De Sitter Black Hole Spacetimes Research Articles

Quasinormal modes and echo effect of a cylindrical anti–de Sitter black hole spacetime with a thin shell

This paper investigates the quasinormal mode (QNM) vibrations of a rotating cylindrical black hole (or black string) spacetime that is surrounded by a thin shell rotating synchronously with the black string's axis. The existence of the thin shell leads to a piecewise metric of the black hole spacetime beyond the horizon, which is divided into two stationary spacetime parts by the radius of the thin shell. As a result, the potential function $V(r)$ of the QNM equation is also discontinuous. To solve the QNM equation with the discontinuous potential function, we propose two methods, the matrix method and the generalized Horowitz-Hubeny method. We find that the influence of the thin shell can reduce the QNM frequency of the black string while alleviating their amplitude decay rate. Our suggested method can be easily applied to other QNM calculations of black hole spacetime with discontinuous potential function, thus facilitating investigations into more intricate and realistic black hole spacetimes, such as those with accretion disks. Additionally, the finite difference method is employed to investigate the spacetime too. This analysis discloses a substantial gap in the potential function when the thin shell's mass and charge achieve sufficiently high values, resulting in the outer spacetime nearing gravitational collapse and extreme black hole scenarios. Within this gap, the QNM wave displays oscillations, producing an echo effect. Moreover, it is established that the closeness of the spacetime to the collapse threshold and charge extremality have positive correlation with the beat interval of this echo.

Lorentz-breaking theory and tunneling radiation correction to Vaidya–Bonner de Sitter Black Hole

In Vaidya–Bonner de Sitter black hole space-time, the tunneling radiation characteristics of fermions and bosons are corrected by taking Lorentz symmetry breaking theory into account. The corresponding gamma matrices and aether-like field vectors of the black hole are constructed, then the new modified form of Dirac equation for the fermion with spin 1/2 and the new modified form of Klein–Gordon equation for boson in the curved space-time of the black hole are obtained. Through solving the two equations, new and corrected expressions of surface gravity, Hawking temperature and tunneling rate of the black hole are obtained, and the results obtained are also discussed.

Conformal Scattering of Maxwell fields on Reissner–Nordström–de Sitter Black Hole Spacetimes

We construct a complete conformal scattering theory for Maxwell fields in the static exterior region of a Reissner–Nordström–de Sitter black hole spacetime. We use uniform energy decay results, which we obtain in a separate paper, to show that the trace operators are injective and have closed ranges. We then solve the Goursat problem (characteristic Cauchy problem) for Maxwell fields on the null boundaries showing that the trace operators are also surjective.

Kerr–(anti–)de Sitter black holes: Perturbations and quasinormal modes in the slow rotation limit

We study the perturbations of scalar, vector, and tensor fields in a slowly rotating Kerr-(Anti-)de Sitter black hole spacetime, presenting new and existing Schr\"odinger style master equations for each type of perturbation up to linear order in black hole spin $a$. For each type of field we calculate analytical expressions for the fundamental quasi-normal mode frequencies. These frequencies are compared to existing results for Schwarzschild-de Sitter, slowly rotating Kerr, and slowly rotating Kerr-de Sitter black holes. In all cases good agreement is found between the analytic expressions and those frequencies calculated numerically. In addition, the axial and polar gravitational frequencies are shown to be isospectral to linear order in $a$ for all cases other than for both non-zero $a$ and $\Lambda$.

Rough initial data and the strength of the blue-shift instability on cosmological black holes with Λ > 0

We consider the wave equation on Reissner–Nordström–de Sitter and more generally Kerr–Newman–de Sitter black hole spacetimes with . The strength of the blue-shift instability associated to the Cauchy horizon of these spacetimes has been the subject of much discussion, since—in contrast to the asymptotically flat case—the competition with the decay associated to the region between the event and cosmological horizons is delicate, especially as the extremal limit is approached. Of particular interest is the question as to whether generic, admissible initial data posed on a Cauchy surface lead to solutions whose local (integrated) energy blows up at the Cauchy horizon, for this statement holds in the asymptotically flat case and would correspond precisely to the blow up required by Christodoulou’s formulation of strong cosmic censorship. Some recent heuristic work suggests that the answer is in general negative for solutions arising from sufficiently smooth data, i.e. there exists a certain range of black hole parameters such that for all such data, the arising solutions have finite local (integrated) energy at the Cauchy horizon. In this short note, we shall show in contrast that, by slightly relaxing the smoothness assumption on initial data, we are able to prove the analogue of the Christodoulou statement in the affirmative, i.e. we show that for generic data in our allowed class, the local energy blow-up statement indeed holds at the Cauchy horizon, for all subextremal black hole parameter ranges. We present two distinct proofs. The first is based on an explicit mode construction while the other is softer and uses only time translation invariance of appropriate scattering maps, in analogy with our previous (Dafermos and Shlapentokh-Rothman 2017 Commun. Math. Phys. 350 985–1016). Both proofs use statements concerning the non-triviality of transmission and reflexion, which are easy to infer by o.d.e. techniques and analyticity considerations. Our slightly enlarged class of initial data is still sufficiently regular to ensure both stability and decay properties in the region between the event and cosmological horizons as well as the boundedness and continuous extendibility beyond the Cauchy horizon. This suggests thus that it is finally this class—and not smoother data—which may provide the correct setting to formulate the genericity condition in strong cosmic censorship.

Reissner–Nordstrøm–de Sitter manifold: photon sphere and maximal analytic extension

This paper is devoted to the study of Reissner–Nordstrøm–de Sitter black holes and their maximal analytic extensions. Here, we find the necessary and sufficient conditions on the parameters of the Reissner–Nordstrøm–de Sitter metric—namely, the mass, the charge, and the cosmological constant—to have three horizons. Under these conditions, we prove that there is only one photon sphere and we locate it. We then give a detailed construction of the maximal analytic extension of the Reissner–Nordstrøm–de Sitter manifold in the case of three horizons. Studying these properties lays the groundwork for obtaining (in separate papers) decay results (Mokdad 2017 Decay of Maxwell fields on Reissner–Nordstrøm–de Sitter black holes (arXiv:1704.06441)) and constructing conformal scattering theories for test fields on such spacetimes (Mokdad 2017 Conformal scattering of Maxwell fields on Reissner–Nordstrøm–de Sitter black hole spacetimes (arXiv:1706.06993)).

A note on Schwarzschild–de Sitter black holes in mimetic F(R) gravity

In this paper, we investigate the conditions under which a Schwarzschild–de Sitter black hole spacetime is a solution of the mimetic [Formula: see text] gravity with Lagrange multiplier and potential. As we demonstrate, the resulting mimetic [Formula: see text] gravity is a slight modification of the ordinary [Formula: see text] gravity case, however the resulting perturbation equations are not in all cases identical to the ordinary [Formula: see text] gravity case. In the latter case, the perturbation equations are identical to the ones corresponding to the Reissner–Nordström anti-de Sitter black hole.

Mass function and particle creation in Schwarzschild–de Sitter spacetime

We construct a mass or energy function for the non-Nariai class Schwarzschild–de Sitter black hole spacetime in the region between the black hole and the cosmological event horizons. The mass function is local, positive definite, continuous and increases monotonically with the radial distance from the black hole event horizon. We derive the Smarr formula using this mass function, and demonstrate that the mass function reproduces the two-temperature Schwarzschild–de Sitter black hole thermodynamics, along with a term corresponding to the negative pressure due to positive cosmological constant. We further give a field theoretic derivation of the particle creation by both the horizons and discuss its connection with the mass function.

Massive spin-2 and spin-1/2no hair theorems for stationary axisymmetric black holes

We present a proof of the no hair theorems corresponding to free massive non-perturbative Pauli-Fierz spin-2 and perturbative massive spin-1/2 fields for stationary axisymmetric de Sitter black hole spacetimes of dimension four with two commuting Killing vector fields. The applicability of these results for asymptotically flat and anti-de Sitter spacetimes are also discussed.

No hair theorems for stationary axisymmetric black holes

We present a nonperturbative proof of the no-hair theorems corresponding to scalar and Proca fields for stationary axisymmetric de Sitter black hole spacetimes. Our method also applies to asymptotically flat and under a reasonable assumption, to asymptotically anti-de Sitter spacetimes.

(Anti-)de Sitter Black Hole Entropy and Generalized Uncertainty Principle

We generalize the method that is used to study corrections toCardy–Verlinde formula due to generalized uncertainty principleand discuss corrections to Cardy–Verlinde formula due togeneralized uncertainty principle in (anti)-de Sitter space.Because in de Sitter black hole spacetime the radiationtemperature of the black hole horizon is different from the one ofthe cosmological horizon, this spacetime is a thermodynamicalnon-equilibrium spacetime.

On the classification of asymptotic quasinormal frequencies for {$d$}-dimensional black holes and quantum gravity

We provide a complete classification of asymptotic quasinormal frequencies for static, spherically symmetric black hole spacetimes in d dimensions. This includes all possible types of gravitational perturbations (tensor, vector and scalar type) as described by the Ishibashi–Kodama master equations. The frequencies for Schwarzschild are dimension independent, while for Reissner–Nordstrom are dimension dependent (the extremal Reissner–Nordstrom case must be considered separately from the non–extremal case). For Schwarzschild de Sitter, there is a dimension independent formula for the frequencies, except in dimension d = 5 where the formula is different. For Reissner–Nordstrom de Sitter there is a dimension dependent formula for the frequencies, except in dimension d = 5 where the formula is different. Schwarzschild and Reissner–Nordstrom Anti–de Sitter black hole spacetimes are simpler: the formulae for the frequencies will depend upon a parameter related to the tortoise coordinate at spatial infinity, and scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the quasinormal frequencies. We also address non–black hole spacetimes, such as pure de Sitter spacetime—where there are quasinormal modes only in odd dimensions—and pure Anti–de Sitter spacetime—where again scalar type perturbations in dimension d = 5 lead to a continuous spectrum for the normal frequencies. Our results match previous numerical calculations with great accuracy. Asymptotic quasinormal frequencies have also been applied in the framework of quantum gravity for black holes. Our results show that it is only in the simple Schwarzschild case which is possible to obtain sensible results concerning area quantization or loop quantum gravity. In an effort to keep this paper self–contained we also review earlier results in the literature.