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Strong Cosmic Censorship: the nonlinear story / Luna, Raimon (ICC, Barcelona U.) ; Zilhão, Miguel (Lisbon, CENTRA ; CERN) ; Cardoso, Vitor (Lisbon, CENTRA) ; Costa, João L. (ISCTE, Lisbon ; U. Lisbon (main)) ; Natário, José (IST, Lisbon (main))
A satisfactory formulation of the laws of physics entails that the future evolution of a physical system should be determined from appropriate initial conditions. The existence of Cauchy horizons in solutions of the Einstein field equations is therefore problematic, and expected to be an unstable artifact of General Relativity. [...]
arXiv:1810.00886; arXiv:2012.08413.- 2019-03-16 - 9 p. Fulltext: PDF; Fulltext from Publisher: PDF; External links: 00001 Mass function~\eqref{eq:mass} and Kretschmann scalar as functions of $\overset{\circ}{v}$ for configurations {\bf B1} (red solid line) and {\bf B2} (blue dashed line). Thin lines are evaluated at $u=u_{\rm EH} + 1$ and thick lines are evaluated at $u=u_{\rm EH} + 2$.; 00000 Scalar field derivative $\partial \Phi /\partial \overset{\circ}{v}$ as a function of $\overset{\circ}{v}$ for configurations {\bf A} (left plot), {\bf B} (middle plot), {\bf C} (right plot) with initial profiles 1 (red solid lines) and 2 (blue dashed lines). $\partial \Phi /\partial \overset{\circ}{v}$ evaluated at $u=u_{\rm EH}$.; 00011 Same as Fig.~\ref{fig:no_inflation}, for configurations {\bf C1} (red solid) and {\bf C2} (blue dashed).; 00007 Mass function~\eqref{eq:mass} and Kretschmann scalar as functions of $\overset{\circ}{v}$ for configurations {\bf A1} (red solid line) and {\bf A2} (blue dashed line). Thin lines are evaluated at $u=u_{\rm EH} + 1$ and thick lines are evaluated at $u=u_{\rm EH} + 2$. These results are consistent with the existence of mass inflation leading to a weak singularity.; 00005 Constraint violations during our evolutions of configurations {\bf B}.; 00004 Constraint violations during our evolutions of configurations {\bf B}.; 00006 Radius function for constant-$u$ slices in a configuration with $M_0 = 1.0$, $Q = 0.9$, $\Lambda = 0.06$, $\mu = 0$, $A = 0.4$, $v_c = 3.0$ and $w = 0.25$. Dashed-dotted green lines reach infinity, full blue lines hit the CH and red dashed lines hit the singularity at $r=0$.; 00010 Massless scalar field along the event horizon with corresponding ``local power'' for a configuration with $M_0 = 1.0$, $Q = 0.95$, $\Lambda = 0$, $\mu = 0$, $A = 0.01$, $v_c = 6.0$ and $w = 0.25$. The power-law decay $\Phi \sim v^{-3}$ matches to a very good precision the one expected from linearized analysis~\cite{Price:1971fb}, and reproduces well previous nonlinear results~\cite{Burko:1997tb}.; 00002 Massless scalar field along the event horizon with corresponding ``local power'' for a configuration with $M_0 = 1.0$, $Q = 0.95$, $\Lambda = 0$, $\mu = 0$, $A = 0.01$, $v_c = 6.0$ and $w = 0.25$. The power-law decay $\Phi \sim v^{-3}$ matches to a very good precision the one expected from linearized analysis~\cite{Price:1971fb}, and reproduces well previous nonlinear results~\cite{Burko:1997tb}.; Fulltext from Publisher; 00003 $\delta_{N,64} (K)$ at $u=18.2$ for configuration {\bf B1}. 20 domains were employed in the $v$ direction, where each domain has $N$ points. The plot clearly shows exponential convergence until $N\approx40$.; Fulltext; 00008 Scalar field derivative $\partial \Phi /\partial \overset{\circ}{v}$ as a function of $\overset{\circ}{v}$ for configurations {\bf A} (left plot), {\bf B} (middle plot), {\bf C} (right plot) with initial profiles 1 (red solid lines) and 2 (blue dashed lines). $\partial \Phi /\partial \overset{\circ}{v}$ evaluated at $u=u_{\rm EH}$.; 00009 Scalar field derivative $\partial \Phi /\partial \overset{\circ}{v}$ as a function of $\overset{\circ}{v}$ for configurations {\bf A} (left plot), {\bf B} (middle plot), {\bf C} (right plot) with initial profiles 1 (red solid lines) and 2 (blue dashed lines). $\partial \Phi /\partial \overset{\circ}{v}$ evaluated at $u=u_{\rm EH}$.

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