Local first law of black hole

We investigated the form and implications of the local first law of black hole thermodynamics in relation to an observer located at a finite distance from the black hole horizon. Our study is based on the quasilocal form of the first law for black hole thermodynamics, given by

\delta {\textsf{E}}=\frac{{\bar{\kappa }}}{8\pi }\delta A

, where

\delta {\textsf{E}}

and

\delta A

represent the changes in the black hole mass and area, respectively, and

{\bar{\kappa }}

denotes the quasilocal surface gravity. We show that even at a finite distance, the quasilocal law still holds. It shows how the first law scales with the observer’s location.

Black holes
Thermodynamics
First law
black hole: thermodynamics
gravitation: surface
black hole: mass
black hole: horizon

References(18)

Figures(2)

[1]

Particle Creation by Black Holes

S.W. Hawking
(
- Cambridge U., DAMTP and
- Caltech
)

- Commun.Math.Phys. 43 (1975) 199-220,
- Commun.Math.Phys. 46 (1976) 206 (erratum),
•
DOI:
- 10.1007/BF02345020

[1]

Particle Creation by Black Holes

S.W. Hawking
(
- Cambridge U., DAMTP and
- Caltech
)

- Commun.Math.Phys. 43 (1975) 199-220,
- Commun.Math.Phys. 46 (1976) 206 (erratum),
•
DOI:
- 10.1007/BF02345020

[2]

Microscopic origin of the Bekenstein-Hawking entropy

Andrew Strominger
(
- UC, Santa Barbara
)
,
Cumrun Vafa
(
- Harvard U.
)

- Phys.Lett.B 379 (1996) 99-104
•
e-Print:
- hep-th/9601029
•
DOI:
- 10.1016/0370-2693(96)00345-0

[3]

Quantum geometry and black hole entropy

A. Ashtekar
(
- Penn State U.
)
,
J. Baez
(
- UC, Riverside
)
,
A. Corichi
(
- Penn State U. and
- Mexico U., ICN
)
,
Kirill Krasnov
(
- Penn State U.
)

- Phys.Rev.Lett. 80 (1998) 904-907
•
e-Print:
- gr-qc/9710007
•
DOI:
- 10.1103/PhysRevLett.80.904

Information is Not Lost in the Evaporation of 2-dimensional Black Holes

Abhay Ashtekar
(
- Penn State U. and
- Raman Research Inst., Bangalore
)
,
Victor Taveras
(
- Penn State U.
)
,
Madhavan Varadarajan
(
- Raman Research Inst., Bangalore and
- Penn State U.
)

- Phys.Rev.Lett. 100 (2008) 211302
•
e-Print:
- 0801.1811
•
DOI:
- 10.1103/PhysRevLett.100.211302

Isolated horizons: Hamiltonian evolution and the first law

Abhay Ashtekar
(
- Penn State U. and
- Santa Barbara, KITP
)
,
Stephen Fairhurst
(
- Penn State U.
)
,
Badri Krishnan
(
- Penn State U.
)

- Phys.Rev.D 62 (2000) 104025
•
e-Print:
- gr-qc/0005083
•
DOI:
- 10.1103/PhysRevD.62.104025

Quasilocal first law for black hole thermodynamics

Ernesto Frodden
(
- Chile U., Catolica and
- Marseille, CPT
)
,
Amit Ghosh
(
- Saha Inst.
)
,
Alejandro Perez
(
- Marseille, CPT
)

- Phys.Rev.D 87 (2013) 12, 121503
•
e-Print:
- 1110.4055
•
DOI:
- 10.1103/PhysRevD.87.121503

[7]

The Four laws of black hole mechanics

- Commun.Math.Phys. 31 (1973) 161-170
•
DOI:
- 10.1007/BF01645742

[8]

General Relativity

Robert M. Wald
(
- Chicago U., EFI
)

DOI:
- 10.7208/chicago/9780226870373.001.0001

Quasilocal first law for black hole thermodynamics

Ernesto Frodden
(
- Chile U., Catolica and
- Marseille, CPT
)
,
Amit Ghosh
(
- Saha Inst.
)
,
Alejandro Perez
(
- Marseille, CPT
)

- Phys.Rev.D 87 (2013) 12, 121503
•
e-Print:
- 1110.4055
•
DOI:
- 10.1103/PhysRevD.87.121503

[10]

On the LambertW function

- Adv.Comput.Math. 5 (1996) 329-359
•
DOI:
- 10.1007/BF02124750

[11]

A Relativist's Toolkit: The Mathematics of Black-Hole Mechanics

E. Poisson

[12]

The Large N limit of superconformal field theories and supergravity

Juan Martin Maldacena
(
- Harvard U.
)

- Int.J.Theor.Phys. 38 (1999) 1113-1133 (reprint),
- Adv.Theor.Math.Phys. 2 (1998) 231-252
•
e-Print:
- hep-th/9711200
•
DOI:
- 10.4310/ATMP.1998.v2.n2.a1

[13]

Gauge/gravity duality : Foundations and applications

•
DOI:
- 10.1017/CBO9780511846373

Quantum Gravity Partition Functions in Three Dimensions

- JHEP 02 (2010) 029
•
e-Print:
- 0712.0155
•
DOI:
- 10.1007/JHEP02(2010)029

Island, Page curve, and superradiance of rotating BTZ black holes

- Phys.Rev.D 105 (2022) 6, 066009
•
e-Print:
- 2112.14361
•
DOI:
- 10.1103/PhysRevD.105.066009

[16]

The Black hole in three-dimensional space-time

Maximo Banados
(
- CECS, Valdivia and
- Chile U., Santiago
)
,
Claudio Teitelboim
(
)
,
Jorge Zanelli
(
- CECS, Valdivia and
- Chile U., Santiago
)

- Phys.Rev.Lett. 69 (1992) 1849-1851
•
e-Print:
- hep-th/9204099
•
DOI:
- 10.1103/PhysRevLett.69.1849

[17]

The (2+1)-Dimensional black hole

Steven Carlip
(
- UC, Davis
)

- Class.Quant.Grav. 12 (1995) 2853-2880
•
e-Print:
- gr-qc/9506079
•
DOI:
- 10.1088/0264-9381/12/12/005