Gravitational Tension, Spacetime Pressure and Black Hole Volume

Abstract

We study the first law of black hole thermodynamics in the presence of surrounding gravitational fields and argue that variations of these fields are naturally incorporated in the first law by defining gravitational tension or gravitational binding energy. We demonstrate that this notion can also be applied in Anti-de Sitter spacetime, in which the surrounding gravitational field is sourced by a cosmological fluid, therefore showing that spacetime volume and gravitational tension encode the same physics as spacetime pressure and black hole volume. We furthermore show that it is possible to introduce a definition of spacetime pressure and black hole volume for any spacetime with characteristic length scales which does not necessarily require a cosmological constant sourcing Einstein equations. However, we show that black hole volume is non-universal in the flat spacetime limit, questioning its significance. We illustrate these ideas by studying the resulting black hole volume of Kaluza-Klein black holes and of a toy model for a black hole binary system in five spacetime dimensions (the black saturn solution) as well as of several novel perturbative black hole solutions. These include the higher-dimensional Kerr-Newman solution in Anti-de Sitter spacetime as well as other black holes in plane wave and Lifshitz spacetimes.

v3: 42pp, improved discussion in section 6, to be published in JHEP

References in corpus (10)

• Instabilities of Black Strings and Branes
• Bicycling Black Rings
• Mechanical First Law of Black Hole Spacetimes with Cosmological Constant and Its Application to Schwarzschild-de Sitter Spacetime
• Holographic Black Hole Chemistry
• Black holes and Boyle's law -- the thermodynamics of the cosmological constant
• Orthogonal black di-ring solution
• Phases of Five-Dimensional Black Holes
• Black Rings in Taub-NUT and D0-D6 interactions
• Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
• Constraints on the effective fluid theory of stationary branes

Cited by in corpus (12)

• Black hole chemistry: thermodynamics with Lambda
• Higher-dimensional origin of extended black hole thermodynamics
• Hyperscaling violating black holes with spherical and hyperbolic horizons
• Holographic entanglement chemistry
• On the throttling process of the Kerr-Newman-anti-de Sitter black holes in the extended phase space
• Forced Fluid Dynamics from Blackfolds in General Supergravity Backgrounds
• Extremal Black Hole Horizons
• Critical behaviour of Lifshitz dilaton black holes
• Stationary Solutions from the Large D Membrane Paradigm
• Instabilities of Thin Black Rings: Closing the Gap
• Holographic duals of the $\mathcal{N}=1$* gauge theory
• New asymptotically (Anti)-de Sitter black holes in (super)gravity