Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime

Abstract

The mechanical first law (MFL) of black hole spacetimes is a geometrical relation which relates variations of mass parameter and horizon area. While it is well known that the MFL of asymptotic flat black hole is equivalent to its thermodynamical first law, however we do not know the detail of MFL of black hole spacetimes with cosmological constant which possess black hole and cosmological event horizons. Then this paper aims to formulate an MFL of the two-horizon spacetimes. For this purpose, we try to include the effects of two horizons in the MFL. To do so, we make use of the Iyer-Wald formalism and extend it to regard the mass parameter and the cosmological constant as two independent variables which make it possible to treat the two horizons on the same footing. Our extended Iyer-Wald formalism preserves the existence of conserved Noether current and its associated Noether charge, and gives the abstract form of MFL of black hole spacetimes with cosmological constant. Then, as a representative application of that formalism, we derive the MFL of Schwarzschild-de Sitter (SdS) spacetime. Our MFL of SdS spacetime relates the variations of three quantities; the mass parameter, the total area of two horizons and the volume enclosed by two horizons. If our MFL is regarded as a thermodynamical first law of SdS spacetime, it offers a thermodynamically consistent description of SdS black hole evaporation process: The mass decreases while the volume and the entropy increase. In our suggestion, the generalized second law is not needed to ensure the second law of SdS thermodynamics for its evaporation process.

arXiv commentAccepted for publication in Classical and Quantum Gravity, 16 pages, no figure

References in corpus (14)

• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Mass, Entropy and Holography in Asymptotically de Sitter Spaces
• Duality between Electric and Magnetic Black Holes
• Thermodynamics of de Sitter Black Holes: Thermal Cosmological Constant
• Proof of Classical Versions of the Bousso Entropy Bound and of the Generalized Second Law
• Action, Mass and Entropy of Schwarzschild-de Sitter black holes and the de Sitter/CFT Correspondence
• Proof of the Generalized Second Law for Quasistationary Semiclassical Black Holes
• de Sitter Black Holes with Either of the Two Horizons as a Boundary
• Gluon Distribution Functions in the kT-factorization Approach
• Black Holes in de Sitter Space: Masses, Energies and Entropy Bounds
• Two-temperature Steady State Thermodynamics for a Radiation Field
• The generalised second law and the black hole evaporation in an empty space as a nonequilibrium process
• Black Hole Evaporation as a Nonequilibrium Process

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