论文标题
能量摩托车的弱场和慢动作限制
Weak field and slow motion limits in energy-momentum powered gravity
论文作者
论文摘要
我们探索了能量摩托车的功率重力（EMPG），即$ f（t_ {μν} t_ {μν} t^{μν} $ f（$ f（$ f）$ f（t_ {μν} $ t_ $ f（T_ $η$是常数。我们已经证明，具有$η\ geq0 $和一般相对（GR）的EMPG无法通过本地测试（例如太阳系测试）区分；由于它们导致了相同的重力势形式，PPN参数和测试粒子的大地测量学。 However, within the EMPG framework, $M_{\rm ast}$, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass $M_{\rm eff}(α,η,M)=M+M_{\rm empg}(α,η,M)$, $M$作为实际的物理质量和$ m _ {\ rm empg} $是由于EMPG引起的修改。因此，在GR中，我们只有关系$ m _ {\ rm ast} = m $，在empg中，我们有$ m _ {\ rm ast} = m+m+m _ {\ rm empg} $。在EMPG的框架内，如果有有关$ \ {α，η\} $对或$ m $的值的信息，则来自其他独立现象（来自宇宙学观察，天体物理对象的结构等），则原则上可以推断出$ m _ {\ rmmm ast a aSt and $ $ $ $ $ $ $ $ $ $ $ MM $ MONM $ M M _ { empg} $分别。要在EMPG框架内进行适当的分析，有必要通过$ | p _ {\ rm eff}/ρ_{\ rm eff} | \ ll1 $（其中$ p _ {$ p _ {\ rm eff} = p+p+p _ {\ rm rm rm em emp _ eff} =ρ+ρ_ {\ rm empg} $），而这种情况则导致$ | p/ρ| \ ll1 $在gr中。
We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy-momentum powered gravity (EMPG), viz., the energy-momentum squared gravity (EMSG) of the form $f(T_{μν}T^{μν})=α(T_{μν}T^{μν})^η$ with $α$ and $η$ being constants. We have shown that EMPG with $η\geq0$ and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, $M_{\rm ast}$, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass $M_{\rm eff}(α,η,M)=M+M_{\rm empg}(α,η,M)$, $M$ being the actual physical mass and $M_{\rm empg}$ being the modification due to EMPG. Accordingly, while in GR we simply have the relation $M_{\rm ast}=M$, in EMPG we have $M_{\rm ast}=M+M_{\rm empg}$. Within the framework of EMPG, if there is information about the values of $\{α,η\}$ pair or $M$ from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only $M_{\rm ast}$ alone from astronomical observations, but $M$ and $M_{\rm empg}$ separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by $|p_{\rm eff}/ρ_{\rm eff}|\ll1$ (where $p_{\rm eff}=p+p_{\rm empg}$ and $ρ_{\rm eff}=ρ+ρ_{\rm empg}$), whereas this condition leads to $|p/ρ|\ll1$ in GR.
