scholarly journals Thermodynamics of a Black Hole

2015 ◽  
Vol 48 ◽  
pp. 123-137
Author(s):  
K.A.I.L. Wijewardena Gamalath ◽  
N.S. Rajapakse
Keyword(s):  
Black Hole ◽  
Visible Region ◽  
Black Hole Entropy ◽  
Mass Variation ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Time Variations ◽  
The Given ◽  
The Universe ◽  
Over Time

A simple model was setup to find the mass variation over time for a Schwarzschild black hole. The temperature and entropy of a black hole was obtained from the numerically solved mass variation and the time variations of the black hole thermodynamic parameters were simulated. The mass of a given black hole reduces rapidly. The time taken for a black hole to vanish increases in an increasing rate with the given initial mass of the black hole. The temperature of a black hole drastically increases at the final stage of the black hole evaporation. The colour attributed to that temperature was found to be in the visible region for a significant amount of time. The black hole entropy also drastically reduces with its mass and through Hawking radiation it is added to the rest of the universe.

Black Hole Entropy from Non-Commutative Geometry and Spontaneous Localisation

2019 ◽  
Author(s):  
Tejinder P. Singh ◽  
Palemkota Maithresh
Keyword(s):  
Black Hole ◽  
Black Hole Entropy ◽  
Entangled State ◽  
Schwarzschild Black Hole ◽  
Spectral Action ◽  
Black Hole Evaporation ◽  
Gravitational Action ◽  
Fluctuation Dissipation ◽  
Fluctuation Dissipation Theorem ◽  
Gravitational Entropy

In our recently proposed theory of quantum gravity, a black hole arises from the spontaneous localisation of an entangled state of a large number of atoms of space-time-matter [STM]. Prior to localisation, the non-commutative curvature of an STM atom is described by the spectral action of non-commutative geometry. By using the techniques of statistical thermodynamics from trace dynamics, we show that the gravitational entropy of a Schwarzschild black hole results from the microstates of the entangled STM atoms and is given (subject to certain assumptions) by the classical Euclidean gravitational action. This action, in turn, equals the Bekenstein-Hawking entropy (Area/$4{L_P}^2$) of the black hole. We argue that spontaneous localisation is related to black-hole evaporation through the fluctuation-dissipation theorem.

scholarly journals A new mass scale, implications on black hole evaporation and holography

2016 ◽  
Vol 31 (16) ◽  
pp. 1650089 ◽  
Author(s):  
Piyabut burikham ◽  
Rujikorn Dhanawittayapol ◽  
Taum Wuthicharn
Keyword(s):  
Black Hole ◽  
Surface Area ◽  
Physical Interpretation ◽  
Mass Formula ◽  
Uncertainty Relation ◽  
Black Hole Entropy ◽  
Mass Scale ◽  
Minimum Length ◽  
Black Hole Evaporation ◽  
The Universe

We consider a new mass scale [Formula: see text] constructed from dimensional analysis by using [Formula: see text], [Formula: see text] and [Formula: see text] and discuss its physical interpretation. Based on the Generalized Uncertainty Relation, a black hole with age comparable to the universe would stop radiating when the mass reaches a new mass scale [Formula: see text] at which its temperature corresponds to the mass [Formula: see text]. Black hole remnants could have masses ranging from a Planck mass to a trillion kilograms. Holography persists even when the uncertainty relation is modified to the Minimum Length Uncertainty Relation (MLUR). The remnant black hole entropy is proportional to the surface area of the black hole in unit of the Planck area in arbitrary noncompact dimensions.

scholarly journals BLACK HOLE EVAPORATION BASED UPON A q-DEFORMATION DESCRIPTION

2005 ◽  
Vol 20 (26) ◽  
pp. 6039-6049 ◽  
Author(s):  
XIN ZHANG
Keyword(s):  
Black Hole ◽  
Degrees Of Freedom ◽  
Radiation Spectrum ◽  
Correlation Effect ◽  
Space Time ◽  
Noncommutative Space ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation ◽  
Starting Point ◽  
New Distribution

A toy model based upon the q-deformation description for studying the radiation spectrum of black hole is proposed. The starting point is to make an attempt to consider the space–time noncommutativity in the vicinity of black hole horizon. We use a trick that all the space–time noncommutative effects are ascribed to the modification of the behavior of the radiation field of black hole and a kind of q-deformed degrees of freedom are postulated to mimic the radiation particles that live on the noncommutative space–time, meanwhile the background metric is preserved as usual. We calculate the radiation spectrum of Schwarzschild black hole in this framework. The new distribution deviates from the standard thermal spectrum evidently. The result indicates that some correlation effect will be introduced to the system if the noncommutativity is taken into account. In addition, an infrared cutoff of the spectrum is the prediction of the model.

scholarly journals BOUND OF NONCOMMUTATIVITY PARAMETER BASED ON BLACK HOLE ENTROPY

2010 ◽  
Vol 25 (38) ◽  
pp. 3213-3218 ◽  
Author(s):  
WONTAE KIM ◽  
DAEHO LEE
Keyword(s):  
Black Hole ◽  
Gauge Group ◽  
Black Hole Entropy ◽  
Brick Wall ◽  
Statistical Entropy ◽  
Schwarzschild Black Hole ◽  
Cutoff Parameter ◽  
Entropy Satisfying ◽  
Area Law ◽  
Wall Method

We study the bound of the noncommutativity parameter in the noncommutative Schwarzschild black hole which is a solution of the noncommutative ISO(3, 1) Poincaré gauge group. The statistical entropy satisfying the area law in the brick wall method yields a cutoff relation which depends on the noncommutativity parameter. Requiring both the cutoff parameter and the noncommutativity parameter to be real, the noncommutativity parameter can be shown to be bounded as Θ > 8.4 × 10-2lp.

scholarly journals A quantum model of Schwarzschild black hole evaporation

1997 ◽  
Vol 395 (3-4) ◽  
pp. 184-190 ◽  
Author(s):  
J. Cruz ◽  
A. Miković ◽  
J. Navarro-Salas
Keyword(s):  
Black Hole ◽  
Quantum Model ◽  
Schwarzschild Black Hole ◽  
Black Hole Evaporation

scholarly journals Black hole entropy sourced by string winding condensate

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Ram Brustein ◽  
Yoav Zigdon
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Effective Field Theory ◽  
Thermal Cycle ◽  
Black Hole Entropy ◽  
Effective Field ◽  
Schwarzschild Black Hole ◽  
Asymptotically Linear ◽  
Linear Dilaton ◽  
Linear Dilaton Black Hole

Abstract We calculate the entropy of an asymptotically Schwarzschild black hole, using an effective field theory of winding modes in type II string theory. In Euclidean signature, the geometry of the black hole contains a thermal cycle which shrinks towards the horizon. The light excitations thus include, in addition to the metric and the dilaton, also the winding modes around this cycle. The winding modes condense in the near-horizon region and source the geometry of the thermal cycle. Using the effective field theory action and standard thermodynamic relations, we show that the entropy, which is also sourced by the winding modes condensate, is exactly equal to the Bekenstein-Hawking entropy of the black hole. We then discuss some properties of the winding mode condensate and end with an application of our method to an asymptotically linear-dilaton black hole.

scholarly journals ON TIME-DEPENDENT BLACK HOLES AND COSMOLOGICAL MODELS FROM A KALUZA–KLEIN MECHANISM

2009 ◽  
Vol 24 (07) ◽  
pp. 1383-1415
Author(s):  
C. CASTRO ◽  
J. A. NIETO ◽  
L. RUIZ ◽  
J. SILVAS
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Cosmological Model ◽  
Black Hole Entropy ◽  
Time Dependent ◽  
Einstein Field Equations ◽  
Schwarzschild Black Hole ◽  
Field Equations ◽  
Newman Black Hole ◽  
Kaluza Klein

Novel static, time-dependent and spatial–temporal solutions to Einstein field equations, displaying singularities, with and without horizons, and in several dimensions, are found based on a dimensional reduction procedure widely used in Kaluza–Klein-type theories. The Kerr–Newman black hole entropy as well as the Reissner–Nordstrom, Kerr and Schwarzschild black hole entropy are derived from the corresponding Euclideanized actions. A very special cosmological model based on the dynamical interior geometry of a black hole is found that has no singularities at t = 0 due to the smoothing of the mass distribution. We conclude with another cosmological model equipped also with a dynamical horizon and which is related to Vaidya's metric (associated with the Hawking radiation of black holes) by interchanging t ↔ r, which might render our universe a dynamical black hole.

The Wheeler–Dewitt Equation for the Superstring World Sheet

1997 ◽  
Vol 06 (01) ◽  
pp. 91-105 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Black Hole ◽  
Ground State ◽  
Total Mass ◽  
Equation Of Motion ◽  
Schwarzschild Black Hole ◽  
World Sheet ◽  
Integral Expression ◽  
Higher Derivative ◽  
The World ◽  
The Universe

The Wheeler–DeWitt equation for the wave function ψ is obtained from the two-dimensional world-sheet action for the bosonic string and the superstring, including higher-derivative terms, as the Schrödinger equation i ∂ ψ/ ∂τ = V(τ)ψ. The potential is given by the rate at which the world-sheet area is swept out, V(τ) = dA(τ)/dτ, and is positive semi-definite, allowing the existence of a ground state, corresponding to the absence of the string, with a non-vanishing probability density ψ ψ*. Integration of this equation yields the solution [Formula: see text], where [Formula: see text] is the action, minus the higher-derivative terms [Formula: see text] (and terms involving ∊ab in the case of the superstring), which, however, are constrained to vanish semi-classically, being constructed from the square of the equation of motion for the bosonic coordinates XA derived from [Formula: see text] alone. This path-integral expression for ψ is consistent with the operator replacements for the canonical momenta used in its derivation, and forms the basis of the approach due to Polyakov of summing over random surfaces. Comparison is made with the Schrödinger equations derived previously from the reduced, four-dimensional effective action for the heterotic superstring, and for the Schwarzschild black hole (by Tomimatsu), where the potential is also positive semi-definite, being (twice) the total mass of the Universe and the mass of the black hole, respectively, showing the unity of the method.

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