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, the scientists hypothesized 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 to the area of the enclosing black hole. It turned out that any violation of the Penrose inequality implies a violation of weak cosmic censorship in the classical formulation and prevents scientists from considering quantum singularities.
However, if we consider 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 bound on entropy—the result is 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 spatial dimensions greater than two.
Antonia Frassino of the University of Alcalá and her colleagues from the UK, Spain, and Italy tested the quantum Penrose inequality by circumventing the spatial dimensionality restrictions 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 verified the resulting inequality on quantum black holes (BTZs), which were chosen deliberately: the geometry and thermodynamics of these objects are easily determined analytically by physicists.
First, the researchers confirmed that the first law of thermodynamics holds for the developed model. After a more detailed analysis of the quantum Penrose inequality, the scientists concluded that achieving exact equality implies the following: quantum effects can create black holes with masses forbidden by classical physics, which, according to theorists, was the first indication of the existence of so-called quantum cosmic censorship. Moreover, cases of potential violation of the inequality were localized to cases of thermodynamically unstable black holes.
The authors of the paper noted that their model needs to be further tested on higher-dimensional anti-de Sitter spaces and other types of quantum black holes should be used to identify new features of semiclassical gravity.
We wrote earlier about how loop quantum gravity predicted the transition between a black hole and a white hole.
