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

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 ($\beta \ll 1$) 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.

arXiv comment35 pages, 10 figures, General Relativity and Gravitation (2018)

References in corpus (22)

• A Dynamical Solution to the Problem of a Small Cosmological Constant and Late-time Cosmic Acceleration
• k-Inflation
• DBI in the Sky
• Ghost Condensation and a Consistent Infrared Modification of Gravity
• Pair Creation of Black Holes During Inflation
• Born-Infeld Black Holes in (A)dS Spaces
• Dirty blackholes: Thermodynamics and horizon structure
• Global topological k-defects
• Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime
• Thermodynamics and phase transitions in the Born-Infeld-anti-de Sitter black holes
• Gravity of higher-dimensional global defects
• Nariai, Bertotti-Robinson and anti-Nariai solutions in higher dimensions
• Gauge k-vortices
• Schwarzschild black hole with global monopole charge
• Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole
• Effective Temperatures and Radiation Spectra for a Higher-Dimensional Schwarzschild-de-Sitter Black-Hole
• Gravitating Global k-monopole
• Phase transitions for the topological de Sitter spaces and Schwarzschild-de Sitter black hole
• A Self-gravitating Dirac-Born-Infeld Global Monopole
• Gravity of a noncanonical global monopole: conical topology and compactification
• Classical defects in higher-dimensional Einstein gravity coupled to nonlinear $\sigma$-models
• Aspects of the Thermo-Dynamics of a Black Hole with a Topological Defect

Cited by in corpus (1)

• Global Monopole in Palatini f(R) gravity