The detection of rapidly variable gamma-ray emission in active galactic nuclei has generated renewed interest in magnetospheric particle acceleration and emission scenarios. In order to explore its potential, we study the possibility of steady gap acceleration around the null surface of a rotating black hole magnetosphere. We employ a simplified (1D) description along with the general relativistic expression of Gauss's law, and we assume that the gap is embedded in the radiation field of a radiatively inefficient accretion flow. The model is used to derive expressions for the radial distribution of the parallel electric field component, the electron and positron charge density, the particle Lorentz factor, and the number density of $\gamma$-ray photons. We integrate the set of equations numerically, imposing suitable boundary conditions. The results show that the existence of a steady gap solution for a relative high value of the global current is in principle possible if charge injection of both species is allowed at the boundaries. We present gap solutions for different choices of the global current and the accretion rate. When put in context, our results suggest that the variable very high energy $\gamma$-ray emission in M87 could be compatible with a magnetospheric origin.

中文翻译：

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旋转超大质量黑洞磁层中的间隙型粒子加速

在活动星系核中检测到快速变化的伽马射线发射，重新引起了人们对磁层粒子加速和发射场景的兴趣。为了探索其潜力，我们研究了旋转黑洞磁层零表面周围稳定间隙加速的可能性。我们采用简化的 (1D) 描述以及高斯定律的一般相对论表达式，并且我们假设间隙嵌入在辐射效率低下的吸积流的辐射场中。该模型用于推导平行电场分量的径向分布、电子和正电子电荷密度、粒子洛伦兹因子和γ射线光子数密度的表达式。我们对方程组进行数值积分，施加合适的边界条件。结果表明，如果在边界处允许两种物质的电荷注入，则对于全局电流的相对高值，原则上可能存在稳定的间隙解。我们为全球电流和吸积率的不同选择提出了差距解决方案。在上下文中，我们的结果表明 M87 中可变的非常高能量的 $\gamma$ 射线发射可能与磁层起源兼容。