- Open Access
Causal structure of higher curvature gravity
Phys. Rev. D 112, 024063 – Published 28 July, 2025
DOI: https://doi.org/10.1103/pzdl-crjb
Abstract
In this paper, we analyze the causal structure of generalized quadratic gravity (GQG) and Einsteinian cubic gravity (ECG). It is well known that gravitons in higher-curvature theories can exhibit superluminal propagation, rendering the conventional definition of causal structures based on null curves inadequate. Instead, the causal structure must be defined using the fastest propagating modes, which travel along characteristic surfaces. The superluminal propagation in higher-curvature theories has significant implications for black holes. Specifically, if the Killing horizon of a black hole is not a characteristic surface corresponding to the fastest propagating mode, the horizon can no longer function as a causal barrier. Our analysis demonstrates that GQG with a genuine fourth-order equation of motion possesses only null characteristics, implying that the horizon is a characteristic surface. Furthermore, we perform a detailed characteristic analysis of ECG. We show that while all null surfaces are characteristic surfaces in ECG, the converse is not true—there exist non-null characteristic surfaces. In particular, we identify a non-null characteristic surface in a Type N spacetime in the algebraic classification of spacetimes. Despite the existence of multiple characteristic surfaces in ECG, we establish that the black hole horizon remains a characteristic surface.
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References (22)
- C. M. Will, The confrontation between general relativity and experiment, Living Rev. Relativity 17, 4 (2014).
- H. Reall, N. Tanahashi, and B. Way, Causality and hyperbolicity of Lovelock theories, Classical Quantum Gravity 31, 205005 (2014).
- N. Tanahashi, H. S. Reall, and B. Way, Causality, hyperbolicity and shock formation in Lovelock theories, in Proceedings of the Second LeCosPA International Symposium: Everything about Gravity, edited by Pisin Chen (World Scientific, Singapore, 2017), pp. 380–385, 10.1142/9789813203952_0050.
- K. Izumi, Causal structures in Gauss-Bonnet gravity, Phys. Rev. D 90, 044037 (2014).
- K. Hajian, S. Liberati, M. M. Sheikh-Jabbari, and M. H. Vahidinia, On black hole temperature in Horndeski gravity, Phys. Lett. B 812, 136002 (2020).
- C. Deffayet, A. Held, S. Mukohyama, and A. Vikman, Global and local stability for ghosts coupled to positive energy degrees of freedom, J. Cosmol. Astropart. Phys. 11 (2023) 031.
- A. Held and H. Lim, Nonlinear evolution of quadratic gravity in dimensions, Phys. Rev. D 108, 104025 (2023).
- D. R. Noakes, The initial value formulation of higher derivative gravity, J. Math. Phys. (N.Y.) 24, 1846 (1983).
- X. O. Camanho, J. D. Edelstein, J. Maldacena, and A. Zhiboedov, Causality constraints on corrections to the graviton three-point coupling, J. High Energy Phys. 02 (2016) 020.
- J. D. Edelstein, R. Ghosh, A. Laddha, and S. Sarkar, Causality constraints in quadratic gravity, J. High Energy Phys. 09 (2021) 150.
- J. D. Edelstein, R. Ghosh, A. Laddha, and S. Sarkar, Restoring causality in higher curvature gravity, arXiv:2409.16935.
- K. Benakli, S. Chapman, L. Darmé, and Y. Oz, Superluminal graviton propagation, Phys. Rev. D 94, 084026 (2016).
- H. S. Reall, Causality in gravitational theories with second order equations of motion, Phys. Rev. D 103, 084027 (2021).
- P. Bueno and P. A. Cano, Einsteinian cubic gravity, Phys. Rev. D 94, 104005 (2016).
- R. A. Hennigar and R. B. Mann, Black holes in Einsteinian cubic gravity, Phys. Rev. D 95, 064055 (2017).
- A. De Felice and S. Tsujikawa, Excluding static and spherically symmetric black holes in Einsteinian cubic gravity with unsuppressed higher-order curvature terms, Phys. Lett. B 843, 138047 (2023).
- P. Bueno, P. A. Cano, and R. A. Hennigar, On the stability of Einsteinian cubic gravity black holes in EFT, Classical Quantum Gravity 41, 137001 (2024).
- P. A. Cano Molina-Niñirola, Higher-curvature gravity, black holes and holography, arXiv:1912.07035.
- M. Durkee, V. Pravda, A. Pravdova, and H. S. Reall, Generalization of the Geroch-Held-Penrose formalism to higher dimensions, Classical Quantum Gravity 27, 215010 (2010).
- V. Pravda, On the algebraic classification of spacetimes, J. Phys. Conf. Ser. 33, 463 (2006).
- S. Deser and B. Tekin, Energy in generic higher curvature gravity theories, Phys. Rev. D 67, 084009 (2003).
- E. Gesteau and H. Liu, Toward stringy horizons, arXiv:2408.12642.
