Gravitational collapse in ($2+1$)-dimensional Eddington-inspired Born-Infeld gravity

We study here the gravitational collapse of dust in ($2+1$)-dimensional spacetimes for the formation of black holes (BH) and naked singularities (NS) as final states in a modified theory of gravity, with vanishing cosmological constant. From the perspective of cosmic censorship, we investigate the collapse of a dust cloud in Eddington-inspired Born-Infeld gravity (EiBI) and compare the results with those of general relativity (GR). It turns out that, as opposed to the general relativistic situation, where the outcome of dust collapse in ($2+1$) dimensions is always a naked singularity, the EiBI theory has a certain range of parameter values that avoid the naked singularity. This indicates that a ($3+1$)-dimensional generalization of these results could be useful and worth examining. Finally, using the results here, we show that the singularity avoidance through homogeneous bounce in cosmology in this modified gravity is not stable.

Figure 1

Plots showing the singularity time $t_s(r)$ (blue) and the apparent horizon time $t_{\mathrm{ah}}(r)$ (orange) for both $\kappa <0$ (solid curves) and $\kappa >0$ (dashed curve). The initial density profile is ${\rho }_i(r)={\rho }_0+{\rho }_2{r}^2$ and $c_1(r)$ given by Eq. (4.5). Here, we have taken $|\kappa |=0.3$, ${\rho }_0=0.3$, ${\rho }_2=-0.175$ and $r_b=\sqrt{-\frac{{\rho }_0}{{\rho }_2}}$. For $\kappa >0$, no apparent horizon or trapped surfaces form till the singularity time.

Figure 2

Plots showing the singularity time $t_s(r)$ (blue) and the apparent horizon time $t_{\mathrm{ah}}(r)$ (orange) for both $\kappa <0$ (solid curves) and $\kappa >0$ (dashed curve). The initial density profile is ${\rho }_i(r)={\rho }_0+{\rho }_2{r}^2$ and $c_1(r)=-r$. Here, we have taken $|\kappa |=0.3$, ${\rho }_0=0.3$, ${\rho }_2=-0.175$ and $r_b=\sqrt{-\frac{{\rho }_0}{{\rho }_2}}$. For $\kappa >0$, no apparent horizon or trapped surfaces form till the singularity time.

Figure 3

Plots showing the singularity time $t_s(r)$ (blue) and the apparent horizon time $t_{\mathrm{ah}}(r)$ (orange) for (a) $c_1(r)$ given by Eq. (4.5) and (b) $c_1(r)=-r$. The initial density profile is ${\rho }_i(r)={\rho }_0+{\rho }_2{r}^2$. Here, we have taken $\kappa =0.3$, ${\rho }_0=0.7$, ${\rho }_2=-0.175$ and $r_b=\sqrt{-\frac{{\rho }_0}{{\rho }_2}}$.