Holographic superconductor phase transition and spontaneous scalarization are
triggered by the instability of the underlying vacuum black hole spacetime.
Although both hairy black hole solutions are closely associated with the
tachyonic instability of the scalar degree of freedom, they are understood to
be driven by distinct causes. It is, therefore, interesting to explore the
interplay between the two phenomena in the context of a scenario where both
mechanisms are present. To this end, we investigate the
Einstein-scalar-Gauss-Bonnet theory in asymptotically anti-de Sitter spacetime
with a Maxwell field. On the one hand, the presence of the charged scalar and
Maxwell fields in anti-de Sitter spacetime furnishes the celebrated framework
for a holographic superconductor. On the other hand, the non-minimal
Gauss-Bonnet coupling between the scalar field and the gravitational sector
triggers spontaneous scalarization. However, near the transition curve, the two
phases are found to be largely indistinguishable regarding both the radial
profile and effective potential. This raises the question of whether the hairy
black holes triggered by different mechanisms are smoothly joined by a phase
transition or whether these are actually identical solutions. To assess the
transition more closely, we evaluate the phase diagram in terms of temperature
and chemical potential and discover a smooth but first-order transition between
the two hairy solutions by explicitly evaluating Gibbs free energy and its
derivatives. In particular, one can elaborate a thermodynamic process through
which a superconducting black hole transits into a scalarized one by raising or
decreasing the temperature. Exhausting the underlying phase space, we analyze
the properties and the interplay between the two hairy solutions.
Introduction
In this article, we examine the conclusions of a recent study on the interplay between holographic superconductors and spontaneous scalarization in black holes. The study investigates the Einstein-scalar-Gauss-Bonnet theory in anti-de Sitter spacetime with a Maxwell field, which provides a framework for both holographic superconductors and spontaneous scalarization. We explore the possibility of a phase transition between these two hairy black hole solutions and analyze the properties and interplay between them.
Holographic Superconductors and Scalarization
Holographic superconductors are systems that exhibit properties similar to superconductors in condensed matter physics, but are described by gravity theories in higher dimensions. The presence of charged scalar and Maxwell fields in anti-de Sitter spacetime allows for the formation of these superconducting black holes.
Spontaneous scalarization, on the other hand, is triggered by the non-minimal Gauss-Bonnet coupling between the scalar field and the gravitational sector. This coupling leads to the emergence of scalar hairs on black holes, which was previously thought to be impossible in Einstein’s theory of gravity.
Exploring the Interplay
The main focus of this study is to investigate the interaction between holographic superconductors and spontaneous scalarization. By considering the Einstein-scalar-Gauss-Bonnet theory with a Maxwell field, the researchers aim to understand whether these two phenomena can coexist and if there is a phase transition between them.
The study finds that near the transition curve, the two phases of hairy black holes are indistinguishable regarding their radial profile and effective potential. This raises questions about their true nature and whether they are actually identical solutions.
Evaluating the Phase Diagram
To assess the phase transition between holographic superconductors and scalarized black holes, the researchers evaluate the phase diagram in terms of temperature and chemical potential. They discover a smooth but first-order transition between the two solutions by analyzing the Gibbs free energy and its derivatives.
This implies that it is possible to transit a superconducting black hole into a scalarized one by raising or decreasing the temperature in a well-defined thermodynamic process.
Challenges and Opportunities
Understanding the interplay between holographic superconductors and spontaneous scalarization opens up new possibilities for exploring exotic phenomena in black hole physics. It provides insights into the nature of these hairy black hole solutions and how they can transition between different phases.
However, there are also challenges in further investigating this interplay. The underlying phase space needs to be thoroughly exhausted to analyze the properties and behavior of both solutions. Additionally, more research is needed to fully understand the significance of the phase transition and its implications for the broader field of gravity theories.
Conclusion
Overall, this study highlights the intriguing connection between holographic superconductors and spontaneous scalarization in black holes. It demonstrates that there is a smooth but first-order phase transition between these two hairy solutions. By evaluating the phase diagram and analyzing thermodynamic processes, we gain a deeper understanding of the interplay between these phenomena. Further exploration of this field holds promise for uncovering new insights into the nature of black holes and gravity theories.
Sources:
- Research paper: [INSERT LINK]