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Register a new userScale-invariant rotating black holes in quadratic gravity
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Added by
Massimiliano Rinaldi
Publication date
2015
fields
Physics
and research's language is
English
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Black hole solutions in pure quadratic theories of gravity are interesting since they allow to formulate a set of scale-invariant thermodynamics laws. Recently, we have proven that static scale-invariant black holes have a well-defined entropy, which characterizes equivalent classes of solutions. In this paper, we generalize these results and explore the thermodynamics of rotating black holes in pure quadratic gravity.
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We construct slowly rotating black-hole solutions of Einsteinian cubic gravity (ECG) in four dimensions with flat and AdS asymptotes. At leading order in the rotation parameter, the only modification with respect to the static case is the appearance of a non-vanishing $g_{tphi}$ component. Similarly to the static case, the order of the equation determining such component can be reduced twice, giving rise to a second-order differential equation which can be easily solved numerically as a function of the ECG coupling. We study how various physical properties of the solutions are modified with respect to the Einstein gravity case, including its angular velocity, photon sphere, photon rings, shadow, and innermost stable circular orbits (in the case of timelike geodesics).
We study static, spherically symmetric vacuum solutions to Quadratic Gravity, extending considerably our previous Rapid Communication [Phys. Rev. D 98, 021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we arrive at a much simpler form of the field equations in comparison with their expression in the standard spherically symmetric coordinates. We present details of the derivation of this compact form of two ordinary differential field equations for two metric functions. Next, we apply analytical methods and express their solutions as infinite power series expansions. We systematically derive all possible cases admitted by such an ansatz, arriving at six main classes of solutions, and provide recurrent formulas for all the series coefficients. These results allow us to identify the classes containing the Schwarzschild black hole as a special case. It turns out that one class contains only the Schwarzschild black hole, three classes admit the Schwarzschild solution as a special subcase, and two classes are not compatible with the Schwarzschild solution at all since they have strictly nonzero Bach tensor. In our analysis, we naturally focus on the classes containing the Schwarzschild spacetime, in particular on a new family of the Schwarzschild-Bach black holes which possesses one additional non-Schwarzschild parameter corresponding to the value of the Bach tensor invariant on the horizon. We study its geometrical and physical properties, such as basic thermodynamical quantities and tidal effects on free test particles induced by the presence of the Bach tensor. We also compare our results with previous findings in the literature obtained using the standard spherically symmetric coordinates.
In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we focus on order-reduced Einstein dilaton Gauss-Bonnet gravity (EDGB), a higher curvature beyond-GR theory with motivations in string theory. The stability of single, rotating black holes in EDGB is unknown, but is a necessary condition for being able to simulate binary black hole systems (especially the early-inspiral and late ringdown stages) in EDGB. We thus investigate the stability of rotating black holes in order-reduced EDGB. We evolve the leading-order EDGB scalar field and EDGB spacetime metric deformation on a rotating black hole background, for a variety of spins. We find that the EDGB metric deformation exhibits linear growth, but that this level of growth exponentially converges to zero with numerical resolution. Thus, we conclude that rotating black holes in EDGB are numerically stable to leading-order, thus satisfying our necessary condition for performing binary black hole simulations in EDGB.
With the assumptions of a quartic scalar field, finite energy of the scalar field in a volume, and vanishing radial component of 4-current at infinity, an exact static and spherically symmetric hairy black hole solution exists in the framework of Horndeski theory with parameter $Q$, which encompasses the Schwarzschild black hole ($Q=0$). We obtain the axially symmetric counterpart of this hairy solution, namely the rotating Horndeski black hole, which contains as a special case the Kerr black hole ($Q=0$). Interestingly, for a set of parameters ($M, a$, and $Q$), there exists an extremal value of the parameter $Q=Q_{e}$, which corresponds to an extremal black hole with degenerate horizons, while for $Q<Q_{e}$, it describes a nonextremal black hole with Cauchy and event horizons, and no black hole for $Q>Q_{e}$. We investigate the effect of the $Q$ on the rotating black hole spacetime geometry and analytically deduce corrections to the light deflection angle from the Kerr and nonrotating Horndeski gravity black hole values. For the S2 source star, we calculate the deflection angle for the Sgr A* model of rotating Horndeski gravity black hole for both prograde and retrograde photons and show that it is larger than the Kerr black hole value.
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.
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