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Register a new userAn alternative scenario for critical scalar field collapse in $AdS_3$
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In the context of gravitational collapse and black hole formation, we reconsider the problem to describe analytically the critical collapse of a massless and minimally coupled scalar field in $2+1$ gravity.
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We compute the Hamiltonian for spherically symmetric scalar field collapse in Einstein-Gauss-Bonnet gravity in D dimensions using slicings that are regular across future horizons. We first reduce the Lagrangian to two dimensions using spherical symmetry. We then show that choosing the spatial coordinate to be a function of the areal radius leads to a relatively simple Hamiltonian constraint whose gravitational part is the gradient of the generalized mass function. Next we complete the gauge fixing such that the metric is the Einstein-Gauss-Bonnet generalization of non-static Painleve-Gullstrand coordinates. Finally, we derive the resultant reduced equations of motion for the scalar field. These equations are suitable for use in numerical simulations of spherically symmetric scalar field collapse in Gauss-Bonnet gravity and can readily be generalized to other matter fields minimally coupled to gravity.
We construct analytical models to study the critical phenomena in gravitational collapse of the Husain-Martinez-Nunez massless scalar field. We first use the cut-and-paste technique to match the conformally flat solution ($c=0$ ) onto an outgoing Vaidya solution. To guarantee the continuity of the metric and the extrinsic curvature, we prove that the two solutions must be joined at a null hypersurface and the metric function in Vaidya spacetime must satisfy some constraints. We find that the mass of the black hole in the resulting spacetime takes the form $Mpropto (p-p^*)^gamma$, where the critical exponent $gamma$ is equal to $0.5$. For the case $c eq 0$, we show that the scalar field must be joined onto two pieces of Vaidya spacetimes to avoid a naked singularity. We also derive the power-law mass formula with $gamma=0.5$. Compared with previous analytical models constructed from a different scalar field with continuous self-similarity, we obtain the same value of $gamma$. However, we show that the solution with $c eq 0$ is not self-similar. Therefore, we provide a rare example that a scalar field without self-similarity also possesses the features of critical collapse.
We study the dynamic collapse driven by a scalar field, when a relativistic observer falls co-moving with the collapse and cross the horizon of a Schwarzschild black-hole (BH), at $t=t_0$. During the collapse the scale of time is considered as variable. Back-reaction effects and gravitational waves produced during the exponential collapse are studied. We demonstrate that back-reaction effects act as the source of gravitational waves emitted during the collapse, and wavelengths of gravitational waves (GW) are in the range: $lambda ll r_sequiv {e^{-2h_0t_0}over 2 h_0}$, that is, smaller than the Schwarzschild radius. We demonstrate that during all the collapse the global topology of the space-time remains hyperbolic when the observer cross the horizon.
The phenomena of collapse and dispersal for a massless scalar field has drawn considerable interest in recent years, mainly from a numerical perspective. We give here a sufficient condition for the dispersal to take place for a scalar field that initially begins with a collapse. It is shown that the change of the gradient of the scalar field from a timelike to a spacelike vector must be necessarily accompanied by the dispersal of the scalar field. This result holds independently of any symmetries of the spacetime. We demonstrate the result explicitly by means of an example, which is the scalar field solution given by Roberts. The implications of the result are discussed.
We derive a partially gauge fixed Hamiltonian for black hole formation via real scalar field collapse. The class of models considered includes many theories of physical interest, including spherically symmetric black holes in $D$ spacetime dimensions. The boundary and gauge fixing conditions are chosen to be consistent with generalized Painleve-Gullstrand coordinates, in which the metric is regular across the black hole future horizon. The resulting Hamiltonian is remarkably simple and we argue that it provides a good starting point for studying the quantum dynamics of black hole formation.
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