Scalar-Tensor Theories and Black Hole Solutions
Summary
Scalar-tensor theories generalise Einstein’s gravity by introducing a scalar field that modifies the gravitational interaction. These models often arise in attempts to unify gravity with other forces or to address cosmological puzzles. The scalar field typically couples to curvature invariants, such as the Ricci scalar or higher-order combinations like the Gauss-Bonnet term, leading to novel black-hole solutions. In contrast to the classical no-hair theorems of general relativity, which restrict black holes to mass, charge and spin, scalar-tensor theories can evade these constraints and permit “hair”—nontrivial scalar profiles outside the event horizon. Spontaneous scalarisation, driven by tachyonic instabilities, can endow charged or rotating black holes with scalar hair, enriching the spectrum of compact objects. Such hairy solutions exhibit distinct horizon geometries, modified light rings and ergospheres, and altered thermodynamic properties. The study of these configurations not only probes the limits of classical gravity but also offers potential observational signatures in gravitational-wave signals and black-hole imaging.
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Scalar-Tensor Theories and Black Hole Solutions publication trend
The graph below shows the total number of articles in scalar-tensor theories and black hole solutions across all publications each year (not limited to Nature Index journals).
Technical terms
Scalar-tensor theory: A modification of general relativity that includes one or more scalar fields coupled to curvature invariants.
Scalar hair: A nontrivial scalar-field configuration outside a black hole’s event horizon, providing additional degrees of freedom beyond mass, charge and spin.
No-hair theorem: A principle in general relativity stating that black holes are uniquely characterised by mass, charge and angular momentum, typically forbidding other external fields.
Gauss-Bonnet term: A specific quadratic combination of curvature invariants that, when coupled to scalar fields, alters black-hole solutions in modified gravity theories.
Tachyonic instability: A condition in which the effective mass-squared of a field becomes negative, triggering spontaneous growth of that field near a compact object.
Kerr-Newman black hole: A solution of the Einstein–Maxwell equations describing a rotating, electrically charged black hole in general relativity.
References
- Scalarized Kerr-Newman black holes. Journal of High Energy Physics (2023).
- Static de-Sitter black holes abhor charged scalar hair. European Physical Journal C (2023).
- Evasion of No-Hair Theorems and Novel Black-Hole Solutions in Gauss-Bonnet Theories. Physical Review Letters (2018).
- Black-hole solutions with scalar hair in Einstein-scalar-Gauss-Bonnet theories. Physical Review D (2018).
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