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arXiv · 2003.09304

Gaussian null coordinates, near-horizon geometry and conserved charges on the horizon of extremal non-dilatonic black $p$-branes

Mirjam Cvetič·Paulo J. Porfírio·Alejandro Satz
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Abstract

In this paper, we examine the emergence of conserved charges on the horizon of a particular class of extremal non-dilatonic black $p$-branes (which reduce to extremal dilatonic black holes in $D=4$ dimensions upon toroidal compactification) in the presence of a probe massless scalar field in the bulk. This result is achieved by writing the black $p$-brane geometry in a Gaussian null coordinate system which allows us to get a non-singular near-horizon geometry description. We find that the near-horizon geometry is $AdS_{p+2}\times S^2$ and that the $AdS_{p+2}$ section has an internal structure which can be seen as a warped product of $AdS_{2}\times S^{p}$ in Gaussian null coordinates. We show that the bulk scalar field satisfying the field equations is expanded in terms of non-normalizable and normalizable modes, which for certain suitable quantization conditions are well-behaved at the boundary of $AdS_{p+2}$ space. Furthermore, we show that picking the normalizable modes results in the existence of conserved quantities on the horizon. We discuss the impact of these conserved quantities in the late time regime.

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Mirjam Cvetič, Paulo J. Porfírio, Alejandro Satz. 2020-03-20. Gaussian null coordinates, near-horizon geometry and conserved charges on the horizon of extremal non-dilatonic black $p$-branes. https://doi.org/10.1142/s0218271820410047

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