Black Holes In Quadratic Gravity Research Articles

Instability of spherically symmetric black holes in quadratic gravity

We investigate the linear stability of the two known branches of spherically symmetric black holes in quadratic gravity. We extend previous work on the long-wavelength (Gregory-Laflamme) instability of the Schwarzschild branch to a corresponding long-wavelength instability in the non-Schwarzschild branch. In both cases, the instability sets in below a critical horizon radius at which the two black-hole branches intersect. This suggests that classical perturbations enforce a lower bound on the horizon radius of spherically symmetric black holes in quadratic gravity.

Topological black holes in higher derivative gravity

We study static black holes in quadratic gravity with planar and hyperbolic symmetry and non-extremal horizons. We obtain a solution in terms of an infinite power-series expansion around the horizon, which is characterized by two independent integration constants – the black hole radius and the strength of the Bach tensor at the horizon. While in Einstein’s gravity, such black holes require a negative cosmological constant Lambda , in quadratic gravity they can exist for any sign of Lambda and also for Lambda =0. Different branches of Schwarzschild–Bach–(A)dS or purely Bachian black holes are identified which admit distinct Einstein limits. Depending on the curvature of the transverse space and the value of Lambda , these Einstein limits result in (A)dS–Schwarzschild spacetimes with a transverse space of arbitrary curvature (such as black holes and naked singularities) or in Kundt metrics of the (anti-)Nariai type (i.e., dS_2times S^2, AdS_2times H^2, and flat spacetime). In the special case of toroidal black holes with Lambda =0, we also discuss how the Bach parameter needs to be fine-tuned to ensure that the metric does not blow up near infinity and instead matches asymptotically a Ricci-flat solution.

Gravitational waves from inspiraling black holes in quadratic gravity

We perform a study of gravitational waves emitted by inspiraling black holes in the context of quadratic gravity. By linearizing the field equations around a flat background, we demonstrate that all degrees of freedom satisfy wavelike equations. These degrees of freedom split into three modes: a massive spin-2 mode, a massive spin-0 mode, and the expected massless spin-2 mode. We construct the energy-momentum tensor of gravitational waves and show that, due to the massive spin-2 mode, it presents the Ostrogradsky instability. We also show how to deal with this possible pathology and obtain consistent physical interpretations for the system. Using the energy-momentum tensor, we study the influence of each massive mode in the orbital dynamics and compare it with the standard result of general relativity. Moreover, we present two methods to constrain the parameter $\ensuremath{\alpha}$ associated with the massive spin-2 contribution. From the first method, using the combined waveform for the spin-2 modes, we obtain the constraint $\ensuremath{\alpha}\ensuremath{\lesssim}1.1\ifmmode\times\else\texttimes\fi{}{10}^{21}\text{ }\text{ }{\mathrm{m}}^{2}$. In the second method, using the coalescence time, we get the constraint $\ensuremath{\alpha}\ensuremath{\lesssim}1.1\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{ }{\mathrm{m}}^{2}$.

Petrov type, principal null directions, and Killing tensors of slowly rotating black holes in quadratic gravity

The ability to test general relativity in extreme gravity regimes using gravitational wave observations from current ground-based or future space-based detectors motivates the mathematical study of the symmetries of black holes in modified theories of gravity. In this paper we focus on spinning black hole solutions in two quadratic gravity theories: dynamical Chern-Simons and scalar Gauss-Bonnet gravity. We compute the principal null directions, Weyl scalars, and complex null tetrad in the small-coupling, slow rotation approximation for both theories, confirming that both spacetimes are Petrov type I. Additionally, we solve the Killing equation through rank 6 in dynamical Chern-Simons gravity and rank 2 in scalar Gauss-Bonnet gravity, showing that there is no nontrivial Killing tensor through those ranks for each theory. We therefore conjecture that the still-unknown, exact, quadratic-gravity, black-hole solutions do not possess a fourth constant of motion.

A note on the linear stability of black holes in quadratic gravity

Black holes in f(R)-gravity are known to be unstable, especially the rotating ones. In particular, an instability develops that looks like the classical black hole bomb mechanism: the linearized modified Einstein equations are characterized by an effective mass that acts like a massive scalar perturbation on the Kerr solution in general relativity, which is known to yield instabilities. In this note, we consider a special class of f(R) gravity that has the property of being scale-invariant. As a prototype, we consider the simplest case f(R)=R^2 and show that, in opposition to the general case, static and stationary black holes are stable, at least at the linear level. Finally, the result is generalized to a wider class of f(R) theories.

Exact Black Holes in Quadratic Gravity with any Cosmological Constant.

We present a new explicit class of black holes in general quadratic gravity with a cosmological constant. These spherically symmetric Schwarzschild-Bach-(anti-)de Sitter geometries, derived under the assumption of constant scalar curvature, form a three-parameter family determined by the black-hole horizon position, the value of the Bach invariant on the horizon, and the cosmological constant. Using a conformal to Kundt metric ansatz, the fourth-order field equations simplify to a compact autonomous system. Its solutions are found as power series, enabling us to directly set the Bach parameter and/or cosmological constant equal to zero. To interpret these spacetimes, we analyze the metric functions. In particular, we demonstrate that for a certain range of positive cosmological constant there are both black-hole and cosmological horizons, with a static region between them. The tidal effects on free test particles and basic thermodynamic quantities are also determined.

Regular black holes in quadratic gravity

The first-order correction of the perturbative solution of the coupled equations of the quadratic gravity and nonlinear electrodynamics is constructed, with the zeroth-order solution coinciding with the ones given by Ay\'on-Beato and Garc{\'\i}a and by Bronnikov. It is shown that a simple generalization of the Bronnikov's electromagnetic Lagrangian leads to the solution expressible in terms of the polylogarithm functions. The solution is parametrized by two integration constants and depends on two free parameters. By the boundary conditions the integration constants are related to the charge and total mass of the system as seen by a distant observer, whereas the free parameters are adjusted to make the resultant line element regular at the center. It is argued that various curvature invariants are also regular there that strongly suggests the regularity of the spacetime. Despite the complexity of the problem the obtained solution can be studied analytically. The location of the event horizon of the black hole, its asymptotics and temperature are calculated. Special emphasis is put on the extremal configuration.

Charged black holes in quadratic gravity

Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. The obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit the exact location of the (degenerate) event horizon is given by ${r}_{+}=|e|.$ Similarly to the classical Reissner-Nordstr\"om solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for boundary conditions of the second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed.

Perturbative metric of charged black holes in quadratic gravity.

We consider perturbative solutions to the classical field equations coming from a quadratic gravitational lagrangian in four dimensions. We study the charged, spherically symmetric black hole and explicitly give corrections up to third order (in the coupling constant $\beta$ multiplying the $R_{\mu\nu}R^{\mu\nu}$ term) to the Reissner--Nordstr\"om hole metric. We consider the thermodynamics of such black holes, in particular, we compute explicitly its temperature and entropy--area relation which deviates from the usual $S=A/4$ expression.