非度规引力II：类星体的球对称解、质量缺失和红移
Non-Metric Gravity II: Spherically Symmetric Solution, Missing Mass and Redshifts of Quasars
摘要：
我们继续研究了hep-th/0611182和gr-qc/0703002中介绍的非度规引力理论，得到了它的一般球对称真空解。它尊重Birkhoff定理的类比，即，真空球对称解必然是静态的。就像在广义相对论中一样，球对称解被看作描述了一个黑洞。外部几何基本上与史瓦西情形相同，只是对牛顿势做了幂律修正。黑洞区域内的行为与史瓦西情形不同，因为通常的时空奇点被一种新类型的奇异曲面所取代，在这种奇异曲面中，理论的所有基本场仍然是有限的，但度规不再存在。这个理论不承认任意小的黑洞：对于小的物体，可能的视界上的曲率是如此之强，以至于非度规的修改阻止了视界的形成。这个理论允许对引力进行非常有趣的修改。我们讨论了三个物理效应，即（i）在附近的源牛顿定律的校正，（ii）重整化的有效引力和宇宙学常数在大距离的源，和（iii）不同曲率的空间区域之间的额外的红移因子。前两种效应可分别造成观察到的先锋号航天器加速异常和螺旋星系及其他天体质量据称缺失。第三种效应可以用来对类星体和伽马射线暴的高红移提出非宇宙学的解释。
英文摘要：
We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behavior inside the black-hole region is different from the Schwarzschild case in that the usual spacetime singularity gets replaced by a singular surface of a new type, where all basic fields of the theory remain finite but metric ceases to exist. The theory does not admit arbitrarily small black holes: for small objects, the curvature on the would-be horizon is so strong that non-metric modifications prevent the horizon from being formed. The theory allows for modifications of gravity of very interesting nature. We discuss three physical effects, namely, (i) correction to Newton's law in the neighborhood of the source, (ii) renormalization of effective gravitational and cosmological constants at large distances from the source, and (iii) additional redshift factor between spatial regions of different curvature. The first two effects can be responsible, respectively, for the observed anomaly in the acceleration of the Pioneer spacecraft and for the alleged missing mass in spiral galaxies and other astrophysical objects. The third effect can be used to propose a non-cosmological explanation of high redshifts of quasars and gamma-ray bursts.
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