موجة ثقالية

لمعلومات عن للمفهوم الآخر في ديناميكا الموائع، انظر أمواج ثقالية.

الأمواج الثقالية Gravitational wave نوع من الأمواج ينتج عن الأجسام الفيزيائية المتسارعة. ز هي أمواج ذات الطاقة معينة تنتقل خلال الحقل الثقالي للزمكان .

طبقا للنسبية العامة، يمكن للثقالة أن تحدث اهتزازات او امواج ضمن الزمكان مما يسمح بنقل الطاقة. ويمكن القول ان قوة الثقالة تتغير بمرور هذه الأمواج الثقالية. بصياغة اخرى فان قوة واتجاه القوى المدية ستهتز محدثة تغيرات اهتزازية في شكل الاجسام (وليس حجمها)الموجودة في طريق هذه الأمواج.

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 مقدمة

History of the Universe - gravitational waves are hypothesized to arise from cosmic inflation, a faster-than-light expansion just after the Big Bang (17 March 2014).

Linearly polarised gravitational wave

 آثار العبور

The effect of a plus-polarized gravitational wave on a ring of particles.

The effect of a cross-polarized gravitational wave on a ring of particles.

 المصادر

The gravitational wave spectrum with sources and detectors. Credit: NASA Goddard Space Flight Center

 Power radiated by orbiting bodies

Two stars of dissimilar mass are in circular orbits. Each revolves about their common center of mass (denoted by the small red cross) in a circle with the larger mass having the smaller orbit.

Two stars of similar mass are in circular orbits about their center of mass

Two stars of similar mass are in highly elliptical orbits about their center of mass

Gravitational waves carry energy away from their sources and, in the case of orbiting bodies, this is associated with an inspiral or decrease in orbit. Imagine for example a simple system of two masses — such as the Earth-Sun system — moving slowly compared to the speed of light in circular orbits. Assume that these two masses orbit each other in a circular orbit in the x–y plane. To a good approximation, the masses follow simple Keplerian orbits. However, such an orbit represents a changing quadrupole moment. That is, the system will give off gravitational waves.

Suppose that the two masses are $m_{1}$ and $m_{2}$, and they are separated by a distance $r$. The power given off (radiated) by this system is:

$P={\frac {\mathrm {d} E}{\mathrm {d} t}}=-{\frac {32}{5}}\,{\frac {G^{4}}{c^{5}}}\,{\frac {(m_{1}m_{2})^{2}(m_{1}+m_{2})}{r^{5}}}$ ,

where G is the gravitational constant, c is the speed of light in vacuum and where the negative sign means that power is being given off by the system, rather than received. For a system like the Sun and Earth, $r$ is about 1.5×10¹¹ m and $m_{1}$ and $m_{2}$ are about 2×10³⁰ and 6×10²⁴ kg respectively. In this case, the power is about 200 watts. This is truly tiny compared to the total electromagnetic radiation given off by the Sun (roughly 3.86×10²⁶ watts).

In theory, the loss of energy through gravitational radiation could eventually drop the Earth into the Sun. However, the total energy of the Earth orbiting the Sun (kinetic energy + gravitational potential energy) is about 1.14×10³⁶ joules of which only 200 joules per second is lost through gravitational radiation, leading to a decay in the orbit by about 1×10^-15 meters per day or roughly the diameter of a proton. At this rate, it would take the Earth approximately 1×10¹³ times more than the current age of the Universe to spiral onto the Sun. This estimate overlooks the decrease in r over time, but the majority of the time the bodies are far apart and only radiating slowly, so the difference is unimportant in this example.

A more dramatic example of radiated gravitational energy is represented by two solar mass (M_☉) neutron stars orbiting at a distance from each other of 1.89×10⁸ m (only 0.63 light-seconds apart). [The Sun is 8 light minutes from the Earth.] Plugging their masses into the above equation shows that the gravitational radiation from them would be 1.38×10²⁸ watts, which is about 100 times more than the Sun's electromagnetic radiation.

 Orbital decay from gravitational radiation

انظر أيضاً: Two-body problem in general relativity

Gravitational radiation robs the orbiting bodies of energy. It first circularizes their orbits and then gradually shrinks their radius. As the energy of the orbit is reduced, the distance between the bodies decreases, and they rotate more rapidly. The overall angular momentum is reduced however. This reduction corresponds to the angular momentum carried off by gravitational radiation. The rate of decrease of distance between the bodies versus time is given by:

${\frac {\mathrm {d} r}{\mathrm {d} t}}=-{\frac {64}{5}}\,{\frac {G^{3}}{c^{5}}}\,{\frac {(m_{1}m_{2})(m_{1}+m_{2})}{r^{3}}}\$,

where the variables are the same as in the previous equation.

 الفيزياء الفلكية

Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other.

 الكشف عن الأمواج الثقالية

المقالة الرئيسية: Gravitational-wave observatory and Gravitational wave detection

Possible evidence for gravitational waves in the infant universe was found by the BICEP2 radio telescope. The microscopic examination of the focal plane of the BICEP2 detector is shown here. In 2015, however, the BICEP2 findings were confirmed to be the result of cosmic dust.

في الحقيقة ان دخول الأمواج الثقالية لأي مختبر يؤدي إلى اهتزاز جميع الاجسام فيه . فتشوهات الزمكان تؤدي إلى اضطرابات اهتزازية في جميع الأجسام المعترضة لها سيما اذا كانت ذات حجم مناسب مثل بعض القضبان المعدنية أو البلورات . تستخدم بشكل خاص قضبانا مصنوعة من الياقوت الصافي بجم ذراع الانسان مرتبطة بكواشف قادرة على كشف اهتزلزات بقطر الذرة. و هناك العديد من التجارب يستعمل فيها تقنية التداخل الليزري laser interferometry لمحاولة رصد هذه الأمواج. إلا أن قياسا مباشر لهذه الموجات مازال متعذرا إلى اليوم. غير أن علماء تمكنوا من البرهنة على وجود هذه الموجات و بذلك تأكيد نظرية أينستاين من خلال تفسيرهم لحركة نجمين توأمين عن طريق نظرية الأمواج الثقالية و مقارنة حساباتهم النظرية على أساس هذه النظرية مع ملاحظتهم لحركة النجمين.

 تاريخ

• On 17 March 2014, astronomers at the Harvard–Smithsonian Center for Astrophysics erroneously claimed that they had detected and produced "the first direct image of gravitational waves across the primordial sky" within the cosmic microwave background, providing flawed evidence for inflation and the Big Bang. On 19 June 2014, lowered confidence in confirming the cosmic inflation findings was reported and on 19 September 2014, a further reduction in confidence was reported. On 30 January 2015, even less confidence yet was reported; Nature went as far as publishing a news article entitled "Gravitational waves discovery now officially dead".

• A study published in 2016 proposed that dark energy may distort gravitational waves, and cites this circumstance as a reason for a lack of direct detection.

• In February 2016, the Advanced LIGO team announced that they had detected gravitational waves from a black hole merger about 400 megaparsecs (1.3 billion light-years) from Earth. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1 × 10 ^-21.

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 صعوبات

Gravitational waves are not easily detectable. When they reach the Earth, they have a small amplitude, meaning that an extremely sensitive detector is needed, and that other sources of noise can overwhelm the signal. Gravitational waves are expected to have frequencies 10⁻¹⁶ Hz < f < 10⁴ Hz.

 Ground-based interferometers

A schematic diagram of a laser interferometer

Though the Hulse-Taylor observations were very important, they give only indirect evidence for gravitational waves. A more conclusive observation would be a direct measurement of the effect of a passing gravitational wave, which could also provide more information about the system that generated it. Any such direct detection is complicated by the extraordinarily small effect the waves would produce on a detector. The amplitude of a spherical wave will fall off as the inverse of the distance from the source (the 1/R term in the formulas for h above). Thus, even waves from extreme systems like merging binary black holes die out to very small amplitude by the time they reach the Earth. Astrophysicists expect that some gravitational waves passing the Earth may be as large as h ≈ 10⁻²⁰, but generally no bigger.

A simple device theorised to detect the expected wave motion is called a Weber bar — a large, solid bar of metal isolated from outside vibrations. This type of instrument was the first type of gravitational wave detector. Strains in space due to an incident gravitational wave excite the bar's resonant frequency and could thus be amplified to detectable levels. Conceivably, a nearby supernova might be strong enough to be seen without resonant amplification. With this instrument, Joseph Weber claimed to have detected daily signals of gravitational waves. His results, however, were contested in 1974 by physicists Richard Garwin and David Douglass. Modern forms of the Weber bar are still operated, cryogenically cooled, with superconducting quantum interference devices to detect vibration. Weber bars are not sensitive enough to detect anything but extremely powerful gravitational waves.

MiniGRAIL is a spherical gravitational wave antenna using this principle. It is based at Leiden University, consisting of an exactingly machined 1150 kg sphere cryogenically cooled to 20 mK. The spherical configuration allows for equal sensitivity in all directions, and is somewhat experimentally simpler than larger linear devices requiring high vacuum. Events are detected by measuring deformation of the detector sphere. MiniGRAIL is highly sensitive in the 2–4 kHz range, suitable for detecting gravitational waves from rotating neutron star instabilities or small black hole mergers.

 Gravitational wave detection, 2016

LIGO measurement of the gravitational waves at the Livingston (left) and Hanford (right) detectors, compared to the theoretical predicted values.

المقالة الرئيسية: Gravitational wave detection

On 11 February 2016, the LIGO collaboration announced the detection of gravitational waves, from a signal detected at 10.51 GMT on 14 September 2015 of two black holes with masses of 29 and 36 solar masses merging together around 1.3 billion light years away. The mass of the new black hole obtained from merging the two was 62 solar masses. Energy equivalent to 3 solar masses was emitted as gravitational waves. The signal was seen by both LIGO detectors, in Livingston and Hanford, with a time difference of 7 milliseconds due to the angle between the two detectors and the source. The signal came from the Southern Celestial Hemisphere, in the rough direction of (but much further away than) the Magellanic Clouds. The confidence level of the discovery was 99.99994 %.

 انظر أيضاً

• General Relativity
• Linearised Einstein field equations
• Gravitomagnetism
• LIGO, VIRGO, GEO 600, and TAMA 300 — Gravitational wave detectors
• LISA the proposed Laser Interferometer Space Antenna.
• Big Bang Observer (BBO), proposed successor to LISA.
• Sticky bead argument, for a physical way to see that gravitational radiation should carry energy.
• pp-wave spacetime, for an important class of exact solutions modeling gravitational radiation.
• Hawking Radiation, for gravitationally induced electromagnetic radiation from black holes

• Spin-flip, a consequence of gravitational wave emission from binary supermassive black holes.
• Gravitational field

 المصادر

• Chakrabarty, Indrajit, "Gravitational Waves: An Introduction". arXiv:physics/9908041 v1, Aug 21, 1999.
• Landau, L. D. and Lifshitz, E. M., The Classical Theory of Fields (Pergamon Press),(1987).
• Will, Clifford M., The Confrontation between General Relativity and Experiment. Living Rev. Relativity 9 (2006) 3.

 ببليوگرافيا

• Berry, Michael, Principles of cosmology and gravitation (Adam Hilger, Philadelphia, 1989). ISBN 0-85274-037-9
• P. J. E. Peebles, Principles of Physical Cosmology (Princeton University Press, Princeton, 1993). ISBN 0691019339.
• Wheeler, John Archibald and Ciufolini, Ignazio, Gravitation and Inertia (Princeton University Press, Princeton, 1995). ISBN 0-691-03323-4.
• Woolf, Harry, ed., Some Strangeness in the Proportion (Addison-Wesley, Reading, Massachusetts, 1980). ISBN 0201099241.

 وصلات خارجية

• Caltech's Physics 237-2002 Gravitational Waves by Kip Thorne Video plus notes: Graduate level but does not assume knowledge of General Relativity, Tensor Analysis, or Differential Geometry; Part 1: Theory (10 lectures), Part 2: Detection (9 lectures)
• www.astronomycast.com January 14, 2008 Episode 71: Gravitational Waves
• Laser Interferometer Gravitational Wave Observatory. LIGO Laboratory, California Institute of Technology.
• Einstein's Messengers - The LIGO Movie by NSF
• Home page for Einstein@Home project, a distributed computing project processing raw data from LIGO Laboratory, searching for gravity waves
• The National Center for Supercomputing Applications -- a numerical relativity group
• Caltech Relativity Tutorial -- A basic introduction to gravitational waves, and astrophysical systems giving off gravitational waves
• Resource Letter GrW-1: Gravitational waves -- a list of books, journals and web resources compiled by Joan Centrella for research into gravitational waves
• Mathematical and Physical Perspectives on Gravitational Radiation -- written by B F Schutz of the Max Planck Institute explaining the significance and background of some key concepts in gravitational radiation
• Binary BH Merger -- estimating the radiated power and merger time of a BH binary using dimensional analysis