论文标题
修饰的重力（MOG），宇宙学和黑洞
Modified Gravity (MOG), Cosmology and Black Holes
论文作者
论文摘要
通过增加两个新的自由度，标量场重力耦合强度$ g = 1/χ$和一个重力旋转1矢量场$ ϕ_μ $，可以通过增加两个新的自由度，标量场重力耦合强度来制定协变量的重力（MOG）。 $ g $写为$ g = g_n（1+α）$，其中$ g_n $是牛顿的常数，并且向量场的重力源费用为$ q_g = \ sqrt {αg_n} m $，其中$ m $是一个身体的质量。该理论的宇宙学解决方案以同质和各向同性的宇宙学得出。 MOG中的黑洞是静止的，作为引力塌陷的最终产物，是带球形拓扑的轴对称溶液。结果表明，对于渐近平坦边界条件的孤立黑洞，标量场$χ$无处不在。结果是标量场失去了其单极矩辐射。
A covariant modified gravity (MOG) is formulated by adding to general relativity two new degrees of freedom, a scalar field gravitational coupling strength $G= 1/χ$ and a gravitational spin 1 vector field $ϕ_μ$. The $G$ is written as $G=G_N(1+α)$ where $G_N$ is Newton's constant, and the gravitational source charge for the vector field is $Q_g=\sqrt{αG_N}M$, where $M$ is the mass of a body. Cosmological solutions of the theory are derived in a homogeneous and isotropic cosmology. Black holes in MOG are stationary as the end product of gravitational collapse and are axisymmetric solutions with spherical topology. It is shown that the scalar field $χ$ is constant everywhere for an isolated black hole with asymptotic flat boundary condition. A consequence of this is that the scalar field loses its monopole moment radiation.
