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(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Lie Theory and Special Functions

A geometric inequality in general relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr?Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse; they are closely related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problems is presented.

Geometric inequalities for axially symmetric black holes

We investigate the effects of quintessence dark energy on the shadows of black hole, surrounded by various profiles of accretions. For the thin-disk accretion, the images of the black hole comprises the dark region and bright region, including direct emission, lensing rings and photon rings. Although their details depend on the form of the emission, generically, direct emission plays a major role for the observed brightness of the black hole, while the lensing ring makes a small contribution and the photon ring makes a negligible contribution. The existence of a cosmological horizon also plays an important role in the shadows, since the observer in the domain of outer communications is near the cosmological horizon. For spherically symmetric accretion, static and infalling matters are considered. We find that the positions of photon spheres are the same for both static and infalling accretions. However, the observed specific intensity of the image for infalling accretion is darker than for static accretion, due to the Doppler effect of the infalling motion.

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Influence of quintessence dark energy on the shadow of black hole

A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse, they are closed related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problem is presented.

Basing on the ideas used by Kiselev, we study the Hayward black hole surrounded by quintessence. The values critical of mass and the normalization factor are obtained. We also described the horizons and the extremal condition of the Hayward black hole surrounded by quintessence. By setting for the quintessence state parameter at the particular case of $$\omega =-\frac{2}{3}$$
 , we study the effective potential, and we analyzed in detail the null geodesics for different energies as well as the behavior of horizons. Finally, the shadow of the black hole is explored.

Geodesics of Hayward black hole surrounded by quintessence

Unequal binary configurations of interacting Kerr black holes

Corotating two-body system of identical Kerr sources

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.

http://homepage.cem.itesm.mx/fdelgado/ciencia/cadi/ref07.pdf

Beyond conventional factorization: non-Hermitian Hamiltonians with radial oscillator spectrum

A four-parametric exact solution describing a two-body system of identical Kerr-Newman counterrotating black holes endowed with opposite electric/magnetic charges is presented. The axis conditions are solved in order to really describe two black holes separated by a massless strut. Moreover, the explicit form of the horizon half length parameter $\ensuremath{\sigma}$ in terms of physical Komar parameters, i.e., Komar's mass $M$, electric charge ${Q}_{E}$, angular momentum $J$, and a coordinate distance $R$ is derived. Additionally, magnetic charges ${Q}_{B}$ arise from the rotation of electrically charged black holes. As a consequence, in order to account for the contribution to the mass of the magnetic charge, the usual Smarr mass formula should be generalized, as it is proposed by A. Tomimatsu, Prog. Theor. Phys. 72, 73 (1984).

I. Cabrera-Munguia

Papers

Geodesics of Hayward black hole surrounded by quintessence

Unequal binary configurations of interacting Kerr black holes

Corotating two-body system of identical Kerr sources

Beyond conventional factorization: non-Hermitian Hamiltonians with radial oscillator spectrum

Opposite charged two-body system of identical counterrotating black holes