## Gravitational Time Dilation for a Free-Fall on Neutron Black Hole

**Authors:** Sylwester Kornowski

Within the Scale-Symmetric Theory (SST) we showed that for a free-fall on neutron black hole (NBH), the relativistic mass is real so synchronization of clocks via the Lorentz Transformation is logically inconsistent. To obtain correct formula for gravitational time dilation, instead of using the Lorentz Transformation, we must start from the law of conservation of spin. Near and inside the Schwarzschild surface the gravitating grainy Einstein spacetime (ES) inspirals towards the centre of NBH (the ES leaks from NBH via the NBH jets). It causes that near the Schwarzschild surface down to the surface of NBH (its equatorial radius is two times smaller than the Schwarzschild radius) the time dilation does not follow from pure radial motions but from orbital motions as well. We showed that time practically stops when vector sum of orbital and radial velocities of freely falling body is close to the velocity of light in “vacuum” c. Due to the inspiralling ES, the trajectory of the body is deflected from the radial direction but trajectories of a freely falling initially radial photon and the body do not overlap. The inspiralling ES causes that for a distant observer, the radial speed on the Schwarzschild surface of a freely falling body is lower than c. For radii smaller than the equatorial radius of NBH, time is going as in frame of reference in the absolute rest - it follows from the fact that inside NBH both NBH and ES have the same angular velocities.

**Comments:** 4 Pages.

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### Submission history

[v1] 2017-03-14 05:27:00

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