Finite Gravitational Time Dilation in Black Holes Using Dynamic Newtonian Advanced Gravity (DNAg) Andrew Worsley 1 Joseph Worsley 2 1 UCL, Gower Street, London WC1E 6BT, UK. [email protected] 2 Bristol University UK. [email protected] Key words/PACS: gravitation, 95.30.Sf; time dilation, 06.30Ft; black holes, 04.70Bw; Cygnus X-1. 1
Abstract In this paper we use a dynamic form of modified Newtonian gravity to reformulate the equations for gravitational time dilation. Here we introduce the generic equations for gravitational time dilation. It is shown that these equations agree exactly with gravitational time dilation in satellite navigation systems. The equations are also in agreement with a reanalysis of observations of gravitational red shifts in black hole accretion discs. Using these equations, we translate the time dilation into a finite value at the black hole event horizon. Thus this reformulation resolves the difficulties of the existence of black hole singularities. Importantly these dynamic gravitational equations provide testable predictions in the vicinity of black holes. 2
1. Introduction: The current description of gravity in modern classical physics has been successful at predicting gravitational observations in low and medium gravitational fields. However, there remain some outstanding issues particularly with regards galactic rotation curves, and the presence of dark matter. We have previously shown that using a dynamic form of Newtonian advanced gravity (DNAg), it is possible to explain both the galactic rotation curves [1, 2], and the presence of dark matter [2, 3]. It is however, essential to have an understanding of time dilation and black hole gravitational physics and in particular the effects of gravitational time dilation in the vicinity of black holes. The generic equations for time dilation for this model have not previously been published. Here we present original equations for gravitational time dilation. The current interpretation of the gravitational equations predicts that the effects of time dilation, leads to infinite time dilation at the event horizon and the formation of singularities [4, 5] . Classical model of gravitational time dilation : 2 2 1 1 1 Rc GM z (1) where M is the gravitational mass, c is the speed of light and G the gravitational constant, R is the radius for space. However, it is possible that an adaptation to the gravitational equations can be made, which can account for time dilation in the presence of black holes. To do this it is first possible to parameterize the gravitational equations for space and time separately. 3
For space, the perihelion advance, in Straumann  is given by: 2 2 6 tan L m (2) where m= GM/c 2 and L 2 /m = a(1- e 2 ), a is the semi-major axis and e is the eccentricity .
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- General Relativity, Time Dilation, dilation.