Time-like geodesic structure of a spherically symmetric black hole in the brane-world

doi:10.1088/1674-1056/20/10/100401

Abstract Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analysing the particle effective potential, we have investigated the time-like geodesic structure of the spherically symmetric black hole in the brane-world. We mainly take account of how the cosmological constant α and the stellar pressure β affect the time-like geodesic structure of the black hole. We find that the radial particle falls to the singularity from a finite distance or plunges into the singularity, depending on its initial conditions. But the non-radial time-like geodesic structure is more complex than the radial case. We find that the particle moves on the bound orbit or stable (unstable) circle orbit or plunges into the singularity, or reflects to infinity, depending on its energy and initial conditions. By comparing the particle effective potential curves for different values of the stellar pressure β and the cosmological constant α, we find that the stellar pressure parameter β does not affect the time-like geodesic structure of the black hole, but the cosmological constant α has an impact on its time-like geodesic structure.

Keywords: time-like geodesics effective potential spherically symmetric black hole

Received: 29 March 2011
Revised: 23 April 2011
Accepted manuscript online:

PACS:	04.20.-q	(Classical general relativity)
	04.50.-h	(Higher-dimensional gravity and other theories of gravity)
	04.25.-g	(Approximation methods; equations of motion)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10873004), the Program for Excellent Talents in Hunan Normal University (Grant No. ET10803), the State Key Development Program for Basic Research Project of China (Grant No. 2010CB832803), the Key Project of the National Natural Science Foundation of China (Grant No. 10935013), the Constructing Program of the National Key Discipline, and the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0964).

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Zhou Sheng(周盛), Chen Ju-Hua(陈菊华), and Wang Yong-Jiu(王永久) Time-like geodesic structure of a spherically symmetric black hole in the brane-world 2011 Chin. Phys. B 20 100401

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