Dynamical generation of wormholes with charged fluids in quadratic Palatini gravity

The dynamical generation of wormholes within an extension of General Relativity (GR) containing (Planck’s scale-suppressed) Ricci-squared terms is considered. The theory is formulated assuming the metric and connection to be independent (Palatini formalism) and is probed using a charged null fluid as a matter source. This has the following effect: starting from Minkowski space, when the flux is active the metric becomes a charged Vaidya-type one, and once the flux is switched off the metric settles down into a static configuration such that far from the Planck scale the geometry is virtually indistinguishable from that of the standard Reissner-Nordström solution of GR. However, the innermost region undergoes significant changes, as the GR singularity is generically replaced by a wormhole structure. Such a structure becomes completely regular for a certain charge-to-mass ratio. Moreover, the nontrivial topology of the wormhole allows us to define a charge in terms of lines of force trapped in the topology such that the density of lines flowing across the wormhole throat becomes a universal constant. In light of our results, we comment on the physical significance of curvature divergences in this theory and the topology change issue, which support the view that space-time could have a foamlike microstructure pervaded by wormholes generated by quantum gravitational effects.

Figure 1

The minimum of the radial function $z(x)$ implies the existence of a wormhole extension of the geometry, with $x$ covering the whole real axis $-\infty <x<+\infty$. Note the smoothness of the function $dG/dx$ and the bounce of $z(x)$ at $x=0$. In this plot, $r_c=1$.

Figure 2

Penrose diagram for the nonsingular case ${\delta }_1={\delta }_1^{*}$ without event horizon, $N_q<N_q^c$. Consider first that the initial state is flat Minkowski space. Next, assume that a charged perturbation of compact support propagates within the interval $[v_i,v_f]$. We verify that the area of the two-spheres of constant $x$ and $v$ increases and never becomes smaller than $r_c^2(v)$. If we consider now the region $v>v_f$, where the ingoing flux of charge and radiation is switched off, the result is a static geometry identical to that described in Sec. 5c. This change in the geometry can be interpreted as the formation of a wormhole whose throat has an area $A_{WH}=4\pi r_c^2(v_f)$. See the text for more details.

Figure 3

Penrose diagram for the formation of a wormhole (with ${\delta }_1={\delta }_1^{*}$ and $N_q<N_q^c$) out of Minkowski space resulting from the perturbation of a charged null fluid of integrated charge $+q$, and its subsequent removal due to a second flux of integrated charge $-q$. Note that we have chosen positive energy fluxes in both cases, which implies that the final state is a Schwarzschild black hole instead of Minkowski space.