Taking black holes (as a real object) as a test material, scientists from the Ural Federal university (UrFU, Yekaterinburg) found out that a popular theory of gravity which had seemed to work perfectly at the cosmological level (a subclass of Horndeski theory) is hardly applicable to the real world. They presented their study in the *Classical and Quantum Gravity*journal.

At the moment, according to the authors of the paper, black holes are believed to be existing rather than hypothetical objects. The gravitational-wave signal received in 2015 and marked by the Nobel Prize in physics in 2017 confirmed this fact again. Black holes exist, and this is one of the proofs that the general theory of relativity (GR) is correct.

However, modern physics has accumulated a lot of prerequisites for the revision of general relativity, for example, the accelerated expansion of the universe, the presence of dark matter and, finally, the impossibility to renormalize gravity. All the fundamental interactions known to science have already been described in quantum language, except for gravitation. These small inconsistencies indicate that the theory of relativity is not the final theory of gravitation, but only one of the approximations to it (a similar story occurred with Newton's theory). Theoretical physicists constantly formulate and propose extended theories of gravity, and we need to check these models and compare them with observations.

One of the simplest versions of such an extended theory appears under the assumption that the gravitational constant (a fundamental physical quantity that is the same in time and at all points in the universe) is not a constant, but a field that can vary in time and space. Scientists cannot measure this slowly changing field at current level of accuracy and only therefore perceive it as a constant. If we accept this hypothesis, then there appears gravity with a scalar field (given only one number at each point). This is how the first and simplest theory of gravity with a scalar field, the Brans-Dicke theory, was formulated. Today the class of gravity theories with a scalar field is very wide. Such theories are considered to be one of the most promising ways of expanding the general relativity.

In his work, DariaTretyakova, PhD from UrFU, together with her colleague from the University of Tokyo explored one of the theories of this class - the so-called Horndeski theory. Horndeski framework gives the most general theory of gravity with a scalar field, without instabilities and containing "healthy" physics, that is, no unusual parameters of matter(for example, negative or imaginary mass) occur.

At the cosmological level (the scale at which the universe can be viewed as a single object of study), a subclass of Horndeski models, which are symmetric with respect to the shift of the scalar field in space and time, have proved themselves well and helped scientists describe the accelerated expansion of the universe without resorting to additional theories. These models were chosen for rigorous and comprehensive testing. The authors of the paper "moved" the Horndeski models to the astrophysical scale (the scale of individual objects of the universe) and found out that black holes (as real objects) turn out to be unstable in the models which previously successfully proved themselves in cosmology.

Consequently, these models are hardly suitable for describing the real universe, because today black holes are believed to exist in space as stable objects. The situation, however, is not hopeless: the scientists proposed a way to construct Horndeski models that ensure black holes stability.

The paper is a next step to a new theory of gravity that will meet all the requirements of modern physics. Now the authors are planning to subject the newly proposed models to standard tests: to check their adequacy at the cosmological and astrophysical scale.