Black Hole variable speed of light due to singularity: the Noncommutative black hole frequencies secret

 https://www.quora.com/If-mass-becomes-infinite-at-the-speed-of-light-then-why-arent-all-black-holes-infinitely-massive

While it is true that the infalling object’s speed approaches the vacuum speed of light at its location, that vacuum speed of light rapidly approaches zero near the horizon, as viewed by that distant observer! The reason is gravitational time dilation: To the distant observer, everything appears to slow down near the horizon, including light.

So the two effects (the rise in the infalling object’s speed vs. increased time dilation) cancel each other out, and the resulting energy-content remains finite. The infalling object does gain kinetic energy at the expense of gravitational potential energy, but energy conservation remains valid, and the total mass of black hole + infalling object remains constant at all times, unless the process, due to its geometric asymmetry (e.g., an inspiral), results in some energy loss in the form of gravitational radiation.

https://www.ligo.org/science/GW-Inspiral.php 

 Inspiral gravitational waves are generated during the end-of-life stage of binary systems where the two objects merge into one.  These systems are usually two neutron stars, two black holes, or a neutron star and a black hole whose orbits have degraded to the point that the two masses are about to coalesce.  As the two masses rotate around each other, their orbital distances decrease and their speeds increase, much like a spinning figure skater who draws his or her arms in close to their body.  This causes the frequency of the gravitational waves to increase until the moment of coalescence.  The sound these gravitational waves would produce is a chirp sound (much like when increasing the pitch rapidly on a slide whistle) since the binary system’s orbital frequency is increasing (any increase in frequency corresponds to an increase in pitch).

 https://www.sciencedirect.com/science/article/abs/pii/S2212686423002169

 stronger non-commutative parameters lead to slower damping oscillations of gravitational waves and higher partial absorption cross sections. Furthermore, we study the geodesics of massless and massive particles, highlighting that the non-commutative parameter significantly impacts the paths of light and event horizons.

 When a BH is formed through the gravitational collapse of matter, it emanates radiation that includes a bundle of characteristic frequencies unrelated to the process which generated it. These perturbations are called the quasinormal modes.

 https://arxiv.org/abs/2305.06838

[Submitted on 11 May 2023 (v1), last revised 27 Nov 2023 (this version, v2)]

Gravitational signatures of a non--commutative stable black hole

N. Heidari, H. Hassanabadi, A. A. Araújo Filho, J. Kriz, S. Zare, P. J. Porfírio

 

  notable trend caused by the non–commutativity of the spacetime: as
Θ2 increases, the maximum value of the effective potential decrease

 we observed that increasing the NC parameter
results in a decrease in the propagating frequency (ωln) when comparing the real part of
the frequencies. However, the imaginary part of the frequency decreases as the Θ value
increases, indicating that higher values of the NC parameter lead to greater stability for the BH.

 P. Nicolini, A model of radiating black hole in noncommutative geometry. J. Phys. A Math. Gen. 38(39), L631 (2005)

  When matter undergoes gravitational collapse, giving rise to the formation of a black hole, it enters a perturbed state, emitting radiation that encompasses an array of discrete frequencies unrelated to the collapse process itself [55]. Termed quasinormal modes, these perturbations exhibit distinct frequencies that define their unique nature [56, 57].

 https://link.springer.com/article/10.1140/epjc/s10052-023-12328-7

 introduction to noncommutative math