Gravitational Theories and Black Hole Solutions

Gravitational theories extend from Einstein’s general relativity to a range of higher-order and alternative frameworks that seek to reconcile gravity with quantum mechanics and to explain cosmological observations. At their core, these theories modify the Einstein–Hilbert action by adding terms nonlinear in curvature invariants, such as the Ricci scalar squared or contractions of the Weyl tensor. These generalisations yield a richer spectrum of static, spherically symmetric spacetimes, including standard Schwarzschild black holes, non-Schwarzschild solutions, horizonless compact objects and traversable wormholes. The interplay between higher-derivative corrections and classical horizons has led to fresh insight into phase spaces of solutions, stability criteria and observable signatures. In particular, the study of geodesic motion and light propagation around compact objects has revealed how deformations from general relativity alter photon spheres and black hole shadows, offering novel tests with very-long-baseline interferometry. On the theoretical side, analyses of perturbations and degrees of freedom in modified actions have clarified the role of scalar and tensor modes, the absence or emergence of ghost degrees and the conditions under which Birkhoff-type uniqueness theorems fail. Collectively, these developments enrich our understanding of gravitational collapse, horizon formation and the ultimate compatibility of gravity with quantum principles.

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Gravitational Theories and Black Hole Solutions publication trend

The graph below shows the total number of articles in gravitational theories and black hole solutions across all publications each year (not limited to Nature Index journals).

Technical terms

Quadratic gravity: A modification of general relativity in which the action includes terms quadratic in curvature invariants, such as R² or R_{μν}R^{μν}, often introduced for renormalisability.

Photon sphere: The unstable spherical region around a black hole where null geodesics can orbit, crucial for determining the apparent shadow.

Black hole shadow: The dark silhouette cast by a compact object against background light, shaped by photon trajectories near the horizon.

Quasinormal modes: Characteristic damped oscillations of perturbations around a black hole, whose frequencies depend on the spacetime geometry and underlying theory.

Scalar degree of freedom: A single-component perturbative field arising in modified theories of gravity, distinct from the two tensor polarizations of the graviton in general relativity.

References

1. Probing quadratic gravity with the Event Horizon Telescope. Astronomy & Astrophysics (2023).
2. On the degrees of freedom of R2 gravity in flat spacetime. Journal of High Energy Physics (2024).
3. Features and stability analysis of non-Schwarzschild black hole in quadratic gravity. Journal of High Energy Physics (2016).