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基于Ricci的引力理论中的边界项与壳上作用量：哈密顿表述

Boundary terms and on-shell action in Ricci-based gravity theories: the Hamiltonian formulation

Gerardo Mora-Pérez, Gonzalo J. Olmo, Diego Rubiera-Garcia, Diego Sáez-Chillón Gómez

备注：
11 pages. Version published in PRD
发表信息：
Phys.Rev.D 110 (2024) 8, 084051
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AI总结：

本文通过分解独立联络并利用3+1分解与ADM方法，建立了任意基于Ricci的引力理论的哈密顿表述，并在Schwarzschild时空中验证了该形式体系。

摘要：

考虑所谓的基于Ricci的引力理论，这是一类广义相对论的推广，其作用量由独立联络的Ricci张量（对称部分）的收缩与乘积的非线性函数给出，本文得到了该理论的哈密顿表述。为此，将独立联络分解为两部分：一部分与度规张量相容，另一部分由一个3秩张量给出。随后，将Riemann张量用其投影到超曲面上的分量表示，从而能够构造理论的$3+1$分解及相应的Gauss-Codazzi关系，其中边界项自然出现在引力作用量中。最后，遵循ADM分解以构造任意基于Ricci的引力理论对应的哈密顿量和ADM能量。该形式体系被应用于Schwarzschild时空这一简单情形。

英文摘要：

Considering the so-called Ricci-based gravity theories, a family of extensions of General Relativity whose action is given by a non-linear function of contractions and products of the (symmetric part of the) Ricci tensor of an independent connection, the Hamiltonian formulation of the theory is obtained. To do so, the independent connection is decomposed in two parts, one compatible with a metric tensor and the other one given by a 3-rank tensor. Subsequently, the Riemann tensor is expressed in terms of its projected components onto a hypersurface, allowing to construct the $3+1$ decomposition of the theory and the corresponding Gauss-Codazzi relations, where the boundary terms naturally arise in the gravitational action. Finally, the ADM decomposition is followed in order to construct the corresponding Hamiltonian and the ADM energy for any Ricci-based gravity theory. The formalism is applied to the simple case of Schwarzschild space-time.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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