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Charged Randall-Sundrum black holes and N=4 super Yang-Mills in AdS(2)xS(2)

Alexander Kaus, Harvey S. Reall

TL;DR

The paper investigates extremal charged black holes on a single brane in the original Randall-Sundrum model, focusing on their near-horizon geometry and its holographic interpretation. By solving the bulk Einstein equations with a warped near-horizon ansatz and imposing Israel junction conditions, the authors obtain a one-parameter family of regular bulk solutions whose induced brane geometry is AdS2 x S2 with unequal radii, and they quantify how these radii deviate from the 4d Reissner-Nordström case. In the large-charge regime, the radii corrections scale as $L_1^2 = Q^2 - \frac{3}{4}\ell^2 + \ldots$ and $L_2^2 = Q^2 - \frac{1}{4}\ell^2 + \ldots$, while the 5d entropy exhibits a logarithmic correction $S_5 = \frac{\pi \ell Q^2}{G_5} - \frac{\pi \ell^3}{G_5} \log\left(\frac{Q}{\ell}\right) + \ldots$, signaling quantum effects from the dual CFT. The analysis shows agreement with 4d GR for large black holes, with subleading CFT corrections calculable within the brane-world framework, and it provides a holographic dual description of N=4 SYM on AdS2 x S2 for arbitrary radii. Overall, the work supports the viability of the RS single-brane setup to reproduce classical GR results at large scales while encoding quantum corrections via holography, and it points to rich generalizations to other product-space CFT holography scenarios.

Abstract

We obtain some exact results for black holes in the Randall-Sundrum model with a single brane. We consider an extreme black hole charged with respect to a Maxwell field on the brane. The near-horizon geometry is determined. The induced metric on the brane and the black hole entropy are compared with the predictions of 4d General Relativity. There is good agreement for large black holes, with calculable subleading corrections. As a separate application, the bulk solution provides a gravitational dual for (strongly coupled, large N) N=4 SYM in AdS(2)xS(2) for arbitrary relative size of AdS(2) and S(2).

Charged Randall-Sundrum black holes and N=4 super Yang-Mills in AdS(2)xS(2)

TL;DR

The paper investigates extremal charged black holes on a single brane in the original Randall-Sundrum model, focusing on their near-horizon geometry and its holographic interpretation. By solving the bulk Einstein equations with a warped near-horizon ansatz and imposing Israel junction conditions, the authors obtain a one-parameter family of regular bulk solutions whose induced brane geometry is AdS2 x S2 with unequal radii, and they quantify how these radii deviate from the 4d Reissner-Nordström case. In the large-charge regime, the radii corrections scale as and , while the 5d entropy exhibits a logarithmic correction , signaling quantum effects from the dual CFT. The analysis shows agreement with 4d GR for large black holes, with subleading CFT corrections calculable within the brane-world framework, and it provides a holographic dual description of N=4 SYM on AdS2 x S2 for arbitrary radii. Overall, the work supports the viability of the RS single-brane setup to reproduce classical GR results at large scales while encoding quantum corrections via holography, and it points to rich generalizations to other product-space CFT holography scenarios.

Abstract

We obtain some exact results for black holes in the Randall-Sundrum model with a single brane. We consider an extreme black hole charged with respect to a Maxwell field on the brane. The near-horizon geometry is determined. The induced metric on the brane and the black hole entropy are compared with the predictions of 4d General Relativity. There is good agreement for large black holes, with calculable subleading corrections. As a separate application, the bulk solution provides a gravitational dual for (strongly coupled, large N) N=4 SYM in AdS(2)xS(2) for arbitrary relative size of AdS(2) and S(2).

Paper Structure

This paper contains 8 sections, 42 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Near-horizon geometry of charged braneworld black hole
  3. The bulk
  4. The brane
  5. The solutions
  6. Small black holes
  7. Large black holes
  8. Discussion

Figures (2)

  • Figure 1: Bulk solutions for $A_0 = 0.05,0.2,0.4,0.5,0.6,0.8,1.0$ (from bottom to top on left plot, from left to right on right plot, units $\ell=1$).
  • Figure 2: Left: $L_2/Q$ (top), $L_1/Q$ (middle) and $S_5/S_4$ (bottom). Note that the first two curves diverge at small $Q$. Right: $\rho_0$, the proper length of the horizon transverse to the brane. (Units $\ell=1$.)