Black holes are intriguing objects in general relativity which exhibit thermodynamic behavior and
can be assigned temperature and entropy. Understanding its thermodynamic properties is a fundamental
issue in black hole physics. Surprisingly, recently the study of black holes has also been relevant
to explore the properties of realistic theories such as QCD, plasma and superconductors in the context
of the gauge/gravity correspondence.
Black holes first appeared as classical solutions of general relativity. Almost a century ago,
Schwarzschild presented the first explicit black hole solution. More general black hole solutions were
only discovered much later. All black hole solutions have a point-like curvature singularity, which is
separated from the outside world by a hypothetical surface known as the event horizon.
Low energy limit of string theory gives rise to gravity coupled to other fields. As a results these
theories have black hole solutions. In this way string theory gives a framework for studying classical
and quantum properties of black holes. Interestingly, study of them has led to new results in string theory.
We study thermodynamic properties of dyonic black hole and its dual field theory. We observe that
the phase diagram of a dyonic black hole in constant electric potential and magnetic charge ensemble
is similar to that of a Van der Waals fluid with chemical potential. Phase transitions and other critical
phenomena have been studied in presence of magnetic charge and chemical potential. We also analyse
magnetic properties of dual conformal field theory and observe a ferromagnetic like behavior of boundary
theory when the external magnetic field vanishes. Finally, we compute susceptibility of different phases
of boundary CFT and find that, depending on the strength of the external magnetic field and temperature,
these phases are either paramagnetic or diamagnetic.
References: Suvankar Dutta, Akash Jain, Rahul Soni, "Dyonic Black Hole and Holography,"