In this paper, we examine the emergence of conserved charges on the horizon of a particular class of extremal nondilatonic black [Formula: see text]-branes (which reduce to extremal dilatonic black holes in [Formula: see text] dimensions upon toroidal compactification) in the presence of a probe massless scalar field in the bulk. This result is achieved by writing the black [Formula: see text]-brane geometry in a Gaussian null coordinate system which allows us to get a nonsingular near-horizon geometry description. We find that the near-horizon geometry is [Formula: see text] and that the [Formula: see text] section has an internal structure which can be seen as a warped product of [Formula: see text] in Gaussian null coordinates. We show that the bulk scalar field satisfying the field equations is expanded in terms of nonnormalizable and normalizable modes, which for certain suitable quantization conditions are well-behaved at the boundary of [Formula: see text] 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.

中文翻译：

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极值非膨胀黑色 p 膜视界上的高斯零坐标、近视界几何和守恒电荷

在本文中，我们研究了在特定类别的极端非膨胀黑色 [公式：见文本]-膜（在环形紧化时减少为 [公式：见文本] 维度中的极端膨胀黑洞）的视界上守恒电荷的出现在体积中存在探针无质量标量场的情况下。这个结果是通过在高斯零坐标系中编写黑色[公式：见文本]-膜几何来实现的，这使我们能够获得非奇异的近水平几何描述。我们发现近地平线几何是[公式：见文本]，并且[公式：见文本]部分有一个内部结构，可以看作是高斯零坐标中[公式：见文本]的扭曲产物。我们表明，满足场方程的体标量场在不可归一化和可归一化模式方面进行了扩展，对于某些合适的量化条件，这些模式在 [公式：参见文本] 空间的边界处表现良好。此外，我们表明，选择可归一化模式会导致在地平线上存在守恒量。我们讨论了这些守恒量在后期状态中的影响。