An eigenvalue inequality of the Newton potential

2016 ◽  
Author(s):  
Durvudkhan Suragan
Keyword(s):  
Newton Potential ◽  
Eigenvalue Inequality

scholarly journals Post-Newtonian properties of EMRI with power law potential

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Chinmay N. Gandevikar ◽  
Divyesh N. Solanki ◽  
Dipanjan Dey
Keyword(s):  
Velocity Profile ◽  
Power Law ◽  
Average Energy ◽  
Mass Ratio ◽  
Matter Distribution ◽  
Energy Radiation ◽  
Newton Potential ◽  
Test Particles ◽  
Orbital Frequency ◽  
Radiation Rate

AbstractThere are many astrophysical scenarios where extreme mass ratio inspiral (EMRI) binaries can be surrounded by inhomogenous matter distribution. The distribution of mass can affect the dynamical properties (e.g. orbital frequency, average energy radiation rate, etc.) of the EMRI. In this matter distribution, instead of Kepler–Newton potential, one may consider a more general form of potential i.e. power law potential. Moreover, due to the power law potential, at the Newtonian order itself, the velocity profile of test particles does not fall as much as that predicted by Kepler–Newton potential and this feature of the velocity profile may be observationally important. In this study, we have obtained the first post-Newtonian (1PN) expressions for dynamical quantities and the average energy radiation rate from the circular orbit EMRI which is surrounded by a matter distribution. We show that the energy radiation rate and orbital frequency of EMRI can be significantly different in the presence of power law potential as compared to that in the Kepler–Newton potential, signatures of which may be observed in gravitational waves from EMRI.

A generalized Hölder type eigenvalue inequality

2017 ◽  
Vol 65 (10) ◽  
pp. 2145-2151 ◽  
Author(s):  
Jun-Tong Liu ◽  
Yiu-Tung Poon ◽  
Qing-Wen Wang
Keyword(s):  
Eigenvalue Inequality
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