Black Holes May Not Exist in Torsion-Based Rival of Einstein Gravity

Black holes are the most celebrated predictions of Einstein’s general relativity, but a new mathematical investigation suggests that one of the leading alternatives to Einstein’s theory may struggle to host them at all. In a study published in General Relativity and Gravitation, D. F. López, A. A. Coley and B. Yildirim of Dalhousie University in Halifax, Canada, examined what happens to static, spherically symmetric black hole solutions in a torsion-based modification of gravity known as new general relativity, or NGR. Their conclusion is striking: the mere requirement that a physically sensible black hole horizon exists forces the theory’s free parameters into regions of parameter space already known to be pathological, leaving NGR without any physically meaningful black holes beyond those it shares with the teleparallel equivalent of general relativity.

New general relativity belongs to the broader family of teleparallel theories of gravity. Instead of describing gravity through the curvature of a Levi-Civita connection, as Einstein did, teleparallel theories use a flat connection with torsion, built from an object called the tetrad field. The original formulation dates back to the work of Hayashi and Shirafuji in 1979, who proposed a general quadratic Lagrangian in the three basic torsion invariants. That construction introduces three free dimensionless parameters, conventionally labelled with the coefficients associated with the axial, vector and symmetric traceless pieces of the torsion tensor. Special choices of these parameters recover the teleparallel equivalent of general relativity, often abbreviated TEGR, which is dynamically identical to Einstein’s theory despite its geometrically distinct formulation.

The difficulty is that most choices of the three parameters do not yield a healthy theory. A physically admissible subset of the parameter space must simultaneously satisfy three demanding conditions: the theory must be free of ghost instabilities, meaning that its propagating degrees of freedom must not carry negative kinetic energy; it must genuinely propagate a massless spin-2 mode, the gravitational wave carrier expected of any relativistic theory of gravity; and it must reproduce Newtonian gravity in the weak-field, slow-motion limit, so that ordinary attraction is recovered. Earlier work, including studies of gravitational waves and stability in NGR by Golovnev, Semenova and Vandeev and by Bahamonde and collaborators, has mapped out which corners of parameter space survive these tests. Beltrán Jiménez and Dialektopoulos had already identified non-linear obstructions for consistent versions of the theory, foreshadowing the kind of problem the new analysis uncovers.

López, Coley and Yildirim asked a deceptively simple question: assuming that a static, spherically symmetric configuration in NGR possesses a local black-hole horizon, what do the field equations say about the theory’s free parameters? A local black-hole horizon, in the sense used by Ashtekar, Krishnan, Hayashi and other researchers in black-hole mechanics, is a quasi-locally defined null surface that traps light, and its existence can be imposed without any detailed knowledge of the interior region. The authors considered configurations in vacuum, in the presence of a perfect fluid, and in the presence of an electromagnetic field, covering Reissner-Nordström-like charged holes as well as matter-filled geometries. They worked within a static, spherically symmetric, perturbative framework, expanding the field equations to first order in a small parameter near the horizon.

The result is a systematic exclusion argument rather than the discovery of a new solution. Whenever the existence of a horizon is imposed, the field equations, together with the matter conservation equation, drive the NGR parameters toward the very values that correspond to known pathological models: theories that contain ghost instabilities, theories that fail to propagate the spin-2 graviton, or theories that lack a consistent Newtonian limit. Conversely, in any corner of parameter space that passes the ghost-freedom, spin-2 propagation and Newtonian limit tests, the required black-hole configurations either do not exist or reduce to the TEGR case. In other words, the class of acceptable theories and the class of acceptable black holes do not overlap except in the trivial intersection with general relativity’s teleparallel twin.

Crucially, the authors emphasize that the obstruction is not geometric. They showed that the remaining admissible geometries are perfectly regular at the horizon: the torsion scalar invariants that define the NGR Lagrangian remain finite there, and the spacetime admits a consistent black-hole interpretation. This point matters because it separates two very different kinds of failure. If the invariants diverged at the horizon, the Lagrangian density of the teleparallel theory would itself be undefined there, and the horizon and its interior would be excluded from the manifold, a phenomenon the same group recently documented in the Schwarzschild geometry of TEGR, where regular and singular subclasses emerge according to the behavior of the Lorentz sector. Here, by contrast, the geometry survives; it is the underlying theory that breaks down. The pathology is theoretical, not a breakdown of spacetime at the horizon.

The perturbative machinery behind this conclusion is considerable. The authors constructed general static, spherically symmetric teleparallel geometries with free radial functions, substituted them into the NGR field equations, and solved the resulting system perturbatively near the horizon. Appendix material catalogues the auxiliary functions and the exact expressions for the coefficients entering the matter and geometrical sectors, including cases with electric charge, where combinations of the horizon radius and the charge appear in the parameter constraints. The upshot of the algebra is that the consistency conditions at the horizon act as a filter: only a measure-zero slice of parameter space allows the equations to close, and that slice coincides with the pathological regions or with TEGR itself.

Why should anyone outside mathematical relativity care? The answer lies in the current experimental landscape. Gravitational-wave astronomy and black-hole imaging have made it possible to test gravity in the strong-field regime for the first time, and modified gravity theories are frequently invoked as explanations for dark energy, dark matter, or the earliest moments of the cosmos. But a modification of gravity that cannot support the very objects we observe—stellar-mass black holes detected through LIGO and Virgo, and the supermassive shadows imaged by the Event Horizon Telescope—faces an immediate observational problem. If NGR admits no physically meaningful non-vacuum black holes, then any attempt to use it to model astrophysical compact objects is on unstable ground, and the theory’s viability must be sought in other arenas, such as cosmology, if at all.

The authors are careful to state the scope of their result. The conclusion holds within the static, spherically symmetric, perturbative framework they examined, and their definition of a black-hole horizon is deliberately minimal, remaining valid regardless of the detailed nature of the interior, including proposals for so-called singularity-free black holes. Rotating black holes, dynamical collapse, and fully non-linear solutions remain open questions, and extending the analysis to those regimes is a natural next step. Nevertheless, the pattern established here echoes earlier findings in teleparallel torsion theories, where black-hole existence has repeatedly proven to be a severe consistency filter. For new general relativity, the message of this work is stark and elegant at once: demand a healthy graviton, a Newtonian limit, and a black hole horizon, and the theory hands you back nothing new—only the geometries it inherits from Einstein.

Subject of Research: Black hole solutions in new general relativity, a torsion-based modification of general relativity

Article Title: On non-vacuum black holes in new general relativity

Article References: López, D. F., Coley, A. A., & Yildirim, B. (2026). On non-vacuum black holes in new general relativity. General Relativity and Gravitation, 58(9), Article 101. https://doi.org/10.1007/s10714-026-03605-3

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03605-3

Keywords: new general relativity, teleparallel gravity, black holes, torsion invariants, event horizons, ghost instabilities, Newtonian limit, spin-2 graviton, modified gravity, general relativity, spherically symmetric spacetimes, non-vacuum solutions