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Register a new userThe linear stability of Reissner-Nordstrom spacetime: the full subextremal range
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Elena Giorgi
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We prove the linear stability of subextremal Reissner-Nordstrom spacetimes as solutions to the Einstein-Maxwell equation. We make use of a novel representation of gauge-invariant quantities which satisfy a symmetric system of coupled wave equations. This system is composed of two of the three equations separately derived in previous works, where the estimates required arbitrary smallness of the charge. Here, the estimates are obtained by defining a combined energy-momentum tensor for the system in terms of the symmetric structure of the right hand sides of the equations. We obtain boundedness of the energy, Morawetz estimates and decay for the full subextremal range |Q|<M, completely in physical space. Such decay estimates, together with the estimates for the gauge-dependent quantities of the perturbations previously obtained, settle the problem of linear stability to gravitational and electromagnetic perturbations of Reissner-Nordstrom solution in the full subextremal range |Q|< M.
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In classical General Relativity, the values of fields on spacetime are uniquely determined by their values at an initial time within the domain of dependence of this initial data surface. However, it may occur that the spacetime under consideration extends beyond this domain of dependence, and fields, therefore, are not entirely determined by their initial data. This occurs, for example, in the well-known (maximally) extended Reissner-Nordstrom or Reissner-Nordstrom-deSitter (RNdS) spacetimes. The boundary of the region determined by the initial data is called the Cauchy horizon. It is located inside the black hole in these spacetimes. The strong cosmic censorship conjecture asserts that the Cauchy horizon does not, in fact, exist in practice because the slightest perturbation (of the metric itself or the matter fields) will become singular there in a sufficiently catastrophic way that solutions cannot be extended beyond the Cauchy horizon. Thus, if strong cosmic censorship holds, the Cauchy horizon will be converted into a final singularity, and determinism will hold. Recently, however, it has been found that, classically this is not the case in RNdS spacetimes in a certain range of mass, charge, and cosmological constant. In this paper, we consider a quantum scalar field in RNdS spacetime and show that quantum theory comes to the rescue of strong cosmic censorship. We find that for any state that is nonsingular (i.e., Hadamard) within the domain of dependence, the expected stress-tensor blows up with affine parameter, $V$, along a radial null geodesic transverse to the Cauchy horizon as $T_{VV} sim C/V^2$ with $C$ independent of the state and $C eq 0$ generically in RNdS spacetimes. This divergence is stronger than in the classical theory and should be sufficient to convert the Cauchy horizon into a strong curvature singularity.
The strong cosmic censorship conjecture proposes that starting from generic initial data on some Cauchy surface, the solutions of the Einstein equation should not be extendable across the boundary of the domain of dependence of that surface. For the case of the Reissner-Nordstrom-de Sitter spacetime this means that any perturbation should blow up sufficiently badly when approaching this boundary, called the Cauchy horizon. However, recent results indicate that for highly charged black holes classical scalar perturbations allow for a violation of strong cosmic censorship. In a recent paper arXiv:1912.06047, two of us have argued that quantum effects will restore censorship for generic values of the black hole parameters. But, due to practical limitations, the precise form of the divergence was only calculated for a small number of parameters. Here we perform a thorough parameter scan using an alternative, more efficient semi-analytic method. Our analysis confirms arXiv:1912.06047 in the sense that the quantum stress tensor is found to diverge badly generically. However, the sign of the divergence can be changed by changing the mass of the field or the spacetime parameters, leading to a drastically different type of singularity on the Cauchy horizon.
The Reissner-Nordstrom-de Sitter (RN-dS) spacetime can be considered as a thermodynamic system. Its thermodynamic properties are discussed that the RN-dS spacetime has phase transitions and critical phenomena similar to that of the Van de Waals system or the charged AdS black hole. The continuous phase transition point of RN-dS spacetime depends on the position ratio of the black hole horizon and the cosmological horizon. We discuss the critical phenomenon of the continuous phase transition of RN-dS spacetime with Landau theory of continuous phase transition, that the critical exponent of spacetime is same as that of the Van de Waals system or the charged AdS black hole, which have universal physical meaning. We find that the order parameters are similar to those introduced in ferromagnetic systems. Our universe is an asymptotically dS spacetime, thermodynamic characteristics of RN-dS spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of accelerated expansion of the universe.
In the present article we study the Inverse Electrodynamics Model. This model is a gauge and parity invariant non-linear Electrodynamics theory, which respects the conformal invariance of standard Electrodynamics. This modified Electrodynamics model, when minimally coupled to General Relativity, is compatible with static and spherically symmetric Reissner-Nordstrom-like black-hole solutions. However, these black-hole solutions present more complex thermodynamic properties than their Reissner-Nordstrom black-hole solutions counterparts in standard Electrodynamics. In particular, in the Inverse Model a new stability region, with both the heat capacity and the free energy negative, arises. Moreover, unlike the scenario in standard Electrodynamics, a sole transition phase is possible for a suitable choice in the set of parameters of these solutions.
Black hole spectroscopy is a powerful tool to probe the Kerr nature of astrophysical compact objects and their environment. The observation of multiple ringdown modes in gravitational waveforms could soon lead to high-precision gravitational spectroscopy, so it is critical to understand if the quasinormal mode spectrum is stable against perturbations. It was recently shown that the pseudospectrum can shed light on the spectral stability of black hole quasinormal modes. We study the pseudospectrum of Reissner-Nordstrom spacetimes and we find a spectral instability of scalar and gravitoelectric quasinormal modes in subextremal and extremal black holes, extending similar findings for the Schwarzschild spacetime. The asymptotic structure of pseudospectral contour levels is the same for scalar and gravitoelectric perturbations. By making different gauge choices in the hyperboloidal slicing of the spacetime, we find that the broad features of the pseudospectra are remarkably gauge-independent. The gravitational-led and electromagnetic-led quasinormal modes of extremal Reissner-Nordstrom black holes exhibit strong isospectrality: both the spectra and the pseudospectra coincide within numerical precision, because the Greens function as a whole (and not just the poles) is the same for the two classes of perturbations.
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