In this paper, we examine massless scalar field by using unimodular f(R) theory. It is taken into account unimodular and cylindrically symmetric spacetime which provides convenience in researching black hole. The field equations in unimodular f(R) theory for given spacetime with massless scalar field and additional Bianchi identities are solved. Cylindrically symmetric anti-de Sitter (AdS)–Schwarzschild-like and AdS–Reissner–Nordström-like black hole spacetimes are achieved. Equations of motion are derived by using Hamiltonian. Orbits of massless test particles are depicted. Obtained line element asymptotically converges to dS/AdS spacetime. Weak and strong energy conditions of the massless scalar field are obtained with Raychaudhuri equations in unimodular f(R) theory. Also, stiff fluid interpretation of scalar field is reviewed.

中文翻译：

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圆柱对称单模 f(R) 黑洞

在本文中，我们使用单模研究无质量标量场F(R)理论。考虑到单模和柱对称时空，为研究黑洞提供了方便。单模场方程F(R)解决了具有无质量标量场和附加 Bianchi 恒等式的给定时空理论。实现了圆柱对称的反德西特 (AdS)-Schwarzschild-like 和 AdS-Reissner-Nordström-like 黑洞时空。运动方程是通过使用哈密顿量导出的。描绘了无质量测试粒子的轨道。获得的线元渐近收敛到 dS/AdS 时空。用单模Raychaudhuri方程得到无质量标量场的弱能和强能条件F(R)理论。此外，还回顾了标量场的刚性流体解释。