Abstract We develop an augmented characteristic, first-order formulation of the field equations in f(R) gravity governing the global evolution of a (possibly) massive scalar field $\phi$ under spherical symmetry. This formulation is designed to isolate the genuine dynamical degrees of freedom while preserving the geometric structure of the theory. By treating the spacetime scalar curvature as an independent unknown, we obtain a closed first-order nonlocal system for the pair (\phi,R). This augmentation eliminates the higher-derivative character of the original equations at the level of the principal part. Our formulation allows us to pose the characteristic initial value problem and to establish several structural properties of solutions. More precisely, we work in generalized Bondi–Sachs coordinates and prescribe initial data on an asymptotically flat future light cone with vertex at the center of symmetry, and we identify the minimal regularity conditions required at the center. These regularity conditions are shown to be precisely those ensuring equivalence between the reduced system and the full f(R) equations. Extending Christodoulou’s method for the Einstein–scalar-field system, we recast the f(R) field equations as an integro-differential system of two coupled, first-order, nonlocal, nonlinear hyperbolic equations, whose principal unknowns are the scalar field and the spacetime scalar curvature. In deriving this reduced two-equation system, we impose natural assumptions on the scalar-field potential and on the function f(R) governing the gravitational Lagrangian density. These hypotheses correspond to standard viability and positivity conditions commonly imposed in the f(R) literature.
We prove several equivalence and monotonicity properties, including for the Hawking mass in this setting.The proposed formulation separates the essential null evolution from the radial constraint reconstruction (via explicit integral relations) on the future domain of dependence of the initial light cone. This structure makes the system amenable to characteristic energy estimates and to stable numerical implementation in spherical symmetry.

Abstract This paper discusses the behavior of a rotating relativistic kinetic gas surrounding a Schwarzschild black hole
is studied. We are interested in the description and analysis of the morphology of the resulting configurations for
kinetic gas clouds with and without total angular momentum, and we also compare the macroscopic observables
with configurations of finite total mass. Considering models for the one-particle distribution function based on
a polytropic ansatz and the inclination angle of the orbits of the particles in the kinetic gas, a collisionless gas
in the Schwarzschild spacetime background is analyzed. Profiles of the macroscopic observables of the gas
configurations are presented, which are derived from the density current vector field and energy-momentum-
stress tensor.

Abstract We develop the covariant phase space formulation of Weyl-transverse gravity (WTG) in the presence of general timelike and spacelike boundaries. WTG is classically equivalent to General Relativity (GR) but possesses a reduced gauge symmetry consisting of Weyl transformations and transverse diffeomorphisms, together with a fixed background volume form. This structure modifies the variational principle and the definition of conserved quantities relative to GR.We derive the symplectic potential, presymplectic current, and Hamiltonian generators associated with transverse diffeomorphisms, and we identify a set of boundary conditions under which the WTG action is differentiable. These include Dirichlet and Neumann conditions for both the auxiliary Weyl-invariant metric and the dynamical metric, as well as a natural implementation of York boundary conditions, for which WTG exhibits a particularly transparent geometric formulation.We obtain the Noether current and surface charge, clarify the role of the Lagrangian ambiguity related to the cosmological constant, and evaluate the Hamiltonian identity on spacetimes containing a bifurcate Killing horizon. The resulting first-law relation shows that variations of the cosmological constant can contribute nontrivially unless additional physical restrictions are imposed.

Abstract We explore how quantum properties of spacetime—specifically the curvature of momentum space—can backreact on classical gravity within a tractable semiclassical $(2+1)$-dimensional framework with negative cosmological constant. Motivated by quantum-gravity scenarios, we investigate how Planck-scale modifications of particle kinematics influence both dynamics and gravitational solutions. Starting from a first-order action, we derive an effective configuration-space description and show that particle trajectories remain geodesic, preserving the weak equivalence principle despite the underlying deformation. Coupling this modified matter sector to Einstein gravity, we obtain a deformed BTZ black hole solution. Remarkably, the local geometric structure and thermodynamic relations retain their standard form, while all quantum-gravity effects are encoded in a nonlinear mapping between the microscopic mass parameter and the ADM mass. This induces a renormalization of the horizon radius and thermodynamic quantities without altering their functional dependence. As a concrete observable consequence, we compute corrections to the return time of massless probes traveling along null geodesics between the horizon and the $AdS_3$ boundary. Our results demonstrate that Planck-scale kinematic effects can leave controlled and potentially measurable imprints on classical geometry, providing a clear and consistent bridge between quantum gravity ideas and semiclassical observables.

Abstract We analyze the particle spectrum of a second-order (in derivatives) theory based on a rank-2 tensor field with both symmetric and antisymmetric components. By demanding the existence of a propagating massless spin-2 particle and invariance under linearized transverse diffeomorphisms, we derive a new class of stable models with two massless scalars and a single massless spin-2 particle. A natural nonlinear completion is proposed in terms of a dynamical metric field. The identification of the spectrum is carried out using a fully Lagrangian, gauge-invariant approach which makes use of Bardeen variables in a constructive manner. The approach significantly reduces the number of steps in the spectrum determination in some cases.