abbott et al.(LIGO Scientific Collaboration and the Virgo phys.J.810,58(2015). Collaboration),"Observation of Gravitational Waves from a Bi- [11]N.Yunes and X.Siemens,"Gravitational-Wave Tests of Gen- nary Black Hole Merger,"Phys.Rev.Lett.116,061102(2016). eral Relativity with Ground-Based Detectors and Pulsar-Timing [2]D.Kennefick,Traveling at the Speed of Thought:Einstein and Arrays,"Living Rev.Relativity 16,9(2013). the Quest for Gravitational Waves(Princeton University Press, [12]E.Berti et al.,"Testing General Relativity with Present and Fu- Princeton),p.2007. ture Astrophysical Observations,"Class.Quantum Grav.32, [3]P.R.Saulson,"Josh Goldberg and the Physical Reality of 243001(2015). Gravitational Waves,"Gen.Relativ.Gravit.43,No.12,3289 (2011). [4]F.A.E.Pirani,"Introduction to Gravitational Radiation Theory," in Lectures on General Relativity,1964,Volume 1.Brandeis 10.1103/Physics.9.17 physics.aps.org C2016 American Physical Society 11 February 2016 Physics 9,17

for astrophysics in the near future are dazzling. Multiple de￾tections will allow us to study how often black holes merge in the cosmos and to test astrophysical models that describe the formation of binary systems [9, 10]. In this respect, it’s encouraging to note that LIGO may have already detected a second event; a very preliminary analysis suggests that if this event proves to have an astrophysical origin, then it is likely to also be from a black hole binary system. The detection of strong signals will also allow physicists to test the so-called no-hair theorem, which says that a black hole’s structure and dynamics depend only on its mass and spin. Observing gravitational waves from black holes might also tell us about the nature of gravity. Does gravity really be￾have as predicted by Einstein in the vicinity of black holes, where the fields are very strong? Can dark energy and the acceleration of the Universe be explained if we modify Ein￾stein’s gravity? We are only just beginning to answer these questions [11, 12]. REFERENCES [1] B. P. Abbott et al. (LIGO Scientific Collaboration and the Virgo Collaboration), ‘‘Observation of Gravitational Waves from a Bi￾nary Black Hole Merger,’’ Phys. Rev. Lett. 116, 061102 (2016). [2] D. Kennefick, Traveling at the Speed of Thought: Einstein and the Quest for Gravitational Waves (Princeton University Press, Princeton), p. 2007. [3] P. R. Saulson, ‘‘Josh Goldberg and the Physical Reality of Gravitational Waves,’’ Gen. Relativ. Gravit. 43, No. 12, 3289 (2011). [4] F. A. E. Pirani, ‘‘Introduction to Gravitational Radiation Theory,’’ in Lectures on General Relativity, 1964, Volume 1. Brandeis Summer Institute of Theoretical Physics, edited by A. Traut￾man, F. A. E. Pirani, and H. Bondi (Prentice-Hall, Englewood, NJ, 1965), p. 249-273. [5] R. Weiss, ‘‘Electromagnetically Coupled Broadband Gravita￾tional Antenna,’’ Quarterly Progress Report of the MIT Re￾search Laboratory of Electronics, No. 105, 54 (1972), available online at http://dspace.mit.edu/bitstream/handle/1721.1/56271 /RLE_QPR_105_V.pdf. [6] E. Berti, V. Cardoso, and A. O. Starinets, ‘‘Quasinormal Modes of Black Holes and Black Branes,’’ Class. Quantum Grav. 26, 163001 (2009). [7] B. P. Abbott et al., ‘‘Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Ad￾vanced Virgo,’’ Living Rev. Relativity 19, 1 (2016). [8] P. Amaro-Seoane et al., ‘‘eLISA: Astrophysics and Cosmology in the Millihertz Regime,’’ arXiv:1201.3621. [9] M. Dominik, E. Berti, R. O’Shaughnessy, I. Mandel, K. Belczyn￾ski, C. Fryer, D. E. Holz, T. Bulik, and F. Pannarale, ‘‘Double Compact Objects. III. Gravitational-Wave Detection Rates,’’ Astrophys. J. 806, 263 (2015). [10] S. Stevenson, F. Ohme, and S. Fairhurst, ‘‘Distinguishing Com￾pact Binary Population Synthesis Models Using Gravitational Wave Observations of Coalescing Binary Black Holes,’’ Astro￾phys. J. 810, 58 (2015). [11] N. Yunes and X. Siemens, ‘‘Gravitational-Wave Tests of Gen￾eral Relativity with Ground-Based Detectors and Pulsar-Timing Arrays,’’ Living Rev. Relativity 16, 9 (2013). [12] E. Berti et al., ‘‘Testing General Relativity with Present and Fu￾ture Astrophysical Observations,’’ Class. Quantum Grav. 32, 243001 (2015). 10.1103/Physics.9.17 physics.aps.org c 2016 American Physical Society 11 February 2016 Physics 9, 17