A tale of two theories…

“A tale of two theories of gravity in asymptotically Anti-de Sitter spacetime,” i.e. an analysis of similarities and differences of two different formulations of gravity in space-time with a negative cosmological constant.

Gravity is one of the basic forces of nature, but it is also one of the most mysterious and difficult to understand phenomena. There are many ways to define gravity with mathematical models, but not all of them are consistent in defining its effects in certain situations, such as near black holes or on the edge of space-time.

In the new article published in the Journal of High Energy Physics, dr Remigiusz Durka and prof. Jerzy Kowalski-Glikman studied two such models, known as the Plebanski theory (applied among others by the Loop Theory of Gravity) and the MacDowell-Mansouri theory (popular among physicists interested in supergravity models). Both models are based on a geometrical approach applying the so-called formalism of BF theory to describe gravity but vary in certain details with substantial consequences.

The authors focused on a special type of space-time, called the asymptotically Anti-de Sitter spacetime (AAdS), which defines the Universe with a negative cosmological constant. This means that it possesses a constant negative curve affecting the behaviour of gravity over long distances. Such space-time is interesting for many reasons: it is the basic solution to Einstein’s general relativity theory equations, it is relevant to studies of black holes and quantum gravity, and is related to the hypothetical correspondence between gravity and quantum field theory, known as AdS/CFT.

The work shows that both theories mentioned lead to the same Einstein’s equations in the volume of the AAdS space, but differ in their description of the boundary conditions. Those conditions are related to retained charges that measure the energy and momentum of the system. The authors counted those charges for some of the precise solutions to Einstein’s equations: upon analysing the space-time around a static black hole, the calculations were repeated for a spinning black hole, as well as a configuration which, in addition to mass, also contains dual mass (which is the gravitational analogue of magnetic monopole).

It turned out that, while the Plebanski theory gives (infinite) divergent charges that require additional corrective components for them to become finite and correct, the considered MacDowell-Mansouri theory directly gives finite charges that match the expected values. Moreover, the authors demonstrated that this result is true for any asymptotic AdS space, not only for specific solutions. They also proved that the MacDowell-Mansouri BF theory has a finite operation and symplectic structure, relevant for determining the dynamics and quantisation of gravity.

“Our work shows that the MacDowell-Mansouri theory is better suited for description of gravity in an asymptotic AdS space than the Plebanski theory. We do not need then any additional segments or renormalisation in order to obtain correct results,” comments dr Durka.

The publication titled A tale of two theories of gravity in asymptotically Anti-de Sitter spacetime is available online at https://arxiv.org/abs/2210.10154.

Authors:

Remigiusz Durka (adjunct at the Faculty of Physics and Astronomy of the University of Wrocław) and
Jerzy Kowalski-Glikman (professor at the Faculty of Physics and Astronomy of the University of Wrocław and researcher at the National Center for Nuclear Research)