Avoidance of singularity during the gravitational collapse with string T-duality effects

Abstract

In this paper, we explore the gravitational collapse of matter (dust) under the effect of zero-point length $l_0$. During the gravitational collapse, we have neglected the backreaction effect of the pre-Hawking radiation (in the sense that it is small effect and cannot prevent the formation of apparent horizon), then we recast the internal metric of a collapsing star as a closed FRW universe for any spherically symmetric case and, finally, we obtain the minimal value for the scale factor meaning that the particles never hit the singularity. We argue that the object emerging at the end of the gravitational collapse can be interpreted as Planck stars (black hole core) hidden inside the event horizon of the black hole with radius proportional to $(GM{l}_0^2/c^2{)}^{1/3}$. Quite interestingly, we found the same result for radius of the Planck star using a free falling observer point of view. In addition, we pointed out a correspondence between the modified Friedmann's equations in loop quantum gravity and the modified Friedmann's equation in string T-duality. In the end, we discuss two possibilities regarding the final stage of the black hole. The first possibility is that we end up with a Planck-size black hole remnants. The second possibility is that the inner core can be unstable and, due to the quantum tunnelling effect, the spacetime can undergo a black hole-to-white hole transition (a bouncing Planck star).

arXiv comment9 pages, no figures. Published in Universe https://www.mdpi.com/2218-1997/9/1/41

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• Generalized Uncertainty Principle from the Regularized Self-Energy
• Canonical quantization of modified non-gauge invariant Einstein-Maxwell gravity and stability of spherically symmetric electrostatic stars
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