The 5-D Choptuik critical exponent and holography

Recently, a holographic argument was used to relate the saturation exponent, $\gamma_{BFKL}$, of four-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, $\gamma_{5d}$, in 5-dimensional black hole formation via scalar field collapse \cite{alvarez-gaume}. Remarkably, the numerical value of the former agreed quite well with previous calculations of the latter. We present new results of an improved calculation of $\gamma_{5d}$ with substantially decreased numerical error. Our current result is $\gamma_{5d} = 0.4131 \pm 0.0001$, which is close to, but not in strict agreement with, the value of $\gamma_{BFKL}=0.409552$ quoted in \cite{alvarez-gaume}.Comment: 11 pagers, 2 figure

Higher Dimensional Choptuik Scaling in Painleve Gullstrand Coordinates

We investigate Choptuik scaling in the spherically symmetric collapse of a massless scalar field in higher dimensions using Painleve-Gullstrand (P-G) coordinates. Our analysis confirms the presence in higher dimensions of the cusps in the periodic scaling relationship recently observed in four dimensional collapse. In addition, we address the issue of the asymptotic behaviour of the critical exponent as the number of spacetime dimensions gets large. Our results are consistent with earlier work suggesting that the critical exponent monotonically approaches 1/2 in this limit.Comment: 11 pages, 5 figure

Hamiltonian dynamics of Lovelock black holes with spherical symmetry

We consider spherically symmetric black holes in generic Lovelock gravity. Using geometrodynamical variables we do a complete Hamiltonian analysis, including derivation of the super-Hamiltonian and super-momentum constraints and verification of suitable boundary conditions for asymptotically flat black holes. Our analysis leads to a remarkably simple fully reduced Hamiltonian for the vacuum gravitational sector that provides the starting point for the quantization of Lovelock block holes. Finally, we derive the completely reduced equations of motion for the collapse of a spherically symmetric charged, self-gravitating complex scalar field in generalized flat slice (Painlev\'{e}-Gullstrand) coordinates.Comment: 53 pages, including two major appendices; some typos fixed; version published in CQ

Quantum Mechanics of the Interior of Radiating 2-D Black Holes

We study the homogeneous sector of the RST model describing the gravitational dynamics, including back-reaction, of radiating 2-d black holes. We find the exact solutions both in conformal gauge and in time-parametrized form, isolate the black hole sector of the classical phase space and quantize the near singularity dynamics in conformal gauge. We show that different choices of measure and different self-adjoint extensions can lead to inequivalent quantum theories, all of which resolve the singularity. For a specific range of extension parameters, the Hamiltonian spectrum admits bound states that correspond physically to stable remnants. Finally, we argue that our work provides a good starting point for quantization of the full homogeneous theory using both reduced and Dirac quantization