Higher derivative gravity and holography

During the past century, the effort of the physicists led to a unified description of three fundamental interactions: electromagnetic, weak and strong. However, every attempt of unifying the only known interaction left out, the gravitational one, has been inconclusive. Inspired by the physical properties of black holes, the seek of a better understanding of the nature of gravity led to the formulation of the holographic principle. This principle reveals a connection between a gravity theory with a much better understood quantum field theory.

One may then wonder if it possible to find limitations or new effects if we try to step outside of the comfort zone of the original formulation of this principle. This thesis tries to answer this question by using mathematical structures and physical quantities as a tool to explore the holographic principle. This will be done in the context of a modified theory of gravity called New Massive Gravity.

We will observe that such a generalization of the gravity theory gives us more freedom in performing our exploration by providing us a broader range of solutions. Moreover, the study of a physical quantity called entanglement entropy reveals a relationship between the quantum properties of matter and the mathematical properties of a geometric object. This relationship is only possible if we explore the holographic principle with a modified theory of gravity.