Smarr formula for black holes with primary and secondary scalar hair
arXiv:2505.02368 · doi:10.1103/qv3n-r8q9
Abstract
In this work, we revisit the thermodynamics of black holes endowed with primary and secondary scalar hair in the shift and symmetric subclass of beyond Horndeski gravity. Under a specific fine-tuning of the scalar parameter in terms of the black hole mass, the singular black-hole solution with primary scalar hair reduces to the regular Bardeen solution featuring secondary scalar hair. We first demonstrate that the traditional thermodynamic approach fails to yield a consistent Smarr formula for both solutions under consideration. To address this issue, we adopt the approach introduced in [PhysRevLett. 132 (2024) 19, 191401], and we derive both the first law of black hole thermodynamics and the Smarr formula, offering a consistent thermodynamic description for scalar-hairy black holes. As an additional outcome, our analysis reveals a connection between the solutions with primary and secondary scalar hair.
arXiv comment6 pages
References in corpus (17)
- The Stretched Horizon and Black Hole Complementarity
- The Bardeen Model as a Nonlinear Magnetic Monopole
- Thermodynamical Aspects of Gravity: New insights
- Black holes, gravitational waves and fundamental physics: a roadmap
- Healthy theories beyond Horndeski
- Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
- Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
- Dressing a black hole with a time-dependent Galileon
- Dark Energy and Modified Gravity in Degenerate Higher-Order Scalar-Tensor (DHOST) theories: a review
- Black Hole Thermodynamics
- Asymptotically flat black holes in Horndeski theory and beyond
- Exact black hole solutions in shift symmetric scalar-tensor theories
- Corrected form of the first law of thermodynamics for regular black holes
- Black holes with primary scalar hair
- Coupling Constants as Conserved Charges in Black Hole Thermodynamics
- Compact objects with primary hair in shift and parity symmetric beyond Horndeski gravities
- Thermodynamics of black holes featuring primary scalar hair