Download to read offline
重力波
- 1.
- 2. ABSTRACT On September 14,2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10−21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410+160−180 Mpc corresponding to a redshift z=0.09+0.03−0.04. In the source frame, the initial black hole masses are 36+5−4M⊙ and 29+4−4M⊙, and the final black hole mass is 62+4−4M⊙, with 3.0+0.5−0.5M⊙c2radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole system This is the first direct detection of gravitational waves and the first observation of a binary black hole merger. PRLの論文より
- 3. ABSTRACT On September 14,2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10−21. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410+160−180 Mpc corresponding to a redshift z=0.09+0.03−0.04. In the source frame, the initial black hole masses are 36+5−4M⊙ and 29+4−4M⊙, and the final black hole mass is 62+4−4M⊙, with 3.0+0.5−0.5M⊙c2radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole system This is the first direct detection of gravitational waves and the first observation of a binary black hole merger. 重要と思われる部分 について説明します
- 4. On September 14,2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously マイケルソン・モーリーの光干渉計のこと！！
- 5. It matches thewaveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, ・重力波からブラックホールの融合がわかった ・この測定が雑音を勘違いしただけである可能性は 20万年に一度のレアイベントぐらいありえない
- 6. This is thefirst direct detection of gravitational waves and the first observation of a binary black hole merger. 世界ではじめて重力波の“直接観測”に成功した！ （連星パルサーの運動が厳密に相対論に 従うことは知られていたので おそらく重力波も出ているとは思われていた） ・ところで、重力波ってなに？ ・アインシュタインが予言したってほんと？ ・時空の歪みってなに？時空ってなに？ ・どこが難しかったの？
- 7.
- 8.
- 9.
- 10.
- 11.
- 12.
- 13.
- 14.
- 15.
- 16.
- 17. Riemann幾何より 相対論より したがって ここでRiemann幾何より なので とできる。 共変微分(∇)を 掛けると等しくなる 微分する と0になる のがg この係数Λが宇宙項！ 比例係数kは万有引力定数Gを含む アインシュタイン方程式の導出 uvuvG T C 0v uvT 0v uvG 0v uvg uvC g 重力場が弱いときはF=GM/r^2 （実験事実）と一致する にはk∝Gとなるしかない。これでkが決まる。
- 18.
- 19. http://eman-physics.net/relativity/gwave.html g = η+hとおく。ηは平坦な時空。hがズレ量 □h= 0 (と、hのローレンツ条件) （参考）電磁気学の波動方程式＝電磁波 □A= 0 (と、Aのローレンツ条件) 重力場が弱い時には時空の歪みhが形を崩さず伝搬する！（重力波)
- 20.
- 21. 重力波検出の方法 分かれた光が干渉する時、位相差（時間差）をφとすると、検出光強度Pは P∝(1-cosφ) 24dB Occurring within the10-ms intersite propagation time, the events have a combined signal-to noise ratio (SNR) of 24 重力波の振幅レベル（想定） 重力波の周波数 （想定） とらえた信号のSNR（信号と雑音レベルの差）は24dB=10^(2.4)倍の有意差
- 22.
- 23.
- 24.
- 25.
- 26.
- 27.