### Abstract

We find a (quasi)local first law of thermodynamics, ΔE=TΔS-W, connecting gravitational entropy, S, with matter energy and work. For Einstein gravity, S is the Bekenstein-Hawking entropy, while for general theories of gravity, S is the Wald entropy, evaluated on the stretched future light cone of any point in an arbitrary spacetime, not necessarily containing a black hole. The equation can be written as ρΔV=TΔS-pΔV by regarding the energy-momentum tensor as that of a fluid.

Original language | English (US) |
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Article number | 104043 |

Journal | Physical Review D |

Volume | 101 |

Issue number | 10 |

DOIs | |

State | Published - May 15 2020 |

Externally published | Yes |

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

Parikh, M., Sarkar, S., & Svesko, A. (2020). Local first law of gravity.

*Physical Review D*,*101*(10), [104043]. https://doi.org/10.1103/PhysRevD.101.104043