De Sitter Reissner Research Articles

Nonlinear Charged Black Hole Solution in Rastall Gravity

We show that the spherically symmetric black hole (BH) solution of a charged (linear case) field equation of Rastall gravitational theory is not affected by the Rastall parameter and this is consistent with the results presented in the literature. However, when we apply the field equation of Rastall’s theory to a special form of nonlinear electrodynamics (NED) source, we derive a novel spherically symmetric BH solution that involves the Rastall parameter. The main source of the appearance of this parameter is the trace part of the NED source, which has a non-vanishing value, unlike the linear charged field equation. We show that the new BH solution is Anti−de-Sitter Reissner−Nordström spacetime in which the Rastall parameter is absorbed into the cosmological constant. This solution coincides with Reissner−Nordström solution in the GR limit, i.e., when Rastall’s parameter is vanishing. To gain more insight into this BH, we study the stability using the deviation of geodesic equations to derive the stability condition. Moreover, we explain the thermodynamic properties of this BH and show that it is stable, unlike the linear charged case that has a second-order phase transition. Finally, we prove the validity of the first law of thermodynamics.

A de-Sitter weak gravity conjecture

The study of de-Sitter Reissner–Nordstrøm black holes allows us to uncover a Weak Gravity Conjecture in de-Sitter space. It states that for a given mass [Formula: see text] there should be a state with a charge [Formula: see text] bigger than a minimal value [Formula: see text], depending on the mass and the de-Sitter radius [Formula: see text], in Planck units. This reproduces the well-known flat space–time result [Formula: see text] in the large radius limit (large [Formula: see text]). In the highly curved de-Sitter space, ([Formula: see text]) [Formula: see text] behaves as [Formula: see text]. Finally, we discuss the case of backgrounds from gauged R-symmetry in [Formula: see text] supergravity. This paper is based on [I. Antoniadis and K. Benakli, Fortsch. Phys. 68, 2000054 (2020), arXiv:2006.12512 [hep-th]].

Scattering Theory for the Charged Klein–Gordon Equation in the Exterior De Sitter–Reissner–Nordström Spacetime

We show asymptotic completeness for the charged Klein–Gordon equation in the exterior De Sitter–Reissner–Nordström spacetime when the product of the charge of the black with the charge of the Klein-Gordon field is small enough. We then interpret scattering as asymptotic transports along principal null geodesics in a Kaluza–Klein extension of the original spacetime.

Decay of the Local Energy for the Charged Klein–Gordon Equation in the Exterior De Sitter–Reissner–Nordström Spacetime

We show decay of the local energy of solutions of the charged Klein–Gordon equation in the exterior De Sitter–Reissner–Nordström spacetime by means of a resonance expansion of the local propagator.

A Scattering Theory for Linear Waves on the Interior of Reissner\u2013Nordstr\xf6m Black Holes

We develop a scattering theory for the linear wave equation Box _g psi = 0 on the interior of Reissner–Nordström black holes, connecting the fixed frequency picture to the physical space picture. Our main result gives the existence, uniqueness and asymptotic completeness of finite energy scattering states. The past and future scattering states are represented as suitable traces of the solution psi on the bifurcate event and Cauchy horizons. The heart of the proof is to show that after separation of variables one has uniform boundedness of the reflection and transmission coefficients of the resulting radial o.d.e. over all frequencies omega and ell . This is non-trivial because the natural T conservation law is sign-indefinite in the black hole interior. In the physical space picture, our results imply that the Cauchy evolution from the event horizon to the Cauchy horizon is a Hilbert space isomorphism, where the past (resp. future) Hilbert space is defined by the finiteness of the degenerate T energy fluxes on both components of the event (resp. Cauchy) horizon. Finally, we prove that, in contrast to the above, for a generic set of cosmological constants Lambda , there is no analogous finite T energy scattering theory for either the linear wave equation or the Klein–Gordon equation with conformal mass on the (anti-) de Sitter–Reissner–Nordström interior.

Resonance expansions of massless Dirac fields propagating in the exterior of a de Sitter–Reissner–Nordström black hole

We give an expansion of the solution of the evolution equation for the massless Dirac fields in the outer region of de Sitter–Reissner–Nordström black hole in terms of resonances. By means of this method we describe the decay of local energy for compactly supported data. The proof uses the cut-off resolvent estimates for the semi-classical Schrödinger operators from [4]. The method extends to the Dirac operators on spherically symmetric asymptotically hyperbolic manifolds.

Quasi-normal modes for de Sitter–Reissner–Nordström black holes

The quasi-normal modes for black holes are the resonances for the scattering of incoming waves by black holes. Here we consider scattering of massless uncharged Dirac fields propagating in the oute ...

Instability of the de Sitter Reissner–Nordstrom black hole in the expansion

We study the large D effective theory for D dimensional charged (Anti) de Sitter black holes. Then we show that the de Sitter Reissner–Nordstrom black hole becomes unstable against gravitational perturbations at larger charge than a critical charge in a higher dimension. Furthermore, we find that there is a nontrivial zero-mode static perturbation at the critical charge. The existence of static perturbations suggests the appearance of non-spherical symmetric solution branches of static charged de Sitter black holes. This expectation is confirmed by constructing the non-spherical symmetric static solutions of large D effective equations.

Inverse scattering at fixed energy for massive charged Dirac fields in de Sitter–Reissner–Nordström black holes

In this paper, we consider massive charged Dirac fields propagating in the exterior region of de Sitter–Reissner–Nordström black holes. We show that the parameters of such black holes are uniquely determined by the partial knowledge of the corresponding scattering operator at a fixed energy λ. More precisely, we consider the partial wave scattering operators (here is the energy and denotes the angular momentum) defined as the restrictions of the full scattering operator on a well-chosen basis of spin-weighted spherical harmonics. We prove that the knowledge of the scattering operators , for all , where is a subset of that satisfies the Müntz condition , makes it possible to recover the mass, the charge, and the cosmological constant of a de Sitter–Reissner–Nordström black hole. The main tool consists in the complexification of the angular momentum n and in studying the analytic properties of the ‘unphysical’ corresponding data in the complex variable z.

The thermodynamics of a Kerr–Newman–de Sitter black hole

We compute the conserved quantities of the four-dimensional Kerr–Newman–de Sitter (KNdS) black hole through the use of the counterterm renormalization method, and obtain a generalized Smarr formula for the mass as a function of the entropy, the angular momentum, and the electric charge. The first law of thermodynamics associated to the cosmological horizon of KNdS is also investigated. Using the minimal number of intrinsic boundary counterterms, we consider the quasilocal thermodynamics of an asymptotic de Sitter–Reissner–Nordstrom black hole, and find that the temperature is equal to the product of the surface gravity (divided by 2π) and the Tolman red-shift factor. We also perform a quasilocal stability analysis by computing the determinant of Hessian matrix of the energy with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles and obtain a complete set of phase diagrams. We then turn to the quasilocal thermodynamics of four-dimensional Kerr–Newman–de Sitter black hole for virtually all possible values of the mass, the rotation, and the charge parameters that leave the quasilocal boundary inside the cosmological event horizon, and perform a quasilocal stability analysis of KNdS black hole.PACS Nos.:04.70.Dy, 04.62.+v, 04.60.–m

Spherically symmetric Yang–Mills solutions in a 5-dimensional (Anti-) de Sitter space–time

We consider an Einstein–Yang–Mills Lagrangian in a five-dimensional space–time including a cosmological constant. Assuming all fields to be independent of the extra coordinate, a dimensional reduction leads to an effective (3+1)-dimensional Einstein–Yang–Mills–Higgs dilaton model where the cosmological constant induces a Liouville potential in the dilaton field. We construct spherically symmetric solutions analytically in specific limits and study the generic solutions for vanishing dilaton coupling numerically. We find that in this latter case the solutions bifurcate with the branch of (Anti-) de Sitter–Reissner–Nordström ((A)dSRN) solutions.

STANDARD COSMOLOGY FROM THE BRANE COSMOLOGY WITH A LOCALIZED MATTER

We discuss the brane cosmology in the 5D anti de Sitter Reissner–Nordstrom ( AdSRN 5) space–time. A brane with tension σ is defined as the edge of an AdSRN 5 space with mass M and charge Q. In this case we get the CFT-radiation term (ρ CFT ) from M and the charged dust [Formula: see text] from Q2 in the Friedmann-like equation. However, this equation is not justified because it contains [Formula: see text]-term with the negative sign. This is unconventional in view of the standard cosmology. In order to resolve this problem, we introduce a localized dust matter which satisfies Pdm = 0. If [Formula: see text], the unwanted [Formula: see text] is cancelled against [Formula: see text] and thus one recovers a standard Friedmann–Robertson–Walker universe with CFT-radiation and dust matter. For the stiff matter consideration, we can set ρcsti ~ Q2 with the negative sign. Here we introduce a massless scalar which plays the role of a stiff matter with Psca = ρsca to cancel -ρcsti. In this case, however, we find a mixed version of the standard and brane cosmologies.