ar X iv : h ep - t h / 07 02 22 6 v 1 2 8 Fe b 20 07 The 5 - D Choptuik critical exponent and holography
نویسندگان
چکیده
Recently, a holographic argument was used to relate the saturation exponent, γ BF KL , of four-dimensional Yang-Mills theory in the Regge limit to the Choptuik critical scaling exponent, γ 5d , in 5-dimensional black hole formation via scalar field collapse [1]. 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 γ 5d with substantially decreased numerical error. Our current result is γ 5d = 0.4131 ± 0.0001, which is close to, but not in strict agreement with, the value of γ BF KL = 0.409552 quoted in [1]. The critical behaviour exhibited by gravitational collapse to black holes, first discovered by Choptuik [2] (see [3, 4] for reviews), is a small scale, strong gravitational field effect that is by now well understood at the qualitative level. As well, key physical quantities such as the associated critical solution and scaling exponents have been calculated numerically. Precise analytic derivations of these quantities are still, to the best of our knowledge, lacking.
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