The new era of multimessenger astrophysics requires the capability of studying different aspects of the evolution of compact objects. In particular, the merger of neutron star binaries is a strong source of gravitational waves and electromagnetic radiation, from radio to $\gamma$-rays, as demonstrated by the detection of GW170817 and its electromagnetic counterparts. In order to understand the physical mechanisms involved in such systems, it is necessary to employ fully general relativistic magnetohydrodynamic (GRMHD) simulations able to include the effects of a composition and temperature dependent equation of state describing neutron star matter as well as neutrino emission and reabsorption. Here, we present our new code named $\texttt{Spritz}$ that solves the GRMHD equations in 3D Cartesian coordinates and on a dynamical spacetime. The code can support tabulated equations of state, taking into account finite temperature effects and allowing for the inclusion of neutrino radiation. In this first paper, we present the general features of the code and a series of tests performed in special and general relativity to assess the robustness of the basic GRMHD algorithms implemented. Among these tests, we also present the first comparison between a non-staggered and a staggered formulation of the vector potential evolution, which is used to guarantee the divergence-less character of the magnetic field. With respect to other publicly available GRMHD codes, $\texttt{Spritz}$ combines the robust approach of a staggered formulation of the vector potential together with the use of an equation of state driver ($\texttt{EOS_Omni}$) that can allow the code to use finite temperature equations of state. A next version of the code will fully test the $\texttt{EOS_Omni}$ driver by coupling it with a neutrino leakage scheme.

中文翻译：

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Spritz：一种新的完全广义相对论磁流体动力学代码

多信使天体物理学的新时代需要研究致密天体演化的不同方面的能力。特别是，中子星双星的合并是引力波和电磁辐射的强大来源，从无线电到 $\gamma$ 射线，如 GW170817 及其电磁对应物的检测所证明的那样。为了理解此类系统中涉及的物理机制，有必要采用完全通用的相对论磁流体动力学 (GRMHD) 模拟，该模拟能够包括描述中子星物质以及中微子发射和重吸收的成分和温度相关状态方程的影响. 在这里，我们展示了名为 $\texttt{Spritz}$ 的新代码，它可以在 3D 笛卡尔坐标和动态时空上求解 GRMHD 方程。该代码可以支持列表状态方程，考虑到有限温度效应并允许包含中微子辐射。在第一篇论文中，我们介绍了代码的一般特征以及在狭义和广义相对论中执行的一系列测试，以评估所实现的基本 GRMHD 算法的稳健性。在这些测试中，我们还首次比较了矢量势演化的非交错和交错公式，用于保证磁场的无发散特性。关于其他公开可用的 GRMHD 代码，$\texttt{Spritz}$ 结合了向量势交错公式的稳健方法以及状态方程驱动器 ($\texttt{EOS_Omni}$) 的使用，它可以允许代码使用有限温度状态方程. 该代码的下一个版本将通过将 $\texttt{EOS_Omni}$ 驱动程序与中微子泄漏方案耦合来对其进行全面测试。