Fluctuation on a Schwarzschild black hole

2009 ◽  
Vol 87 (9) ◽  
pp. 1009-1012 ◽  
Author(s):  
Xianming Liu ◽  
Wenbiao Liu
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Hawking Radiation ◽  
Apparent Horizon ◽  
Gravitational Anomaly ◽  
Schwarzschild Black Hole ◽  
First Law Of Thermodynamics ◽  
Vaidya Black Hole

When a relativistic perturbation is given to the horizon of a Schwarzschild black hole, a new supersurface near the horizon will be obtained. Using the gravitational anomaly method proposed by Robinson and Wilczek, Hawking radiation from this new supersurface is calculated. It is found that the first law of thermodynamics can also be constructed successfully on this supersurface. The expressions of the characteristic position and temperature are very similar to the previous results for the event horizon of a Vaidya black hole. Comparing with the Vaidya black hole, we conclude that Hawking radiation and the thermodynamics of a Vaidya black hole should be indeed constructed at the apparent horizon instead of the event horizon.

TORTOISE COORDINATE TRANSFORMATION ON APPARENT HORIZON OF A DYNAMICAL BLACK HOLE

2012 ◽  
Vol 12 ◽  
pp. 358-367 ◽  
Author(s):  
XIANMING LIU ◽  
ZHENG ZHAO ◽  
WENBIAO LIU
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Hawking Radiation ◽  
Coordinate Transformation ◽  
Apparent Horizon ◽  
Schwarzschild Black Hole ◽  
First Law Of Thermodynamics ◽  
Vaidya Black Hole ◽  
Tortoise Coordinate ◽  
Tortoise Coordinate Transformation

Thinking of Hawking radiation calculation from a Schwarzschild black hole using Damour-Ruffini method, some key requirements of the tortoise coordinate transformation are pointed out. Extending these requirements to a dynamical black hole, a dynamical tortoise coordinate transformation is proposed. Under this new dynamical tortoise coordinate transformation, Hawking radiation from a Vaidya black hole can be got successfully using Damour-Ruffini method. Moreover, we also find that the radiation should be regarded as originating from the apparent horizon rather than the event horizon at least from the viewpoint of the first law of thermodynamics.

APPARENT HORIZON AND EVENT HORIZON OF A VAIDYA BLACK HOLE

2009 ◽  
Vol 24 (26) ◽  
pp. 2099-2106 ◽  
Author(s):  
SHIWEI ZHOU ◽  
WENBIAO LIU
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Small Deviation ◽  
Apparent Horizon ◽  
Back Reaction ◽  
First Law Of Thermodynamics ◽  
Thermal Spectrum ◽  
Tunneling Method ◽  
Horizon Thermodynamics ◽  
Vaidya Black Hole

Hawking radiation on the apparent horizon of a Vaidya black hole is investigated using Parikh's tunneling method. When back-reaction of particles is neglected, precisely thermal spectrum can be obtained. Then the black hole thermodynamics can be built successfully on the apparent horizon. When a relativistic perturbation is given to the apparent horizon, similar calculation can also lead to a purely thermal spectrum, which is corresponding to a modified temperature from the former. The first law of thermodynamics can also be constructed successfully at a new supersurface which has a small deviation from the apparent horizon. When the event horizon is thought as such a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be built on the event horizon. It is concluded that the thermodynamics should be constructed on the apparent horizon exactly while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.

scholarly journals Interior volume of (1 + D)-dimensional Schwarzschild black hole

2018 ◽  
Vol 33 (02) ◽  
pp. 1850011 ◽  
Author(s):  
Nilanjandev Bhaumik ◽  
Bibhas Ranjan Majhi
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Hawking Radiation ◽  
Mass Change ◽  
Dimensional Case ◽  
Schwarzschild Black Hole ◽  
Interesting Point ◽  
Increase Rate ◽  
Spatial Dimensions ◽  
Interior Volume

We calculate the maximum interior volume, enclosed by the event horizon, of a [Formula: see text]-dimensional Schwarzschild black hole. Taking into account the mass change due to Hawking radiation, we show that the volume increases towards the end of the evaporation. This fact is not new as it has been observed earlier for four-dimensional case. The interesting point we observe is that this increase rate decreases towards the higher value of space dimensions [Formula: see text]; i.e. it is a decelerated expansion of volume with the increase of spatial dimensions. This implies that for a sufficiently large [Formula: see text], the maximum interior volume does not change. The possible implications of these results are also discussed.

Hawking radiation from a dynamical Kerr–Newman black hole

2011 ◽  
Vol 89 (6) ◽  
pp. 667-672 ◽  
Author(s):  
Han Ding ◽  
Xian-Ming Liu ◽  
Wen-Biao Liu
Keyword(s):  
Black Hole ◽  
Hawking Radiation ◽  
Coordinate Transformation ◽  
Apparent Horizon ◽  
Schwarzschild Black Hole ◽  
Static Black Hole ◽  
Newman Black Hole ◽  
Tortoise Coordinate ◽  
Tortoise Coordinate Transformation ◽  
Generalized Tortoise Coordinate Transformation

After Hawking radiation from a Schwarzschild black hole is calculated using the Damour–Ruffini method, the tortoise coordinate transformation in a static black hole is extended to a dynamical axisymmetric black hole, such as a dynamical Kerr–Newman black hole. Under the generalized tortoise coordinate transformation, Hawking radiation from a dynamical Kerr–Newman black hole is obtained successfully. Moreover, it also seems to occur on the apparent horizon instead of the event horizon.

scholarly journals THE MILNE SPACETIME AND THE HADRONIC RINDLER HORIZON

2010 ◽  
Vol 19 (08n10) ◽  
pp. 1379-1384 ◽  
Author(s):  
H. CULETU
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Time Dependent ◽  
Anisotropic Fluid ◽  
Direct Relation ◽  
Schwarzschild Black Hole ◽  
Black Hole Interior ◽  
Flat Metric ◽  
Shear Tensor ◽  
Hadronic Rindler Horizon

A direct relation between the time-dependent Milne geometry and the Rindler spacetime is shown. Milne's metric corresponds to the region beyond Rindler's event horizon (in the wedge t ≻ |x|). We point out that inside a Schwarzschild black hole and near its horizon, the metric may be Milne's flat metric. It was found that the shear tensor associated to a congruence of fluid particles of the RHIC expanding fireball has the same structure as that corresponding to the anisotropic fluid from the black hole interior, even though the latter geometry is curved.

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 The (A)symmetry between the Exterior and Interior of a Schwarzschild Black Hole

2018 ◽  
Author(s):  
Pawel Gusin ◽  
Andy Augousti ◽  
Filip Formalik ◽  
Andrzej Radosz
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Equations Of Motion ◽  
Coordinate Systems ◽  
Schwarzschild Black Hole ◽  
Schwarzschild Spacetime ◽  
The Relationship

A black hole in a Schwarzschild spacetime is considered. A transformation is proposed that describes the relationship between the coordinate systems exterior and interior to an event horizon. Application of this transformation permits considerations of the (a)symmetry of a range of phenomena taking place on both sides of the event horizon. The paper investigates two distinct problems of a uniformly accelerated particle. In one of these, although the equations of motion are the same in the regions on both sides, the solutions turn out to be very different. This manifests the differences of the properties of these two ranges.

scholarly journals Statistical Approach to the Bekenstein-Hawking Entropy

2021 ◽  
Author(s):  
José Hernández Ramírez
Keyword(s):  
Black Hole ◽  
Event Horizon ◽  
Statistical Approach ◽  
Canonical Ensemble ◽  
Schwarzschild Black Hole

Abstract We consider a Schwarzschild black hole type in this work whose particles, only those that lies on its surface, the event horizon (r+), contributes to the entropy and we found it by using the canonical ensemble. We don’t consider any interaction between this particles, but the inner energy.

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