- The paper introduces a novel method adapting the Eriş-Gürses integrability technique to derive explicit rotating solutions in four and five dimensions with a free scalar field.
- It rederives the Bogush-Gal’tsov solution, showing how a radial and angular scalar field modifies Kerr-like metrics in four-dimensional spacetime.
- A new five-dimensional configuration with two angular momenta is presented, linking scalar effects to Myers-Perry metrics and extending higher-dimensional gravity theories.
Rotating Spacetimes with a Free Scalar Field in Four and Five Dimensions
The paper, authored by J. Barrientos, C. Charmousis, A. Cisterna, and M. Hassaine, focuses on the construction of rotating solutions in Einstein's theory of relativity with a minimally coupled free scalar field in both four-dimensional and five-dimensional spacetimes. This work revisits and extends the formulation of spacetime configurations originally derived by Eriş and Gürses, providing insights into solutions that integrate scalar fields while maintaining rotational properties analogous to the Kerr and Kerr-Newman solutions.
Overview of Key Contributions
- Methodological Approach: The authors adapt the Eriş-Gürses integrability method, traditionally applied in spherical coordinates, to a simplified framework using explicit constructions of metric solutions in Boyer-Lindquist-like coordinates. This tactic enables new derivations without transitioning to the cumbersome Weyl coordinates often used in similar contexts.
- Four-Dimensional Solutions:
- The paper rederives the Bogush-Gal’tsov solution for rotating spacetimes with a scalar field, demonstrating how the presence of a scalar field modifies the Kerr solution's metric within non-Killing sectors.
- They extend this framework by incorporating a radial and angular scalar field dependence, further enriching the solution landscape beyond the radial scalar field typically assumed.
- Five-Dimensional Extensions:
- A novel rotating five-dimensional solution is constructed, characterized by two distinct angular momenta. Known as a scalar Myers-Perry-like configuration, this solution reflects a deeper exploration into the role of scalar fields in higher-dimensional gravity theories.
- The method identifies the scalar field effects on metric components and aligns them with the integrability traits of the initial vacuum solutions.
- Theoretical Implications and Extensions:
- The scalar fields in these solutions, devoid of mass, align with harmonic functions guiding their effects through non-linear interactions with gravitational fields. This interaction is pivotal in uncovering singularities related to the scalar fields and their implications on otherwise regular vacuum solutions.
- In static limits, these configurations translate into distinctive Zipoy-Voorhees geometries with scalar hair, emphasizing the scalar fields' impact as both deformations and intrinsic contributors to spacetime structures.
Practical and Theoretical Implications
This research has implications for both theoretical exploration and practical applications:
- Theoretical Relevance: The findings offer insights into modified gravity scenarios where scalar fields coalesce with macroscopic phenomena such as black holes. The scalar fields' backreaction not only alters spacetime topology but also poses questions about the nature of singularity and event horizon alterations.
- Higher-Dimensional Gravity: The generalization into five dimensions not only aligns with string theory and other high-dimensional frameworks but also provides new potential forms for spacetimes that might accommodate charges and other non-Einsteinian features.
- Extensions Beyond GR: Future research may leverage these findings for expanded gravitational theories that consider higher-order interactions, cosmological constants, or additional fields, further exploring the scalar-tensor theory domain.
Conclusion
The comprehensive paper demonstrated by this paper underlines the efficacy of adopting scalar fields in constructing classical solutions in gravity that challenge conventional paradigm stability. By showcasing symmetry adaptations and explicitly formulating integrable aspects of these theories, the paper sets a precedent for future inquiries into more complex gravitational interactions and higher-dimensional physics.
