Physics model¶

gevolution evolves collisionless particles and metric perturbations on a uniform periodic mesh. Its relativistic solver uses a weak-field formulation of general relativity in Poisson gauge. The Newtonian mode provides a controlled limit using the same particle-mesh infrastructure.

Metric convention¶

The spacetime line element is written in a \(3+1\) decomposition. In Poisson gauge, the lapse and spatial metric are parametrised as

\[ \alpha = a e^\psi, \qquad \gamma_{ij} = a^2 e^{-2\phi} (\delta_{ij} + h_{ij}), \]

with a transverse vector perturbation \(B_i\) in the shift and a transverse, traceless tensor perturbation \(h_{ij}\).

The scalar potentials use the exponential convention introduced in later gevolution releases. At linear order it agrees with the conventional weak-field notation; differences appear at higher order.

Weak-field formulation¶

The solver retains the nonlinear shortwave terms required by the weak-field expansion and, with the recommended configuration, terms needed for second-order relativistic consistency. It is designed for cosmological spacetimes with small metric perturbations, while matter density contrasts may be nonlinear.

The scheme is not intended for strong-field compact objects or regions where the metric perturbations cease to be weak.

Particle equations of motion¶

Particles represent collisionless species. Their canonical momenta and positions are updated with kick and drift operations. Metric fields and their derivatives are interpolated from the mesh, while particle stress-energy is projected back to the mesh.

CDM and baryons normally use the global step. Fast non-CDM particles may subdivide their particle updates according to move limit, without increasing the gravity-solver time resolution.

Stress-energy and metric sectors¶

Particle and optional linear sources contribute to stress-energy projections. The metric solver separates scalar, vector, and tensor sectors using distributed Fourier transforms:

\(\phi\): scalar gravitational potential;
\(\chi = \phi - \psi\): gravitational slip;
\(B_i\): transverse vector/frame-dragging perturbation;
\(h_{ij}\): transverse-traceless tensor perturbation.

The vector sector supports parabolic and elliptic methods. Tensor modes use an adiabatic treatment by default and can be evolved dynamically in suitable builds.

Radiation, neutrinos, and fluids¶

With CLASS linked, linear transfer functions can supply radiation, massive neutrino, and additional-fluid perturbations. Massive non-CDM species may also be represented by particles, with configurable redshift switches between linear and particle sources.

Newtonian limit and N-body gauge¶

gravity theory = Newton evolves the Newtonian equations while retaining gevolution's mesh, particle, and output machinery. Newtonian simulation input must follow the appropriate N-body/Newtonian gauge convention; relativistic input must use Poisson gauge.

Anisotropic expansion¶

Builds with ANISOTROPIC_EXPANSION can represent a Bianchi-I homogeneous tensor mode. This is a specialised feature and should be validated against the intended theoretical model.

Principal limitations¶

Uniform mesh with no adaptive refinement.
Collisionless matter only; no hydrodynamics or baryonic feedback.
Weak metric fields are assumed.
Finite mesh resolution and particle sampling affect small-scale results.
Gauge conventions must be handled consistently at input and output.