We investigate the possibility of photon halos (stable photon orbits) forming outside Schwarzschild-$f(R)$ black holes by analyzing null geodesics in these spacetimes. Using methods inspired by studies of spherical photon orbits around Kerr-Newman black holes, we derive conditions for the existence of such halos. We examine several f(R) gravity models, including quadratic, logarithmic, exponential, cubic, power-law, and hyperbolic forms, and find that multiple photon orbits -- both stable and unstable -- can appear outside the event horizon for certain parameter ranges. These additional orbits (halos) provide new insights into spacetime geometry and potential observational signatures of black holes in modified gravity. We present analytical expressions for the orbital radii, perform a numerical stability analysis, and discuss possible observational implications for black hole shadows. Our results indicate that while the standard Schwarzschild black hole admits only a single unstable light ring, Schwarzschild-$f(R)$ black holes can support an additional outer stable photon orbit (a halo) without triggering a black-hole bomb instability. This work deepens the understanding of photon-orbit structures in alternative theories of gravity and highlights how such effects could be detected through deviations in black hole shadow size or morphology.
Observational Signatures of Accretion Disks around a Schwarzschild Black Hole in a Hernquist Dark Matter Halo
College of Physics Science and Technology, Hebei University（河北大学物理科学与技术学院）；Hebei Key Lab of Optic-Electronic Information and Materials, Hebei University（河北大学河北省光电信息与材料重点实验室）；National-Local Joint Engineering Laboratory of New Energy Photoelectric Devices, Hebei University（河北大学新能源光电器件国家地方联合工程实验室）；Key Laboratory of High-pricision Computation and Application of Quantum Field Theory of Hebei Province, Hebei University（河北大学量子场论高精度计算与应用重点实验室）
Geodesics and Thermodynamics of a Schwarzschild Black Hole with Hernquist Dark Matter
Secretaria da Educação do Ceará (SEDUC), Coordenadoria Regional de Desenvolvimento da Educação (CREDE 9)（塞阿拉州教育部（SEDUC），区域教育发展协调局（CREDE 9））；Echahid Cheikh Larbi Tebessi University（埃沙希德谢赫拉里比特贝西大学）；Khazar University（哈扎尔大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal do ABC (UFABC)（ABC联邦大学（UFABC））
Gravitational Wave Signatures of Schwarzschild Black Hole in a Generalized Dehnen-Type $(1,4,γ)$ Dark Matter Halo
National University of Uzbekistan（乌兹别克斯坦国立大学）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；Institute of Fundamental and Applied Research, National Research University TIIAME（塔什干信息技术与应用科学国立研究院基础与应用研究所）；University of Tashkent for Applied Sciences（塔什干应用科学大学）
Constraints on Schwarzschild Black Hole in a Generalized Dehnen-Type $(1,4,γ)$ Dark Matter Halo via the S2 Star Orbit around Sgr A$^\star$
Zhejiang University of Technology（浙江工业大学）；Institute for Theoretical Physics and Cosmology, Zhejiang University of Technology（浙江工业大学理论物理与宇宙学研究所）；United Center for Gravitational Wave Physics (UCGWP), Zhejiang University of Technology（浙江工业大学引力波物理联合中心）；National Research University TIIAME（塔什干国立交通大学）；Institute of Fundamental and Applied Research, National Research University TIIAME（塔什干国立交通大学基础与应用研究所）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）
Schwarzschild-like Black Holes Submerged in an Exponential Density Dark Matter Profile
National Nanotechnology Laboratory of Open Type（开放式国家纳米技术实验室）；Al-Farabi Kazakh National University（哈萨克国立大学）；Center for Theoretical Physics, Khazar University（阿塞拜疆库萨尔大学理论物理中心）；Fesenkov Astrophysical Institute（费森可夫天体物理研究所）；Helsinki Institute of Physics, University of Helsinki（赫尔辛基大学赫尔辛基物理研究所）；California State University, Fresno（加州州立大学弗雷斯诺分校）；University of Hradec Králové（赫拉德茨克拉洛韦大学）；Khazar University, Department of Physics and Electronics（阿塞拜疆库萨尔大学物理与电子系）；Institute for Physical Problems, Baku State University（巴库国立大学物理问题研究所）
Energy and angular momentum of the weak gravitational waves on the Schwarzschild background -- quasilocal gauge-invariant formulation
结果表明，球对称黑洞的轴向扰动和极向扰动可以用规范不变的方式描述。描述视界外引力波的约化相空间由规范不变量描述。两个自由度都满足广义标量波动方程。对于轴向自由度，方程的径向部分对应于Regge-Wheeler结果（Phys.Rev.108，1063-1069（1957）），对于极性的，我们得到Zerilli结果（Phys. Rev. D2，2141-2160（1970）），see also Zurrasekhar（The Mathematical Theory of黑洞，（Clarendon Press Oxford，1983）），Moncrief（Annals of Physics 88，323-342（1974））。分析的一个重要组成部分是准定域性的概念，它在通常的方法中用于分离角变量。此外，不需要用正常模式（具有时间依赖性$\exp(-ikt)$）来表示扰动，我们在时空中有场，它们的柯西问题在视界之外有很好的定义。简化的辛结构解释了轴不变量和极不变量的起源。它允许为引力波引入相对于规范变换不变的能量和角动量。这两个发电机表示ADM非线性公式的二次近似的史瓦西度规的扰动。我们还讨论了视界外史瓦西背景下线性化爱因斯坦方程的边界初值问题。
Optical Signatures of a Schwarzschild Black Hole in a Dehnen-Type Dark Matter Halo
Institute of Fundamental and Applied Research, National Research University TIIAME（基础与应用研究所，国立研究大学TIIAME）；National Pedagogical University of Uzbekistan named after Nizami（以尼扎米命名的乌兹别克斯坦国立师范大学）；School of Advanced Sciences, Vellore Institute of Technology（韦洛尔技术学院高等科学学院）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Tashkent State Technical University（塔什干国立技术大学）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）
Can a Dehnen-type dark matter halo affect the neutrino flavor oscillations?
University of Tashkent for Applied Sciences（塔什干应用科学大学）；School of Physics, Harbin Institute of Technology（哈尔滨工业大学物理学院）；Tashkent State Technical University（塔什干国立技术大学）；Institute of Theoretical Physics, National University of Uzbekistan（乌兹别克斯坦国立大学理论物理研究所）；Institute for Advanced Studies, New Uzbekistan University（新乌兹别克斯坦大学高级研究院）；New Uzbekistan University（新乌兹别克斯坦大学）
Particle production, absorption, scattering, and geodesics in a Schwarzschild-Hernquist black hole
Khazar University（哈扎尔大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）；Damghan University（达姆甘大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal do Piauí（皮奥伊联邦大学）；Universidade Estadual do Maranhão（马拉尼昂州立大学）
