TY - JOUR

T1 - Gravitational eigenstates in weak gravity

T2 - II. Further approximate methods for decay rates

AU - Ernest, Allan

N1 - Imported on 12 Apr 2017 - DigiTool details were: Journal title (773t) = Journal of Physics A: Mathematical and Theoretical. ISSNs: 1751-8113;

PY - 2009

Y1 - 2009

N2 - This paper develops further approximate methods for obtaining the dipole matrix elements and corresponding transition and decay rates of the high-n, high-l gravitational eigenstates. These methods include (1) investigation of the polar spreads of the angular components of the high-n, high-l eigenstates and the effects these have on the limiting values of the angular components of the dipole matrix elements in the case of large l and m, and (2) investigation of the rapid cut off and limited width of the low-p, high-n radial eigenfunctions, and the development of an equation to determine the width, position and oscillatory behaviour of those eigenfunctions in the cases of arbitrarily large values of n, l and p. The methods have wider applicability than dipole transition rate estimates and may be also used to determine limits on the rates for more general interactions. Combining the methods enables the establishment of upper limits to the total dipole decay rates of many high-n, low-p states on the state diagram to be determined, even those that may have many channels available for decay. The results continue to support the hypothetical existence of a specialized set of high-n, low-p gravitational eigenfunctions that are invisible and stable, both with respect to electromagnetic decay and gravitational collapse, making them excellent dark matter candidates.

AB - This paper develops further approximate methods for obtaining the dipole matrix elements and corresponding transition and decay rates of the high-n, high-l gravitational eigenstates. These methods include (1) investigation of the polar spreads of the angular components of the high-n, high-l eigenstates and the effects these have on the limiting values of the angular components of the dipole matrix elements in the case of large l and m, and (2) investigation of the rapid cut off and limited width of the low-p, high-n radial eigenfunctions, and the development of an equation to determine the width, position and oscillatory behaviour of those eigenfunctions in the cases of arbitrarily large values of n, l and p. The methods have wider applicability than dipole transition rate estimates and may be also used to determine limits on the rates for more general interactions. Combining the methods enables the establishment of upper limits to the total dipole decay rates of many high-n, low-p states on the state diagram to be determined, even those that may have many channels available for decay. The results continue to support the hypothetical existence of a specialized set of high-n, low-p gravitational eigenfunctions that are invisible and stable, both with respect to electromagnetic decay and gravitational collapse, making them excellent dark matter candidates.

KW - Dark matter

KW - Gravitational eigenstates

U2 - 10.1088/1751-8113/42/11/115208

DO - 10.1088/1751-8113/42/11/115208

M3 - Article

VL - 42

SP - 1

EP - 22

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1751-8113

IS - 11

ER -