Higher-dimensional black holes with Dirac-Born-Infeld (DBI) global defects

TL;DR

This paper explores higher-dimensional black holes with Dirac-Born-Infeld global defects, revealing their unique thermodynamic behaviors and stability properties, especially contrasting asymptotically flat and AdS spacetimes.

Contribution

It introduces new solutions for black holes with DBI scalar hair in higher dimensions and analyzes their thermodynamics and stability, highlighting the effects of DBI coupling and dimensionality.

Findings

Black hole solutions with DBI scalar hair exist in all dimensions.

Thermodynamic properties vary with DBI coupling and dimension, showing no phase transition in flat spacetime.

AdS black holes exhibit a first-order Hawking-Page phase transition influenced by DBI coupling.

Abstract

It is well-known that the exact solution of non-linear $\sigma$ model coupled to gravity can be perceived as an exterior gravitational field of a global monopole. Here we study Einstein's equations coupled to a non-linear $\sigma$ model with Dirac-Born-Infeld (DBI) kinetic term in $D$ dimensions. The solution describes a metric around a DBI global defects. When the core is smaller than its Schwarzschild radius it can be interpreted as a black hole having DBI scalar hair with deficit conical angle. The solutions exist for all $D$, but they can be expressed as polynomial functions in $r$ only when $D$ is even. We give conditions for the mass $M$ and the scalar charge $\eta$ in the extremal case. We also investigate the thermodynamic properties of the black holes in canonical ensemble. The monopole alter the stability differently in each dimensions. As the charge increases the black hole radiates more, in contrast to its counterpart with ordinary global defects where the Hawking temperature is minimum for critical $\eta$. This behavior can also be observed for variation of DBI coupling, $\beta$. As it gets stronger ($\beta\ll1$) the temperature increases. By studying the heat capacity we can infer that there is no phase transition in asymptotically-flat spacetime. The AdS black holes, on the other hand, undergo a first-ordered phase transition in the Hawking-Page type. The increase of the DBI coupling renders the phase transition happen for larger radius.