Physicists modified the Penrose inequality in anti-de Sitter three-dimensional space and tested it on rotating and stationary quantum black holes. As a result, scientists put forward a hypothesis about the existence of quantum cosmic censorship within the framework of semiclassical gravity. The researchers shared their findings in Physical Review Letters.
Black holes in modern physics are key objects that have helped scientists understand the relationship between geometry and matter: for example, the Penrose inequality (and its special case, the Riemann-Penrose inequality) linked the minimum mass of a body and the area of the black hole enclosing it. It turned out that any violation of the Penrose inequality implies a violation of weak cosmic censorship in the classical formulation and does not allow scientists to consider quantum singularity objects.
However, if we take into account the thermal nature of black holes, whose entropy is proportional to the area of the event horizon, the Penrose inequality can be interpreted as a constraint on the entropy - we get the quantum Penrose inequality, which establishes a correspondence between quantum matter and classical gravity. Numerical evaluation of this inequality requires physicists to solve Einstein's semiclassical equations, which is currently an open problem for space dimensions greater than two.
Antonia Frassino from the University of Alcalá and her colleagues from the UK, Spain and Italy tested the quantum Penrose inequality by circumventing the limitations on the dimensionality of space when solving Einstein's equations. To do this, the scientists considered its modification in anti-de Sitter space under the assumptions of conformal field theory and tested the resulting inequality on quantum black holes BTZ, which were not chosen by chance: the geometry and thermodynamics of these objects are easy for physicists to find analytically.
First of all, the researchers were convinced that the first law of thermodynamics is fulfilled for the developed model, and after a more detailed analysis of the quantum Penrose inequality, the scientists concluded that achieving exact equality means the following: quantum effects can create black holes with masses forbidden by classical physics, which, according to theorists, became the first sign of the existence of the so-called quantum cosmic censorship. At the same time, cases of potential violation of the inequality were localized for cases of thermodynamically unstable black holes.
The authors of the work noted that in the future, their model needs to be tested on anti-de Sitter spaces of higher dimensions and other types of quantum black holes should be used to identify new features of semi-classical gravity.
We wrote earlier about how loop quantum gravity predicted the transition between a black hole and a white hole.
