Massive spin-2 fields on black hole spacetimes: Instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass (1304.6725v3)

Abstract: Massive bosonic fields of arbitrary spin are predicted by general extensions of the Standard Model. It has been recently shown that there exists a family of bimetric theories of gravity - including massive gravity - which are free of Boulware-Deser ghosts at the nonlinear level. This opens up the possibility to describe consistently the dynamics of massive spin-2 particles in a gravitational field. Within this context, we develop the study of massive spin-2 fluctuations - including massive gravitons - around Schwarzschild and slowly-rotating Kerr black holes. Our work has two important outcomes. First, we show that the Schwarzschild geometry is linearly unstable for small tensor masses, against a spherically symmetric mode. Second, we provide solid evidence that the Kerr geometry is also generically unstable, both against the spherical mode and against long-lived superradiant modes. In the absence of nonlinear effects, the observation of spinning black holes bounds the graviton mass to be smaller than 5x10^{-23} eV.

• The paper finds that Schwarzschild black holes are linearly unstable to small spin-2 field masses, similar to the Gregory-Laflamme instability.
• It demonstrates that Kerr black holes exhibit superradiant instabilities, with simulations constraining the graviton mass to about 5×10⁻²³ eV.
• These results provide critical tests for massive gravity theories and offer new insights into black hole dynamics and observational constraints.

Analysis of Massive Spin-2 Fields on Black Hole Spacetimes

The paper "Massive Spin-2 Fields on Black Hole Spacetimes: Instability of the Schwarzschild and Kerr Solutions and Bounds on the Graviton Mass" explores the dynamics and stability of massive spin-2 fields, such as massive gravitons, in the context of Schwarzschild and Kerr black holes. The paper focuses on the implications of nonlinear massive gravity and bimetric theories on black hole stability and provides insights into how massive bosonic fields could influence black hole behavior and astrophysical observations.

Primary Outcomes and Numerical Findings

The paper presents two significant findings regarding linearized perturbations of massive spin-2 fields on black hole backgrounds. First, Schwarzschild black holes are shown to be linearly unstable to small tensor masses, specifically against a spherical mode. This instability resembles the well-known Gregory-Laflamme instability, typically observed in higher-dimensional black string spacetimes. The analytical results of the paper predict that these instabilities occur for small graviton masses, signaling potential challenges in black hole modeling within massive gravity theories.

Second, the paper demonstrates evidence of generic instabilities in Kerr geometries, mainly due to long-lived superradiant modes. Numerical simulations estimate that spinning black holes impose a constraint on the graviton mass, with $\mu \lesssim 5 \times 10^{-23} {\rm eV}$. Detailed calculations show that massive spin-2 fields exhibit the strongest superradiant instability among all bosonic fields studied so far, significantly impacting the rotational dynamics of black holes.

Theoretical and Practical Implications

The paper of massive spin-2 fields on black holes is particularly relevant for massive gravity scenarios and extensions of the Standard Model that predict ultralight bosonic fields. In massive gravity theories, additional spin-2 degrees of freedom could alter the gravitational response and perturbations around compact astrophysical objects, potentially offering new opportunities to test these theories using observational data from high-energy astrophysical phenomena.

The instability of Schwarzschild black holes suggests that nonlinear interactions within massive gravity could lead to rich dynamical outcomes, potentially forming graviton clouds around black holes. Furthermore, the observed strength of superradiant instabilities for rotating black holes indicates that massive bosonic fields might significantly limit the observed spins of black holes, thus providing novel methods for constraining boson masses and testing the limitations of general relativity.

Future Developments

The results advocate for further exploration into the nonlinear development of these instabilities, both for monopole and superradiant cases, which could be achieved through advanced numerical relativity techniques. Investigating the time development and end-states of these instabilities may reveal more about their physical consequences and potential observational signatures. Moreover, extending the analysis to full numerical relativity approaches could help to address complexities beyond the linear regime, offering deeper insights into massive gravity's impact on black hole dynamics.

Continued refinement of massive gravity theories is essential to reconcile these results with observational constraints. Precisely understanding the role of massive gravitons and scalar-tensor couplings in black hole environments may provide essential clues in validating or challenging these theoretical frameworks.

In summary, this paper provides compelling evidence that massive spin-2 fields significantly impact black hole dynamics and constrain graviton masses. These findings are crucial as astrophysical observations progress and theoretical models of gravity evolve.