General relativity predicts that a non-rotating neutron star cannot be arbitrarily massive: there is an upper limit, beyond which the pressure of degenerate neutron gas can no longer withstand gravity. This limit remains poorly defined due to uncertainties in the equation of state of supranuclear matter. Back in the 1930s, Fritz Zwicky suggested that neutron stars are born in supernova explosions, and Subrahmanyan Chandrasekhar discovered the Chandrasekhar limit for white dwarfs — a threshold beyond which collapse was expected. Today, the detection of gravitational waves from the merger of two compact objects — GW190814 — has sharpened the question: what was it? A baby black hole or a giant neutron star? The answer may lie in modifications to the Einstein field equations themselves.
The authors considered Randers-type Finsler gravity — an extension of GR where the spacetime metric depends not only on coordinates but also on direction. In the weak-field limit, a small timelike vector field ξ(r) (|ξ|≪1) is introduced, creating intrinsic anisotropy. A spherically symmetric metric is written using Heintzmann IIa potentials, and matter is modeled by a linear equation of state pr = aρ − b. By solving the modified field equations and matching to the external Schwarzschild solution, closed-form expressions for the model parameters are obtained — the constants are fixed using data from four observed pulsars: LMC X-4, Vela X-1, EXO 1785-248, and Cen X-3. For each, mass, radius, and profiles of density, pressure, and anisotropy are computed.
Within standard GR, the obtained configuration reaches a maximum mass of 2.01 M⊙ at a radius of about 10,99 km — typical for nucleonic equations of state. When Finsler corrections are switched on, the maximum mass rises to 2.67 M⊙, while the radius shrinks to 9,50 km. In other words, the "graininess" of spacetime acts like an extra support, allowing the star to become not only heavier but also more compact: the dimensionless compactness M/R jumps from 0,183 to 0,281. The moment of inertia, estimated via the approximate Bejger–Haensel formula, also increases — from 2,53×$10^{45}$ g·cm² to 2,71×$10^{45}$ g·cm² — indicating a more extended mass distribution and enhanced rotational support. All density and pressure profiles decrease monotonically from the center to the surface, the anisotropy is positive and vanishes at the center, and the conditions of energy dominance, causality, and equilibrium (including the Tolman–Oppenheimer–Volkoff equation) are satisfied. Stability is further confirmed by the adiabatic index and the Harrison–Zeldovich–Novikov criterion.
The work shows that even a minimal modification of the geometry — introducing a directional Finsler field — can shift the mass limit of neutron stars in the right direction without invoking exotic matter. This opens a new window for interpreting the "mass gap": objects whose masses fall between the heaviest neutron stars and the lightest black holes may be described within modified gravity. The predicted enhanced compactness and moment of inertia offer observational tests: future measurements of pulsar radii (e.g., pulsar PSR J0740+6620) and detection of gravitational waves from mergers involving neutron stars will help distinguish Finsler configurations from standard ones.
Future studies may incorporate realistic nuclear-physics equations of state, rapid rotation, and magnetic field effects. It would also be interesting to examine other types of compact objects — quark and hybrid stars — and see whether the "grainy" support persists. Joint analysis of LIGO/Virgo/KAGRA data and new X-ray missions (e.g., NICER) will make it possible to constrain the parameters of Finsler anisotropy.
The results impact neutron star physics, gravitational-wave astronomy, and modified gravity theories, offering new scenarios for the formation of compact objects in binary systems.
Constructing rotating models in Finsler gravity and calculating tidal deformability, needed for comparison with the GW170817 event. It is also important to assess the impact of anisotropy on post-merger signals.
The work is directly connected to the unsolved problem of the maximum mass of neutron stars and to the nature of the mass gap. It also touches on the fundamental question of how symmetric spacetime is at the micro level, and whether a directional microstructure can influence macroscopic gravitational phenomena.
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What the work does
The authors examined neutron stars within the framework of Randers Finslerian gravity, introducing a small temporal vector field that creates anisotropy. By solving the modified field equations with a linear equation of state, they obtained configurations consistent with data from four pulsars and showed that the maximum mass increases to 2.67 M⊙ while the radius decreases, with all stability and causality conditions satisfied.
Where its strength is
This work demonstrates how introducing a directional dependence in the metric—a 'graininess' of spacetime—can serve as additional support against gravitational collapse, shifting the mass and compactness limits of neutron stars without violating known observational constraints.
Where it could go next
Worth trying
Why this may matter
Extending the neutron star mass limit without exotic equations of state could explain the nature of compact objects in the 'mass gap' and provide observational signatures of modified gravity in data from gravitational-wave and X-ray observatories.
Nearby works in our archive
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The idea that space geometry can depend on direction dates back to Bernhard Riemann, but it only developed in the 20th century. Today, Finsler metrics are used not only in gravity but also in optics of inhomogeneous media, robotics, and even in modeling the movement of ants on pheromone trails.