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#### Noether charge formalism for Weyl transverse gravity

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##### Citation

Alonso-Serrano, A., Garay, L. J., & Liška, M. (2023). Noether charge formalism
for Weyl transverse gravity.* Classical and quantum gravity,* *40*(2):
025012. doi:10.1088/1361-6382/acace3.

Cite as: https://hdl.handle.net/21.11116/0000-000A-6FDF-0

##### Abstract

Weyl transverse gravity is a gravitational theory that is invariant under

transverse diffeomorphisms and Weyl transformations. It is characterised by

having the same classical solutions as general relativity while solving some of

its issues with the cosmological constant. In this work, we first find the

Noether currents and charges corresponding to local symmetries of Weyl

transverse gravity as well as a prescription for the symplectic form. We then

employ these results to derive the first law of black hole mechanics in Weyl

transverse gravity (both in vacuum and in the presence of a perfect fluid),

identifying the total energy, the total angular momentum, and the Wald entropy

of black holes. We further obtain the first law and Smarr formula for

Schwarzschild-anti-de Sitter and pure de Sitter spacetimes, discussing the

contributions of the varying cosmological constant, which naturally appear in

Weyl transverse gravity. Lastly, we derive the first law of causal diamonds in

vacuum.

transverse diffeomorphisms and Weyl transformations. It is characterised by

having the same classical solutions as general relativity while solving some of

its issues with the cosmological constant. In this work, we first find the

Noether currents and charges corresponding to local symmetries of Weyl

transverse gravity as well as a prescription for the symplectic form. We then

employ these results to derive the first law of black hole mechanics in Weyl

transverse gravity (both in vacuum and in the presence of a perfect fluid),

identifying the total energy, the total angular momentum, and the Wald entropy

of black holes. We further obtain the first law and Smarr formula for

Schwarzschild-anti-de Sitter and pure de Sitter spacetimes, discussing the

contributions of the varying cosmological constant, which naturally appear in

Weyl transverse gravity. Lastly, we derive the first law of causal diamonds in

vacuum.