**3.1 Indirect**

In 1974, the most plausible indirect detection of gravitational waves was made by Joseph Taylor, Jr. and Russell Alan Hulse, when observing pulsars surrounding a neutron star (neutron stars are less dense cousins of black holes). That is the Hulse-Taylor binary, a pair of stars, which is a pulsar [15]. The characteristics of its orbit can be deduced from the Doppler shift of radio signals emitted by the pulsar. Each of the stars is about 1.4 M (M being the mass of the Sun) and the radius of their orbits is around 0.013 of the distance between Earth and Sun, smaller than the diameter of the Sun. The combination of smaller separation and bigger masses means that the energy emitted by the Hulse and Taylor binary will be much larger than the energy emitted by the Earth and Sun system by a factor of approximately 1022 times.

Information about the orbit can be used to estimate the amount of energy and angular momentum that would be emitted in the form of gravitational radiation. As the energy is emitted, the pulsars must get closer to each other. Measurements in the Hulse-Taylor system were performed over 30 years ago. The change in the orbital period corresponds to the prediction of gravitational radiation, assumed by general relativity to be within 1 part in 500. Russell Hulse and Joe Taylor, in 1993, were awarded the Physics Nobel Prize for this remarkable work, which was the first indirect evidence of gravitational radiation. This binary system, from the present until the time of the merger, is estimated to have a lifespan of a few hundred million years [16].

#### **3.2 Direct**

After that scientists were motivated to prove its existence. In the mid-1990s they were simulating the Black Hole merger, until the arrival of the Laser Interferometer Gravitational-Wave Observatory (LIGO) and the Italian Gravitational Wave Interferometer Detector (Virgo) at the end of the 20th century made slow progress needing much improvement. The challenge was not the physics itself or the equipment only, but the math behind it. Einstein's equations are called constraint equations, in which the solutions must always satisfy specific conditions, which is difficult since there are 10 equations with thousands of terms [17]. These simulations were necessary as the detectors needed a set of templates for the detected signal in order to establish the source of the signal, but using numerical relativity the set of these templates is still being built. Just to remember that Bayesian statistics is used in the detection.

In late 2015, researchers from the LIGO (Laser Interferometer Gravitational-Wave Observatory) project observed "distortions in spacetime" caused by a pair of black holes, about 30 solar masses each, in the process of merging [14, 17]. The signal was detected in the two LIGO sites on September 14, 2015 at 6:50:45 a.m. PDT, the event was named GW150914. The signal oscillated from 35 Hz to 250 Hz, with a time difference of 7 × 10−3 s between the detection of each observatory, and a maximum amplitude of 1.0 × 10−21. Thus, coinciding with the shape predicted by Einstein almost exactly 100 years ago for an encounter of massive bodies, in the case of black holes that surround each other until they meet and merge, thus resulting in a significant warping in spacetime. To the relief of many, the merger took place at a distance of ~1.3 billion light-years from Earth. The masses of the initial black holes were 29 M and 36 M, (solar mass, M, approximately 1.99 × 1030 kg); the mass of the resulting black hole was 62M, and approximately 3.0 Mc2 of energy was converted into gravitational waves to the rest of the Cosmos [14]. The signal of this measurement can be seen in Ref. [14]: the detected signal measured in the two observatories (located in Hanford, WA e Livingston, LA) are shown. First row shows the signal detected in the interferometers; it is shown a difference in time signal over the signal at the Louisiana observatory due to difference in the signal arrival time. Second row shows the expected signal of signal for the optimal source template previously calculated. Third row shows the residuals from rows 1 and 2. Row 4 shows the signal in the frequency domain against time.

In June 2016, the second burst of gravitational waves from merging black holes was announced, suggesting that such detections will soon become routine and part of a new kind of astronomy [18].

On June 1, 2017, for the third time, scientists announced that they had detected the infinitesimal reverberations of spacetime [19].
