Taking quantum corrections into account, the Einstein-Lovelock theory describes black holes with an equation that contains an infinite number of terms. However, according to a physicist at RUDN University, the geometry of a black hole can be represented in this theory in a compact form, and a limited number of terms can be enough to describe the observed values. This could help scientists study black holes in theories using quantum corrections to Einstein’s equations. Photo credit: RUDN University
Taking quantum corrections into account, the Einstein-Lovelock theory describes black holes with an equation that contains an infinite number of terms. According to a physicist from RUDN University, the geometry of a black hole This theory can be presented in compact form and a limited number of terms can suffice to describe the observed values. This could help scientists study black holes in theories using quantum corrections to Einstein’s equations. The work was published in the Physics letter B. Diary.
Einstein’s general theory of relativity predicted the existence of black holes – supermassive objects in the universe that attract everything, including light. Black holes are described by many mathematical models, one of which is the Einstein-Lovelock theory, which imposes quantum corrections to elaborate on general relativity. It describes a black hole by the sum of an infinite number of terms. However, a physicist from RUDN University confirmed that a limited number of terms can suffice to describe the effects observed near a black hole. Other components of the equation have negligibly small contributions that can be ignored. This would greatly simplify the calculations and help researchers study black holes in theories with quantum corrections.
According to Einstein’s theory, heavy objects distort space-time – a 4D construction with three spatial and one temporal dimensions. In 1971 Lovelock generalized this theory to any number of dimensions. The Einstein-Lovelock equation is an infinite sum: the first two terms in it are Einstein’s representation, and each subsequent one describes the space-time curvature.
Each term in the Einstein-Lovelock equation is multiplied by what is known as the coupling constant. According to the physicist of the RUDN University, corrections with high curvature can be “cut off” if one adheres to the positive values of the coupling constants. This is due to the fact that every coupling constant has a critical value: After reaching it, a black hole becomes unstable, ie it can no longer exist in reality. Such a representation is still possible from a mathematical point of view, but has no physical meaning. The more terms, the lower the critical value for the coupling constants. Hence, the stability of a black hole (i.e. the possibility of its physical existence) can be used as a criterion for removing redundant terms.
“With each new Lovelock term, the critical value of the coupling constant becomes lower. This is an important observation: it confirms that all other terms can be considered negligibly small to find the greatest possible correction to black hole geometry caused by a newly added Lovelock term, ”said Roman Konoplya, researcher at the Academic Research Institute for Gravitation and Cosmology, RUDN University.
According to the scientist and his team, the most important observable values (such as the radius of a black hole shadow) remain practically unchanged when the Lovelock corrections with a curvature higher than the fourth order are included. These results can be useful not only for studying processes in the black holes, but also for confirming theoretical predictions associated with possible generalizations of Einstein’s theory.
Reference: “4D Einstein-Lovelock black holes: Hierarchy of the orders of curvature” by RA Konoplya and A. Zhidenko, July 7, 2020, Physics letter B..
DOI: 10.1016 / j.physletb.2020.135607
