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Blake Temple

Publications and source records attributed to Blake Temple.

26 records · Page 2Linked to original sources
arXiv2015

No Regularity Singularities Exist at Points of General Relativistic Shock Wave Interaction between Shocks from Different Characteristic Families

We give a constructive proof that coordinate transformations exist which raise the regularity of the gravitational metric tensor from $C^{0,1}$ to $C^{1,1}$ in a neighborhood of points of shock wave collision in General Relativity. The proof applies to collisions between shock waves coming from different characteristic families, in spherically symmetric spacetimes. Our result here implies that spacetime is locally inertial and corrects an error in our earlier RSPA-publication, which led us to the false conclusion that such coordinate transformations, which smooth the metric to $C^{1,1}$, cannot exist. Thus, our result implies that regularity singularities, (a type of mild singularity introduced in our RSPA-paper), do not exist at points of interacting shock waves from different families in spherically symmetric spacetimes. Our result generalizes Israel's celebrated 1966 paper to the case of such shock wave interactions but our proof strategy differs fundamentally from that used by Israel and is an extension of the strategy outlined in our original RSPA-publication. Whether regularity singularities exist in more complicated shock wave solutions of the Einstein Euler equations remains open.

gr-qc↗
arXiv2014

An Instability of the Standard Model Creates the Anomalous Acceleration Without Dark Energy

We introduce a new asymptotic ansatz for spherical perturbations of the Standard Model of Cosmology (SM) which applies during the $p=0$ epoch, and prove that these perturbations trigger instabilities in the SM on the scale of the supernova data. These instabilities create a large, central region of uniform under-density which expands faster than the SM, and this central region of accelerated uniform expansion introduces into the SM {\it precisely} the same range of corrections to redshift vs luminosity as are produced by the cosmological constant in the theory of Dark Energy. A universal behavior is exhibited because all sufficiently small perturbations evolve to a single stable rest point. Moreover, we prove that these perturbations are consistent with, and the instability is triggered by, the one parameter family of self-similar waves which the authors previously proposed as possible time-asymptotic wave patterns for perturbations of the SM at the end of the radiation epoch. Using numerical simulations, we calculate the unique wave in the family that accounts for the same values of the Hubble constant and quadratic correction to redshift vs luminosity as in a universe with seventy percent Dark Energy, $Ω_Λ\approx.7$. A numerical simulation of the third order correction associated with that unique wave establishes a testable prediction that distinguishes this theory from the theory of Dark Energy. This explanation for the anomalous acceleration, based on instabilities in the SM together with simple wave perturbations from the radiation epoch that trigger them, provides perhaps the simplest mathematical explanation for the anomalous acceleration of the galaxies that does not invoke Dark Energy.

gr-qc↗
arXiv2010

General Relativistic Self-Similar Waves that induce an Anomalous Acceleration into the Standard Model of Cosmology

We prove that the Einstein equations in Standard Schwarzschild Coordinates close to form a system of three ordinary differential equations for a family of spherically symmetric, self-similar expansion waves, and the critical ($k=0$) Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology (FRW), is embedded as a single point in this family. Removing a scaling law and imposing regularity at the center, we prove that the family reduces to an implicitly defined one parameter family of distinct spacetimes determined by the value of a new {\it acceleration parameter} $a$, such that $a=1$ corresponds to FRW. We prove that all self-similar spacetimes in the family are distinct from the non-critical $k\neq0$ Friedmann spacetimes, thereby {\it characterizing} FRW as the unique spacetime lying at the intersection of these two one-parameter families. Expanding solutions about the center in fractional distance to the Hubble Length, we obtain the exact leading order quadratic and cubic corrections to the redshift vs luminosity relation for an observer at the center. It follows by continuity that corrections to the redshift vs luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of the free parameter $a$. The third order correction is then a prediction. Since self-similar expanding waves represent possible time-asymptotic wave patterns for the conservation laws associated with the highly nonlinear radiation phase, we propose to further investigate the possibility that these corrections to the Standard Model might be the source of the anomalous acceleration of the galaxies, an explanation wholly within Einstein's equations with classical sources, and not requiring Dark Energy or the cosmological constant.

gr-qc↗
arXiv2009

A One Parameter Family of Expanding Wave Solutions of the Einstein Equations That Induces an Anomalous Acceleration Into the Standard Model of Cosmology

We derive a new set of equations which describe a continuous one parameter family of expanding wave solutions of the Einstein equations such that the Friedmann universe associated with the pure radiation phase of the Standard Model of Cosmology, is embedded as a single point in this family. All of the spacetime metrics associated with this family satisfy the equation of state $p=ρc^2/3$, correct for the pure radiation phase after inflation in the Standard Model of the Big Bang. By expanding solutions about the center to leading order in the Hubble length, the family reduces to a one-parameter family of expanding spacetimes that represent a perturbation of the Standard Model. We then derive a co-moving coordinate system in which the perturbed spacetimes can be compared with the Standard Model. In this coordinate system we calculate the correction to the Hubble constant, as well as the exact leading order quadratic correction to the redshift vs luminosity relation for an observer at the center of the expanding FRW spacetime. The leading order correction to the redshift vs luminosity relation entails an adjustable free parameter that introduces an anomalous acceleration. We conclude that any correction to the redshift vs luminosity relation observed after the radiation phase of the Big Bang can be accounted for, at the leading order quadratic level, by adjustment of this free parameter. Since exact non-interacting expanding waves represent possible time-asymptotic wave patterns for conservation laws, we propose to further investigate the possibility that these corrections to the Standard Model might account for the anomalous acceleration of the galaxies, without the introduction of the cosmological constant.

astro-ph.CO↗
arXiv2003

Cosmology, Black Holes and Shock Waves Beyond the Hubble Length

We construct exact, entropy satisfying shock wave solutions of the Einstein equations for a perfect fluid which extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\it inside the Black Hole}. These solutions put forth a new Cosmological Model in which the expanding Friedmann-Robertson-Walker (FRW) universe emerges from the Big Bang with a shock wave at the leading edge of the expansion, analogous to a classical shock wave explosion. This explosion is large enough to account for the enormous scale on which the galaxies and the background radiation appear uniform. In these models, the shock wave must lie beyond one Hubble length from the FRW center, this threshhold being the boundary across which the bounded mass lies inside its own Schwarzshild radius, $2M/r>1,$ and thus the shock wave solution evolves inside a Black Hole. The entropy condition, which breaks the time symmetry, implies that the shock wave must weaken until it eventually settles down to a zero pressure OS interface, bounding a {\em finite} total mass, that emerges from the White Hole event horizon of an ambient Schwarzschild spacetime. However, unlike shock matching outside a Black Hole, the equation of state $p=\frac{c^2}{3}ρ,$ the equation of state at the earliest stage of Big Bang physics, is {\em distinguished} at the instant of the Big Bang--for this equation of state alone, the shock wave emerges from the Big Bang at a finite nonzero speed, the speed of light, decelerating to a subluminous wave from that time onward. These shock wave solutions indicate a new cosmological model in which the Big Bang arises from a localized explosion occurring inside the Black Hole of an asymptotically flat Schwarzschild spacetime.

math-ph↗
arXiv2002

Shock-Wave Cosmology Inside a Black Hole

We construct a class of global exact solutions of the Einstein equations that extend the Oppeheimer-Snyder (OS) model to the case of non-zero pressure, {\em inside the Black Hole}, by incorporating a shock wave at the leading edge of the expansion of the galaxies, arbitrarily far beyond the Hubble length in the Friedmann-Robertson-Walker (FRW) spacetime. Here the expanding FRW universe emerges behind a subluminous blast wave that explodes outward from the FRW center at the instant of the Big Bang. The total mass behind the shock decreases as the shock wave expands, and the entropy condition implies that the shock wave must weaken to the point where it settles down to an OS interface, (bounding a {\em finite} total mass), that eventually emerges from the White Hole event horizon of an ambient Schwarzschild spacetime. The entropy condition breaks the time symmetry of the Einstein equations, selecting the explosion over the implosion. These shock wave solutions indicate a new cosmological model in which the Big Bang arises from a localized explosion occurring inside the Black Hole of a Schwarzschild spacetime.

astro-ph↗
arXiv1998

Cosmology with a shock wave

We construct the simplest solution of the Einstein equations that incorporates a shock-wave into a standard Friedmann-Robertson-Walker metric whose equation of state accounts for the Hubble constant and the microwave background radiation temperature. This produces a new solution of the Einstein equations from which we are able to derive estimates for the shock position at present time. We show that the distance from the shock-wave to the center of the explosion at present time is comparable to the Hubble distance. We are motivated by the idea that the expansion of the universe as measured by the Hubble constant might be accounted for by an event more similar to a classical explosion than by the well-accepted scenario of the Big Bang.

astro-ph↗