Asymptotically locally AdS and flat black holes in Horndeski theory (1312.3597v2)

Abstract: In this paper we construct asymptotically locally AdS and flat black holes in the presence of a scalar field whose kinetic term is constructed out from a linear combination of the metric and the Einstein tensor. The field equations as well as the energy-momentum tensor are second order in the metric and the field, therefore the theory belongs to the ones defined by Horndeski. We show that in the presence of a cosmological term in the action, it is possible to have a real scalar field in the region outside the event horizon. The solutions are characterized by a single integration constant, the scalar field vanishes at the horizon and it contributes to the effective cosmological constant at infinity. We extend these results to the topological case. The solution is disconnected from the maximally symmetric AdS background, however, within this family there exits a gravitational soliton which is everywhere regular. This soliton is therefore used as a background to define a finite Euclidean action and to obtain the thermodynamics of the black holes. For a certain region in the space of parameters, the thermodynamic analysis reveals a critical temperature at which a Hawking-Page phase transition between the black hole and the soliton occurs. We extend the solution to arbitrary dimensions grater than four and show that the presence of a cosmological term in the action allows to consider the case in which the standard kinetic term for the scalar it's not present. In such scenario, the solution reduces to an asymptotically flat black hole.

Asymptotically Locally AdS and Flat Black Holes in Horndeski Theory

The paper "Asymptotically locally AdS and flat black holes in Horndeski theory" by Andres Anabalon, Adolfo Cisterna, and Julio Oliva rigorously explores the construction of black hole solutions within the framework of Horndeski theory. This investigation is set in the context of asymptotically locally AdS and flat spaces, with particular attention given to the role of scalar fields whose kinetic terms incorporate both the metric and the Einstein tensor. The work positions itself within the broader landscape of alternative theories of gravity, addressing contemporary challenges such as dark matter, dark energy, and inflationary dynamics.

Core Findings and Technical Aspects

The authors have derived solutions which are primarily characterized by a single integration constant. A salient feature of these solutions is the vanishing scalar field at the horizon, which nonetheless contributes significantly to the effective cosmological constant at infinity. It’s critical to note that while these solutions diverge from the maximally symmetric AdS backgrounds, they encapsulate a regular gravitational soliton within the same family, which proves instrumental as a background for defining a finite Euclidean action and in elucidating the thermodynamics of the black holes.

Of particular interest is the identification of a critical temperature where a Hawking-Page phase transition surfaces between the black holes and the soliton. This phenomenon highlights the thermodynamic richness and complexity inherent in Horndeski frameworks. Moreover, the solutions are proficiently extended to dimensions greater than four, which permits further scenario analysis where standard kinetic terms for the scalar might be absent, yielding, in turn, asymptotically flat black holes.

Numerical Results and Bold Claims

The analytical approach combined with thermodynamic analyses reveals significant results:

• The presence of the cosmological term enables real scalar fields outside the event horizon, a deviation from the solutions with a vanishing cosmological constant where scalar fields become imaginary.
• The inclusion of non-standard kinetic couplings broadens the family of possible black hole configurations, reflecting the paper's departure from traditional frameworks, and suggesting alternative portrayal of gravitational dynamics.
• The region of parameter space governing the entropy of black holes is elucidated, showing conditions under which entropy remains positive, thus maintaining thermodynamic validity.

Implications and Future Directions

The solutions derived in this work expand the boundaries of known configurations in scalar-tensor theories, elucidating new pathways through which scalar fields can interact with gravitational regimes in higher dimensions. This suggests promising avenues for further elucidating the complex dynamics involving scalar fields in higher curvature terms and potentially addressing observational discrepancies in cosmic phenomena.

The paper also raises questions regarding the full range of possible configurations in diverse scalar-tensor frameworks, inviting more exhaustive exploration of Horndeski theories' capabilities. Potentially, leveraging local symmetries such as conformal invariance or exploring further couplings built from Lovelock tensors could unveil new solutions of appreciable practical significance.

Conclusion

The exploration into asymptotically locally AdS and flat black holes within Horndeski theory marks a substantial contribution to theoretical physics, extending our comprehension of gravitational theories inclusive of scalar fields. It engenders novel thermodynamic insights and underscores the imperative for continued theoretical development in scalar-tensor paradigms. The implications for astrophysical observations and theoretical constructs are profound, setting a foundation for further probing into the intersection of quantum fields and gravity.