范德瓦尔斯黑洞的周期轨道
Periodic Orbits of Van der Waals Black Holes
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中文总结 AI 辅助
本文研究范德瓦尔斯黑洞的周期轨道及引力波，发现分子体积参数b强烈影响轨道结构和波形，为通过引力波观测探测黑洞热力学提供新视角。
中文摘要 AI 辅助
渐近反德西特（AdS）时空中的黑洞，若其扩展相空间热力学精确复现范德瓦尔斯流体的行为，则构成一个独特的类别，即范德瓦尔斯黑洞（VBHs）。本文求解了VBHs的类时测地线，对其周期轨道进行了分类，并计算了沿这些轨道发射的引力波，以追踪热力学压力P和分子体积参数b如何塑造轨道动力学。通过数值积分测地线方程，我们得到了最内层稳定圆轨道（ISCO）的能量、角动量和半径，并描绘了束缚轨道族。为了界定有效势保持良好行为的参数窗口，我们引入了临界角动量Ls。在轨道分类方案中，我们针对若干参数组计算了对应有理数q的能量，并展示了由此产生的轨道。沿这些轨道产生的波形是在“Kludge”形式体系内生成的，这使得我们能够量化b对波振幅和周期的影响。结果表明，轨道结构和引力波特征都对b高度敏感。VBHs与Schwarzschild-AdS（SAdS）黑洞的动力学行为存在显著差异，这为通过引力波观测探测黑洞热力学提供了新的视角。
英文摘要
Black holes in asymptotically anti-de Sitter (AdS) spacetime whose extended-phase-space thermodynamics reproduces that of a van der Waals fluid exactly form a distinctive class, the van der Waals black holes (VBHs). The timelike geodesics of VBHs are solved, their periodic orbits are catalogued, and the gravitational waves emitted along them are computed, so as to trace how the thermodynamic pressure P and the molecular-volume parameter b shape the orbital dynamics. Integrating the geodesic equations numerically yields the energy, angular momentum and radius of the innermost stable circular orbit (ISCO) and maps out the family of bound orbits. To delimit the parameter window in which the effective potential stays well behaved, we introduce a critical angular momentum Ls. Within the orbit-classification scheme, we compute the energies corresponding to rational q for several parameter sets and display the resulting orbits. The waveforms produced along these orbits are generated within the "Kludge" formalism, which makes it possible to quantify the imprint of b on the wave amplitude and on the period. Both the orbital architecture and the gravitational-wave signature turn out to be strongly sensitive to b. The dynamical behavior of VBHs and Schwarzschild-AdS (SAdS) black holes differs markedly, providing a new perspective for probing black hole thermodynamics via gravitational wave observations.
发表机构
- College of Physics, Guizhou University（贵州大学物理学院）
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