The Free Energy and Entropy of Schwarzschild Black Hole Due to Scalar Field

2006 ◽  
Vol 45 (10) ◽  
pp. 1936-1942 ◽  
Author(s):  
Zi-Zhen Zhang ◽  
Li-Chun Zhang
Keyword(s):  
Black Hole ◽  
Free Energy ◽  
Scalar Field ◽  
Schwarzschild Black Hole

Entropy in a d-dimensional charged black hole

2018 ◽  
Vol 33 (27) ◽  
pp. 1850159 ◽  
Author(s):  
Shad Ali ◽  
Xin-Yang Wang ◽  
Wen-Biao Liu
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Hawking Radiation ◽  
Space Time ◽  
Charged Black Hole ◽  
Schwarzschild Black Hole ◽  
Proportionality Coefficient ◽  
Proportional Relation ◽  
Hamiltonian Analysis ◽  
Interior Volume

Christodoulou and Rovelli have shown that the interior volume of a Schwarzschild black hole grows linearly with time. The entropy of a scalar field in this interior volume of a Schwarzschild black hole has been calculated and shown to increase linearly with the advanced time too. In this paper, considering Hawking radiation from a d-dimensional charged black hole, we investigate the proportional relation between the entropy of the scalar field in the interior volume and the Bekenstein–Hawking entropy using the method of our previous work. We also derive this proportionality relation using Hamiltonian analysis and find a consistent result. We then investigate the proportionality coefficient with respect to d and find that it gradually decreases as the dimension of space–time increases.

scholarly journals TACHYON CONDENSATION AND OFF-SHELL GRAVITY/GAUGE DUALITY

2007 ◽  
Vol 22 (01) ◽  
pp. 41-65 ◽  
Author(s):  
YUN SOO MYUNG
Keyword(s):  
Black Hole ◽  
Free Energy ◽  
Tachyon Condensation ◽  
Schwarzschild Black Hole ◽  
End Point ◽  
Verlinde Formula ◽  
Β Function ◽  
Canonical Ensembles

We investigate quasilocal tachyon condensation by using gravity/gauge duality. In order to cure the IR divergence due to a tachyon, we introduce two regularization schemes: AdS space and a d = 10 Schwarzschild black hole in a cavity. These provide stable canonical ensembles and thus are good candidates for the end point of tachyon condensation. Introducing the Cardy–Verlinde formula, we establish the on-shell gravity/gauge duality. We propose that the stringy geometry resulting from the off-shell tachyon dynamics matches onto the off-shell AdS black hole, where "off-shell" means nonequilibrium configuration. The instability induced by condensation of a tachyon behaves like an off-shell black hole and evolves toward a large stable black hole. The off-shell free energy and its derivative (β-function) are used to show the off-shell gravity/gauge duality for the process of tachyon condensation. Further, d = 10 Schwarzschild black hole in a cavity is considered for the Hagedorn transition as a possible explanation of the tachyon condensation.

scholarly journals ENTROPY OF SCALAR FIELD NEAR A SCHWARZSCHILD BLACK HOLE HORIZON

2006 ◽  
Vol 21 (30) ◽  
pp. 6183-6190 ◽  
Author(s):  
M. R. SETARE
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Spherical Shell ◽  
Polarization Effect ◽  
Vacuum Polarization ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Massive Scalar ◽  
Schwarzschild Black Hole ◽  
Massive Scalar Field

In this paper we compute the correction to the entropy of Schwarzschild black hole due to the vacuum polarization effect of massive scalar field. The Schwarzschild black hole is supposed to be confined in spherical shell. The scalar field obeying mixed boundary condition on the spherical shell.

scholarly journals Massive scalar field quasinormal modes of a Schwarzschild black hole surrounded by quintessence

Open Physics ◽  
2008 ◽  
Vol 6 (2) ◽  
Author(s):  
Chunrui Ma ◽  
Yuanxing Gui ◽  
Wei Wang ◽  
Fujun Wang
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Quasinormal Modes ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Massive Scalar ◽  
Schwarzschild Black Hole ◽  
Third Order ◽  
Massive Scalar Field ◽  
Absolute Value

AbstractWe present the quasinormal frequencies of the massive scalar field in the background of a Schwarzchild black hole surrounded by quintessence with the third-order WKB method. The mass of the scalar field u plays an important role in studying the quasinormal frequencies, the real part of the frequencies increases linearly as mass of the field u increases, while the imaginary part in absolute value decreases linearly which leads to damping more slowly than the massless scalar field. The frequencies have a limited value, so it is easier to detect the quasinormal modes. Moreover, owing to the presence of the quintessence, the massive scalar field damps more slowly.

scholarly journals Geodesic motion near self-gravitating scalar field configurations

2019 ◽  
Vol 27 (3) ◽  
pp. 231-241
Author(s):  
Ivan M. Potashov ◽  
Julia V. Tchemarina ◽  
Alexander N. Tsirulev
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Circular Orbit ◽  
Naked Singularity ◽  
Schwarzschild Black Hole ◽  
Null Geodesics ◽  
Naked Singularities ◽  
Test Particles ◽  
Stable Circular Orbit ◽  
Innermost Stable Circular Orbit

We study the geodesics motion of neutral test particles in the static spherically symmetric spacetimes of black holes and naked singularities supported by a selfgravitating real scalar field. The scalar field is supposed to model dark matter surrounding some strongly gravitating object such as the centre of our Galaxy. The behaviour of timelike and null geodesics very close to the centre of such a configuration crucially depends on the type of spacetime. It turns out that a scalar field black hole, analogously to a Schwarzschild black hole, has the innermost stable circular orbit and the (unstable) photon sphere, but their radii are always less than the corresponding ones for the Schwarzschild black hole of the same mass; moreover, these radii can be arbitrarily small. In contrast, a scalar field naked singularity has neither the innermost stable circular orbit nor the photon sphere. Instead, such a configuration has a spherical shell of test particles surrounding its origin and remaining in quasistatic equilibrium all the time. We also show that the characteristic properties of null geodesics near the centres of a scalar field naked singularity and a scalar field black hole of the same mass are qualitatively different.

scholarly journals Self-force of a scalar field for circular orbits about a Schwarzschild black hole

2003 ◽  
Vol 67 (10) ◽  
Author(s):  
Steven Detweiler ◽  
Eirini Messaritaki ◽  
Bernard F. Whiting
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Schwarzschild Black Hole ◽  
Circular Orbits ◽  
Self Force

STABILITY OF SCHWARZSCHILD BLACK HOLE IN THE MASSIVE BRANS-DICKE THEORY

1986 ◽  
Vol 01 (03) ◽  
pp. 709-729 ◽  
Author(s):  
O.J. KWON ◽  
Y.D. KIM ◽  
Y.S. MYUNG ◽  
B.H. CHO ◽  
Y.J. PARK
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Gravitational Wave ◽  
Scalar Wave ◽  
Schwarzschild Black Hole ◽  
The Real ◽  
Gravitational Perturbations ◽  
Scalar Perturbations

For the nontachyonic mass (c<0, µ2<6), we have found that all nonstatic perturbations (odd-, even-parity and scalar perturbations) allow only the real values of frequency k. This means that the black hole in the massive Brans-Dicke theory is classically stable. However, for the tachyonic mass of scalar field (c>0, µ2>6), we find that the massive Brans-Dicke theory is classically unstable. We also emphasize that the potential forms of odd-parity perturbations is simply given by the pure-gravitational perturbations. For the even-parity case, we obtain the same potential just as Zerilli’s case by combining the even-parity gravitational wave and scalar wave. For static perturbations (k=0) and c>0, only the odd- and even-parity cases with L=0, 1 is allowed to avoid exponentially growing modes.

ABSORPTION CROSS-SECTION AND EMISSION SPECTRA OF SCHWARZSCHILD BLACK HOLE IN DIRAC FIELD

2008 ◽  
Vol 23 (33) ◽  
pp. 2867-2879 ◽  
Author(s):  
R. SINI ◽  
V. C. KURIAKOSE
Keyword(s):  
Black Hole ◽  
Scalar Field ◽  
Cross Section ◽  
Absorption Cross Section ◽  
Emission Spectra ◽  
Dirac Field ◽  
Absorption Cross ◽  
Schwarzschild Black Hole ◽  
Matter Waves ◽  
Black Hole Spacetime

The behavior of a Dirac field in a Schwarzschild black hole spacetime is studied. In this work the Hawking temperature and the absorption cross-section for Schwarzschild black hole placed in Dirac field are calculated, taking into consideration the matter waves reflected from the event horizon. The absorption cross-section σ abs in Dirac field is found to be ⅛ of absorption cross-section in scalar field. The emission spectra of Schwarzschild black hole placed in an environment of Dirac field is also obtained.

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