Statistical-Mechanical Entropies of Schwarzschild Black Hole due to Arbitrary Spin Fields in Different Coordinates

2007 ◽  
Vol 24 (8) ◽  
pp. 2189-2192 ◽  
Author(s):  
Ding Chi-Kun ◽  
Jing Ji-Liang
Keyword(s):  
Black Hole ◽  
Arbitrary Spin ◽  
Schwarzschild Black Hole ◽  
Spin Fields ◽  
Statistical Mechanical

QUASINORMAL MODES OF THE SCHWARZSCHILD BLACK HOLE WITH ARBITRARY SPIN FIELDS: NUMERICAL ANALYSIS

2006 ◽  
Vol 21 (35) ◽  
pp. 2671-2683 ◽  
Author(s):  
QIYUAN PAN ◽  
JILIANG JING
Keyword(s):  
Black Hole ◽  
Quantum Number ◽  
Imaginary Part ◽  
Quasinormal Modes ◽  
Arbitrary Spin ◽  
Schwarzschild Black Hole ◽  
Surprising Effect ◽  
Spin Number ◽  
Spin Fields ◽  
Angular Quantum Number

The quasinormal modes (QNMs) associated with the decay of massless arbitrary spin fields around a Schwarzschild black hole are investigated by using the continued fraction method in a united form and their universal properties are found. It is shown that these QNMs become evenly spaced for large angular quantum number l (for the boson perturbations) and j (for the fermion perturbations) and the spacing is given by [Formula: see text] which is independent of the spin number s and overtone number n, and in the complex plane they have an interesting trend which depends on n before they become the same value with the increasing l (or j). The distribution of the QNMs with arbitrary spin fields for large values l (or j) and small n can be expressed as [Formula: see text]. It is also shown that the angular quantum number has the surprising effect of increasing real part of the QNMs, but it almost does not affect the imaginary part, especially for the lowest lying mode. In addition, the spacing for imaginary part of the QNMs at high overtones is equidistant and equals to -i/4M, which is independent of l (or j) and s.

MODIFICATIONS TO BEKENSTEIN–HAWKING ENTROPY DUE TO ARBITRARY SPIN FIELDS

2006 ◽  
Vol 21 (23) ◽  
pp. 1821-1827 ◽  
Author(s):  
LI-QIN MI ◽  
ZHONG-HENG LI
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Arbitrary Spin ◽  
Quantum Fields ◽  
Spin Fields ◽  
Massless Quantum ◽  
Modified Entropy

The modified entropy, due to massless quantum fields of arbitrary spin s≤2, of the Kerr–Taub–NUT black hole is evaluated. The appearance of logarithmic terms is demonstrated. The modified entropy can be reduced to the form proportional to the area of the event horizon. However, modified coefficient not only depend on the characteristics of the black hole but also on the spin of the fields.

The Schwarzschild black hole

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Black Hole ◽  
Gravitational Field ◽  
Equilibrium Configuration ◽  
Original Form ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Metric ◽  
Schwarzschild Geometry

This chapter discusses the Schwarzschild black hole. It demonstrates how, by a judicious change of coordinates, it is possible to eliminate the singularity of the Schwarzschild metric and reveal a spacetime that is much larger, like that of a black hole. At the end of its thermonuclear evolution, a star collapses and, if it is sufficiently massive, does not become stabilized in a new equilibrium configuration. The Schwarzschild geometry must therefore represent the gravitational field of such an object up to r = 0. This being said, the Schwarzschild metric in its original form is singular, not only at r = 0 where the curvature diverges, but also at r = 2m, a surface which is crossed by geodesics.

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