scholarly journals Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Alexis Larrañaga ◽  
Natalia Herrera ◽  
Juliana Garcia
Keyword(s):  
Heat Capacity ◽  
Black Hole ◽  
Phase Transitions ◽  
Equilibrium States ◽  
Geometric Description ◽  
Curvature Scalar ◽  
Schwarzschild Black Hole ◽  
Thermodynamic Interaction

The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

scholarly journals BLACK HOLE THERMODYNAMICS AND MODIFIED GUP CONSISTENT WITH DOUBLY SPECIAL RELATIVITY

2012 ◽  
Vol 27 (39) ◽  
pp. 1250227 ◽  
Author(s):  
K. ZEYNALI ◽  
F. DARABI ◽  
H. MOTAVALLI
Keyword(s):  
Heat Capacity ◽  
Black Hole ◽  
Special Relativity ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Black Hole Thermodynamics ◽  
Schwarzschild Black Hole ◽  
Commutation Relations ◽  
Doubly Special Relativity ◽  
Correction Terms

We study the black hole thermodynamics and obtain the correction terms for temperature, entropy, and heat capacity of the Schwarzschild black hole, resulting from the commutation relations in the framework of Modified Generalized Uncertainty Principle suggested by Doubly Special Relativity.

Dyonic and Magnetic Black Holes with Rational Nonlinear Electrodynamics

2020 ◽  
Author(s):  
Sergey Kruglov
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Free Energy ◽  
Phase Transitions ◽  
Helmholtz Free Energy ◽  
Magnetic Charge ◽  
The Self ◽  
Nonlinear Electrodynamics ◽  
Dual Case

The principles of causality and unitarity are studied within rational nonlinear electrodynamics proposed earlier. We investigate dyonic and magnetized black holes and show that in the self-dual case, when the electric charge equals the magnetic charge, corrections to Coulomb's law and Reissner-Nordstrom solutions are absent. In the case of the magnetic black hole, the Hawking temperature, the heat capacity and the Helmholtz free energy are calculated. It is shown that there are second-order phase transitions and it was demonstrated that at some range of parameters the black holes are stable.

scholarly journals MICROSCOPIC BLACK HOLE AND UNCERTAINTY PRINCIPLE WITH MINIMAL LENGTH AND MOMENTUM

2013 ◽  
Vol 28 (10) ◽  
pp. 1350029 ◽  
Author(s):  
M. M. STETSKO
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Emission Rate ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Schwarzschild Black Hole ◽  
Evaporation Time ◽  
Thermodynamical Functions

We investigate a microscopic black hole in the case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that the incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole. Minimal temperature gives rise to appearance of a phase transition. Emission rate equation and black hole's evaporation time are also obtained.

scholarly journals 4D Einstein-Gauss-Bonnet Gravity Coupled with Nonlinear Electrodynamics

2020 ◽  
Author(s):  
Sergey Kruglov
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Phase Transitions ◽  
Black Hole Solution ◽  
Hawking Temperature ◽  
Nonlinear Electrodynamics ◽  
Nonlinearity Parameter ◽  
Spherically Symmetric ◽  
Bonnet Gravity

An exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled to nonlinear electrodynamics (NED) is obtained. The NED Lagrangian is given by ${\cal L}_{NED} = -{\cal F}/(1+\sqrt[4]{2\beta{\cal F}})$, where ${\cal F}$ is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radii are calculated. It is shown that when increasing the nonlinearity parameter $\beta$ the BH shadow radius is decreased.

scholarly journals Maxwell’s Equal Area Law and the Hawking-Page Phase Transition

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Euro Spallucci ◽  
Anais Smailagic
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Black Hole ◽  
Critical Temperature ◽  
Equation Of State ◽  
Schwarzschild Black Hole ◽  
Pure Radiation ◽  
Equal Area ◽  
Gravity Duality ◽  
Area Law

We study the phases of a Schwarzschild black hole in the Anti-deSitter background geometry. Exploiting fluid/gravity duality, we construct the Maxwell equal area isotherm   in the temperature-entropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable BHs are formed at the temperature , while pure radiation persists for . turns out to be below the standard Hawking-Page temperature and there are no unstable BHs as in the usual scenario. Also, we show that, in order to reproduce the correct BH entropy , one has to write a black hole equation of state, that is, , in terms of the geometrical volume .

The geometry of the trajectories

2020 ◽  
Vol 17 (04) ◽  
pp. 2050051
Author(s):  
Mohammadreza Molaei
Keyword(s):  
Black Hole ◽  
Vector Field ◽  
Vector Fields ◽  
Second Step ◽  
Curvature Scalar ◽  
Schwarzschild Black Hole ◽  
Integral Curves ◽  
Trajectory Manifold

In this paper, we use of the geometry of a class of the nature flows to define trajectory manifolds. Trajectory connections as a generalization of the Levi-Civita connections are considered. A method for determining the geometry of the flows created by the integral curves of a vector field is presented. The method contains two steps, the first step is finding the connection by the trajectories of a vector field, and the second step is finding a trajectory metric corresponding to the deduced connection. We show that doing the first step is possible, but for some of the vector fields, the second step may not be possible. In the case of existence of a trajectory manifold a new kind of curvature which we called it “trajectory curvature scalar” appears. We calculate trajectory connections for some vector fields and by an example we show that the trajectory curvature scalar for a trajectory manifold may not be equal to the curvature scalar of it. We find trajectory connection for a vector field close to the Schwarzschild black hole.

scholarly journals Thermodynamic Relations for Kiselev and Dilaton Black Hole

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Bushra Majeed ◽  
Mubasher Jamil ◽  
Parthapratim Pradhan
Keyword(s):  
Phase Transition ◽  
Black Holes ◽  
Black Hole ◽  
Phase Transitions ◽  
Surface Temperature ◽  
Schwarzschild Black Hole ◽  
Event Horizons ◽  
First Law Of Thermodynamics ◽  
Special Cases ◽  
Dilaton Black Hole

We investigate the thermodynamics and phase transition for Kiselev black hole and dilaton black hole. Specifically we consider Reissner-Nordström black hole surrounded by radiation and dust and Schwarzschild black hole surrounded by quintessence, as special cases of Kiselev solution. We have calculated the products relating the surface gravities, surface temperatures, Komar energies, areas, entropies, horizon radii, and the irreducible masses at the Cauchy and the event horizons. It is observed that the product of surface gravities, product of surface temperature, and product of Komar energies at the horizons are not universal quantities for the Kiselev solutions while products of areas and entropies at both the horizons are independent of mass of the above-mentioned black holes (except for Schwarzschild black hole surrounded by quintessence). For charged dilaton black hole, all the products vanish. The first law of thermodynamics is also verified for Kiselev solutions. Heat capacities are calculated and phase transitions are observed, under certain conditions.

Revisit on the thermodynamic stability of the noncommutative Schwarzschild black hole

2017 ◽  
Vol 26 (03) ◽  
pp. 1750018 ◽  
Author(s):  
Meng-Sen Ma ◽  
Yan-Song Liu ◽  
Huai-Fan Li
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Thermodynamic Stability ◽  
Black Hole Thermodynamics ◽  
Positive Temperature ◽  
Schwarzschild Black Hole ◽  
Horizon Thermodynamics ◽  
Thermodynamics Of Black Holes ◽  
Thermodynamic Curvature

In two frameworks, we discuss the thermodynamic stability of noncommutative geometry inspired Schwarzschild black hole (NCSBH). Under the horizon thermodynamics of black holes, we show that the NCSBH cannot be thermodynamically stable if requiring positive temperature. We note the inconsistency in the work of Larrañaga et al. and propose an effective first law of black hole thermodynamics for the NCSBH to eliminate the inconsistency. Based on the effective first law, we recalculate the heat capacity and the thermodynamic curvature by means of geometrothermodynamics (GTD) to revisit the thermodynamic stability.

scholarly journals Legendre Invariance and Geometrothermodynamics Description of the 3D Charged-Dilaton Black Hole

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yiwen Han ◽  
XiaoXiong Zeng
Keyword(s):  
Black Hole ◽  
Phase Transitions ◽  
Information Geometry ◽  
Heat Capacities ◽  
Equilibrium States ◽  
Dilaton Black Hole

We first review Weinhold information geometry and Ruppeiner information geometry of 3D charged-dilaton black hole. Then, we use the Legendre invariant to introduce a 2-dimensional thermodynamic metric in the space of equilibrium states, which becomes singular at those points. According to the analysis of the heat capacities, these points are the places where phase transitions occur. This result is valid for the black hole, therefore, provides a geometrothermodynamics description of black hole phase transitions in terms of curvature singularities.

scholarly journals Nonsingular Model of Magnetized Black Hole Based on Nonlinear Electrodynamics

2019 ◽  
Author(s):  
Sergey I. Kruglov
Keyword(s):  
Black Holes ◽  
Heat Capacity ◽  
Black Hole ◽  
Phase Transitions ◽  
Naked Singularity ◽  
Hawking Temperature ◽  
Nonlinear Electrodynamics ◽  
Modified Theory Of Gravity ◽  
Thermodynamics Of Black Holes ◽  
Modified Theory

We find solutions of a magnetically charged non-singular black hole in some modified theory of gravity coupled with nonlinear electrodynamics. The metric of a magnetized black hole is obtained which has one (an extreme horizon), two horizons, or no horizons (naked singularity). Corrections to the Reissner-Nordstrom solution are found as the radius approaches to infinity. The asymptotic of the Ricci and Kretschmann scalars are calculated showing the absence of singularities. We study the thermodynamics of black holes by calculating the Hawking temperature and the heat capacity. It is demonstrated that phase transitions take place and we show that black holes are thermodynamically stable at some range of parameters.

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