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Black hole thermodynamics with conical defects

Appels, Michael, Gregory, Ruth, Kubizňák, David·2017·Journal of High Energy Physics
DOI 10.1007/jhep05(2017)116
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Figure 1 Left : The slowly accelerating Rindler spacetime shown here with Aℓ = 1 / 4 , and ℓ = 1 for simplicity. The spatial sections of AdS have been compactified to a Poincaré disc, with the constant r Rindler coordinate indicated in black and constant θ in blue. The origin of the Rindler coordinates is clearly visible as being displaced from the centre of the disc, with the limit of the r -coordinate being the thick dashed black line. Right : The black hole distorts the Poincaré disc with a conical deficit, and is displaced from the origin of AdS. The spacetime is again static, and a cross section is shown.
Figure 1 Left : The slowly accelerating Rindler spacetime shown here with Aℓ = 1 / 4 , and ℓ = 1 for simplicity. The spatial sections of AdS have been compactified to a Poincaré disc, with the constant r Rindler coordinate indicated in black and constant θ in blue. The origin of the Rindler coordinates is clearly visible as being displaced from the centre of the disc, with the limit of the r -coordinate being the thick dashed black line. Right : The black hole distorts the Poincaré disc with a conical deficit, and is displaced from the origin of AdS. The spacetime is again static, and a cross section is shown.CC-BY · From the PDF
Figure 2 A plot of thermodynamic length of the south pole tension for regular north pole, µ + = 0 . The limit of the Schwarzschild-AdS black hole is shown in pink ( µ -= 0 ). The slowly accelerating régime, Aℓ < 1 , is shown as a solid line, and Aℓ > 1 is shown dashed.
Figure 2 A plot of thermodynamic length of the south pole tension for regular north pole, µ + = 0 . The limit of the Schwarzschild-AdS black hole is shown in pink ( µ -= 0 ). The slowly accelerating régime, Aℓ < 1 , is shown as a solid line, and Aℓ > 1 is shown dashed.CC-BY · From the PDF
Figure 3 Left: A plot of temperature as a function of mass (in units of ℓ ) for the uncharged black hole. The slowly accelerating régime is shown as a solid line, and the inferred local horizon temperature for Aℓ > 1 is shown dashed. Note how for larger string tension (hence greater acceleration) the region of positive specific heat increases. Right: A similar plot, but now showing the Gibbs free energy as a function of temperature.
Figure 3 Left: A plot of temperature as a function of mass (in units of ℓ ) for the uncharged black hole. The slowly accelerating régime is shown as a solid line, and the inferred local horizon temperature for Aℓ > 1 is shown dashed. Note how for larger string tension (hence greater acceleration) the region of positive specific heat increases. Right: A similar plot, but now showing the Gibbs free energy as a function of temperature.CC-BY · From the PDF
Figure 4 A plot of temperature as a function of mass for the charged black hole, with fixed Q = 0 . 05 ℓ , and varying tension as labelled. As before, the slowly accelerating régime is shown as a solid line, and Aℓ > 1 is shown dashed.
Figure 4 A plot of temperature as a function of mass for the charged black hole, with fixed Q = 0 . 05 ℓ , and varying tension as labelled. As before, the slowly accelerating régime is shown as a solid line, and Aℓ > 1 is shown dashed.CC-BY · From the PDF
Figure 5 A plot of the free energy as a function of temperature for varying tension with Q = 0 . 05 ℓ on the left, and varying charge with 4 µ -= 0 . 3 on the right.
Figure 5 A plot of the free energy as a function of temperature for varying tension with Q = 0 . 05 ℓ on the left, and varying charge with 4 µ -= 0 . 3 on the right.CC-BY · From the PDF
Figure 6 The coexistence line for the charged black hole shown for varying tension and cosmological constant with the black hole charge is fixed at Q = 0 . 05 . On the left, ℓ = 1 , and the value of tension at the critical point is µ c = 0 . 219 . On the right, 4 µ -= 0 . 3 , and the critical value of the AdS radius is ℓ c = 0 . 36 .
Figure 6 The coexistence line for the charged black hole shown for varying tension and cosmological constant with the black hole charge is fixed at Q = 0 . 05 . On the left, ℓ = 1 , and the value of tension at the critical point is µ c = 0 . 219 . On the right, 4 µ -= 0 . 3 , and the critical value of the AdS radius is ℓ c = 0 . 36 .CC-BY · From the PDF
Figure 7 The Gibbs potential in the grand canonical ensemble as a function of temperature, on the left with 4 µ -= 0 . 3 for varying potential as labelled, and on the right with Φ = 0 . 9 and varying tension as labelled in the plot.
Figure 7 The Gibbs potential in the grand canonical ensemble as a function of temperature, on the left with 4 µ -= 0 . 3 for varying potential as labelled, and on the right with Φ = 0 . 9 and varying tension as labelled in the plot.CC-BY · From the PDF
Figure 8 A plot of the critical value of Φ c ( µ -) at which a black hole is always preferred for all temperatures as a function of the tension.
Figure 8 A plot of the critical value of Φ c ( µ -) at which a black hole is always preferred for all temperatures as a function of the tension.CC-BY · From the PDF

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Citations

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Metadata

Authors
Appels, M., Gregory, R., & Kubizňák, D.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2017-05
Volume
2017
Issue
5
ISSN
1029-8479
DOI
10.1007/jhep05(2017)116
Cited by
80
References
4
Language
en

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