Schwarzschild field with maximal acceleration corrections

Massive scalar particles in a modified Schwarzschild geometry

“…For ρ ∼ 2 one findsṼ ef f (ρ) ∼Ẽ 4 ǫ 2 (ρ−2) 2 , which, unlikeṼ ef f (ρ) of Ref. [21], definitely diverges on the Schwarzschild sphere. This suggests that |α| 2 → 0 as r → 2M.…”

“…In all these works space-time is endowed with a causal structure in which the proper accelerations of massive particles are limited. This is achieved by means of an embedding procedure pioneered in [20] and discussed at length in [16], [21] . The procedure stipulates that the line element experienced by an accelerating particle is represented by…”

“…We have recently studied the modifications produced by MA in the motion of a test particle in a Schwarzschild field [21]. We have found that these account for the presence of a spherical shell, external to the Schwarzschild sphere, that is forbidden to any classical particle and hampers the formation of a black hole.…”

“…As in [21], it is convenient to introduce the adimensional quantities λ = L/M = l/(mM), ǫ = (MA m ) −1 = (2mM) −1 and ρ = r/M. The behaviour ofṼ ef f (ρ) = V ef f (ρ)/m 2 is shown in Fig.…”

Evidence for Maximal Acceleration and Singularity Resolution in Covariant Loop Quantum Gravity

“…The resolution of classical singularities under the assumption of a maximal acceleration has been studied using canonical methods for Rindler [24], Schwarzschild [25], Reissner-Nordstrom [26], Kerr-Newman [27] and Friedman-Lemaître [28] metrics. Here we consider a simple homogeneous and isotropic cosmological model, with vanishing spatial curvature and pressure.…”