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Context. High-redshift quasars can be used to constrain the equation of state of dark energy. They can serve as a complementary tool to supernovae Type Ia, especially at z > 1. Aims. The method is based on the determination of the size of the broad line region (BLR) from the emission line delay, the determination of the absolute monochromatic luminosity either from the observed statistical relation or from a model of the formation of the BLR, and the determination of the observed monochromatic flux from photometry. This allows the luminosity distance to a quasar to be obtained, independently from its redshift. The accuracy of the measurements is, however, a key issue. Methods. We modeled the expected accuracy of the measurements by creating artificial quasar monochromatic lightcurves and responses from the BLR under various assumptions about the variability of a quasar, BLR extension, distribution of the measurements in time, accuracy of the measurements, and the intrinsic line variability. Results. We show that the five-year monitoring of a single quasar based on the Mg II line should give an accuracy of 0.06−0.32 mag in the distance modulus which will allow new constraints to be put on the expansion rate of the Universe at high redshifts. Successful monitoring of higher redshift quasars based on C IV lines requires proper selection of the objects to avoid sources with much higher levels of the intrinsic variability of C IV compared to Mg II.

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In this contribution, we summarize our results concerning the observational constraints on the electric charge associated with the Galactic centre black hole -Sgr A*. According to the no-hair theorem, every astrophysical black hole, including supermassive black holes, is characterized by at most three classical, externally observable parameters -mass, spin, and the electric charge. While the mass and the spin have routinely been measured by several methods, the electric charge has usually been neglected, based on the arguments of efficient discharge in astrophysical plasmas. From a theoretical point of view, the black hole can attain charge due to the mass imbalance between protons and electrons in fully ionized plasmas, which yields about ∼ 10 8 C for Sgr A*. The second, induction mechanism concerns rotating Kerr black holes embedded in an external magnetic field, which leads to electric field generation due to the twisting of magnetic field lines. This electric field can be associated with the induced Wald charge, for which we calculate the upper limit of ∼ 10 15 C for Sgr A*. Although the maximum theoretical limit of ∼ 10 15 C is still 12 orders of magnitude smaller than the extremal charge of Sgr A*, we analyse a few astrophysical consequences of having a black hole with a small charge in the Galactic centre. Two most prominent ones are the effect on the X-ray bremsstrahlung profile and the effect on the position of the innermost stable circular orbit.