Abstract In this work we give a thorough derivation of the spherically symmetric Einstein–Vlasov system in Bondi coordinates. The system of partial differential equations obtained differs significantly from the Schwarzschild-coordinate formulation, and it is naturally adapted to the study of radiation and null infinity. This paper provides the raw material whose exploitation, in forthcoming investigations, will give rise to characteristic counterparts of some important previous results known for the standard Cauchy problem associated to the spherically symmetric Einstein–Vlasov system. As the first such results in Bondi coordinates for the characteristic initial value problem, we establish the global well-posedness of the characteristic initial value problem obtained. Furthermore, we prove a nonlinear stability result: for sufficiently small initial data, the solution decays polynomially to the Minkowski spacetime. More precisely, we obtain the decay estimates | λ | , | ν | ⩽ C ε ( 1 + u ) − 1 for the metric coefficients, | ρ | ⩽ C ε ( 1 + u ) − 2 for the matter density, and | m ( u , ∞ ) − m ( 0 , ∞ ) | ⩽ C ϵ for the Bondi mass, which remains bounded and converges to its initial value at late retarded time. To illustrate the physical relevance of our formulation and complement the theoretical analysis, we present numerical simulations comparing the behavior of solutions, both in Bondi and Schwarzschild coordinates. These simulations highlight key phenomena such as the radiative mass loss via the Bondi mass, the outgoing particle trajectories toward null infinity, the characteristic quadrupole gravitational wave pattern, and the contrasted dynamics of gravitational collapse. This work lays the foundation for further investigations of fundamental problems such as black holes formation, gravitational collapse and cosmic censorship in Bondi coordinates.
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