New full relativistic escape velocity and new Hubble related equation for the universe

The escape velocity derived from general relativity coincides with the Newtonian one. However, the Newtonian escape velocity can only be a good approximation when v ≪ c is sufficient to break free of the gravitational field of a massive body, as it ignores higher-order terms of the relativistic kinetic energy Taylor series expansion. Consequently, it does not work for a gravitational body with a radius at which v is close to c such as a black hole. To address this problem, we revisit the concept of relativistic mass, abandoned by Einstein, and derive what we call a full relativistic escape velocity. This approach leads to a new escape radius, where ve = c equal to a half of the Schwarzschild radius. Furthermore, we show that one can derive the Friedmann equation for a critical universe from the escape velocity formula from general relativity theory. We also derive a new equation for a flat universe based on our full relativistic escape velocity formula. Our alternative to the Friedmann formula predicts exactly twice the mass density in our (critical) universe as the Friedmann equation after it is calibrated to the observed cosmological redshift. Our full relativistic escape velocity formula also appears more consistent with the uniqueness of the Planck mass (particle) than the general relativity theory: whereas the general relativity theory predicts an escape velocity above c for the Planck mass at a radius equal to the Planck length, our model predicts an escape velocity c in this case.

The General Relativistic Perspective

The Equations from General Einstein's Relativity Theory can also be framed from a Relativistically distorted perspective. General relativity slows gravitons reducing the force, so escape velocity is limited to c. Atomic structure bosons slowing makes all elements subject to decay. Energy from slowing boson structure particles would increase matter particle velocity. The lower the atomic weight, the greater the speed, so hydrogen escapes in the most significant amounts. Distortion would never be imaginary.

Strong Isotope-dependent Photodissociation Branching Ratios of N2 and Their Potential Implications for the 14N/15N Isotope Fractionation in Titan's Atmosphere

The origin and evolution of the 14N/15N ratio of Titan’s atmosphere has long been a subject of debate. Clearly a better understanding of the N isotopic fractionation mechanism would greatly help resolve this. Photodissociation of N2 by solar radiation has been suggested to either play a negligible role in fractionating the N isotopes in Titan, due to its rather low escape velocity, or to preferentially remove 15N through self-shielding controlled photochemical reactions. Here, we systematically measure the branching ratios of 14N15N between N(4S)+N(2P) and N(4S)+N(2D) channels. We find that many of its absorption states predominantly dissociate into N(4S)+N(2P) with a strong isotope effect between 14N2 and 14N15N. Since N atoms produced from N(4S)+N(2P) acquire velocities close to Titan’s escape velocity, these findings provide a new N isotope fractionation mechanism for Titan that has not been considered before, potentially providing important constraints on the origin and evolution of Titan’s N2-dominated atmosphere.

Fallback Accretion Halted by R-process Heating in Neutron Star Mergers and Gamma-Ray Bursts

The gravitational wave event GW170817 with a macronova/kilonova shows that a merger of two neutron stars ejects matter with radioactivity including r-process nucleosynthesis. A part of the ejecta inevitably falls back to the central object, possibly powering long-lasting activities of a short gamma-ray burst (sGRB), such as extended and plateau emissions. We investigate fallback accretion with r-process heating by performing one-dimensional hydrodynamic simulations and developing a semi-analytical model. We show that the usual fallback rate dM/dt ∝ t −5/3 is halted by the heating because pressure gradients accelerate ejecta beyond an escape velocity. The suppression is steeper than Chevalier’s power-law model through Bondi accretion within a turn-around radius. The characteristic halting timescale is ∼104–108 s for the GW170817-like r-process heating, which is longer than the typical timescale of the long-lasting emission of sGRBs. The halting timescale is sensitive to the uncertainty of the r-process. Future observations of fallback halting could constrain the r-process heating on the scale of a year.

Estimation and Investigation of Mean and Most Probable Velocities of Tropospheric Gases over Ilorin, Nigeria

In this study, the monthly average minimum and maximum temperature meteorological data obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) during the period of thirty eight years (1979 – 2016) were used to estimate the mean velocity and most probable velocity of atomic Oxygen and Hydrogen for Ilorin. The values of the mean velocity and most probable velocity for these atoms were compared to the value of escape velocity. The results revealed that the highest values of mean velocity and most probable velocity for atomic Oxygen were found to be in the month of March with and respectively and the highest values of mean velocity and most probable velocity for atomic Hydrogen were found to be in the month of March with and respectively. Based on the values of the mean velocity and most probable velocity for atomic Oxygen and Hydrogen obtained during the studied period suggests that these atoms cannot escape the gravitational field as their values are less than the escape velocity .

Impact-crater ejecta on Bennu indicate a surface with very low strength

A planetary surface’s resistance to change is generally described as its “strength” (units of stress). The surface strength of small, rubble-pile asteroids, which consist of fragments of larger bodies that were collisionally disrupted, is poorly constrained due to their wide departure from terrestrial analogs. Here, we report the observation of an ejecta deposit surrounding an impact crater that limits the maximum surface strength of the near-Earth rubble-pile asteroid (101955) Bennu. The presence of this deposit implies that ejecta were mobilized with velocities less than the escape velocity of Bennu, 20 cm/s. Because ejecta velocities increase with surface strength, the ejecta deposit can only be explained if the effective strength of the surface material near the crater is exceedingly low, ≤100 Pa. This is three orders of magnitude below values commonly used for asteroid surfaces, but is supported by previous observations of an artificial impact crater on a similar asteroid, Ryugu. Our findings indicate a mobile surface that has likely been renewed multiple times since Bennu’s initial assembly and have far-reaching implications for interpreting observations of Bennu and other rubble piles.

Path Tracing Photons Oscillating Through Alternate Universes Inside a Black Hole

In case of the maximally rotating Black Holes (BH) through Kerr-Neumann frames, or as described in Boyer-Lindquist coordinates metrics, the rotation axis of the BHs inputs a frame dragging effect i.e., relativistically a Lens-Thirring Precession that accelerates the photon trajectories oscillates with a shaped induced rotations through the ring singularity, between alternate universes, as a means of an induced geodesics that takes a sharp turning points back and forth provided, in the prograde photon sphere, due to magnetorotational instability, the path tracing of a photons circulates as a smooth fiber bundles over the event horizon curves, that when gets interpolate between mixed trajectories behaves as a geodesics and thus forms a smooth Jacobi-fields through Jacobi-lines by mutual intersection of geodesics over the photon sphere which when somehow gets leaked inside the event horizon, then gets sucked in with not sufficient escape velocity for retardation and trapped in the compact singularity, oscillating back and forth through alternate universes.

The General Relativistic Perspective

This paper formulates additional General Relativistic [GR] equations. They do not contradict General Relativity. They examine Dr. Einstein’s equations from a Relativistically distorted Perspective. The equations examine the distorted Escape velocity [vesc]a GR object, determining its Real vesc after the distortions of Relativity slow Bosons||Gravitons. In contrast to the variables in the Classical equations of Relativity, variables are more specific in their own respect and in their relationship to vesc, not simply the Time distortion. The values for the quantities of rate (Time and Velocity) are the quantities for zero vesc ||zero deformation. The slowdown of all Bosons also can be showed to mean an absolute limit to vesc. The form of all atoms is not the permanent thing supposed in current thinking. Slowdown of atomic structure Bosons would mean all elements subject to decay. The energy in Boson Structure particles would mean a increase in in particle velocity. With a light speed limit to vesc, all Elements could eventually escape. Hydrogen would be the most likely, with a transformation of free energy into the Kinetic energy needed for escape.

The General Relativistic Perspective

This paper formulates additional General Relativistic [GR] equations that do not contradict the originals. They rephrase Dr. Einstein's equations from a Relativistically distorted Perspective. The equations reason the distorted Escape velocity of a GR object, determining its real Escape velocity after the distortions of Relativity slow Bosons||Gravitons. In contrast to the variables in the Classical equations of Relativity, variables are more specific in their respect and relationship to Escape Velocity and Graviton distortion, not just the Time distortion.