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Register a new userCoupled gravitational and electromagnetic perturbations of Reissner-Nordstrom spacetime in a polarized setting II - Combined estimates for the system of wave equations
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Elena Giorgi
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In a previous paper on coupled gravitational and electromagnetic perturbations of Reissner-Nordstrom spacetime in a polarized setting, we derived a system of wave equations for two independent quantities, one related to the Weyl curvature and one related to the Ricci curvature of the perturbed spacetime. We analyze here the system of coupled wave equations, deriving combined energy-Morawetz and $r^p$-estimates for the system, in the case of small charge.
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We present a new convenient framework for modeling Reissner-Nordstrom black hole perturbations from charged distributions of matter. Using this framework, we quantify how gravitational wave observations of compact binary systems would be affected if one or both components were charged. Our approach streamlines the (linearized) Einstein-Maxwell equations through convenient master functions that we designed to ameliorate certain disadvantages of prior strategies. By solving our improved master equations with a point source, we are able to quantify the rate of orbital energy dissipation via electromagnetic and gravitational radiation. Through adiabatic and quasicircular approximations, we apply our dissipative calculations to determine trajectories for intermediate and extreme mass-ratio inspirals. By comparing trajectories and waveforms with varied charges to those with neutral components, we explore the potential effect of electric charge on gravitational wave signals. We observe that the case of opposite charge-to-mass ratios has the most dramatic impact. Our findings are largely interpreted through the lens of the upcoming LISA mission.
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 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.
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.
We study the instability of a Reissner-Nordstrom-AdS (RNAdS) black hole under perturbations of a massive scalar field coupled to Einstein tensor. Calculating the potential of the scalar perturbations we find that as the strength of the coupling of the scalar to Einstein tensor is increasing, the potential develops a negative well outside the black hole horizon, indicating an instability of the background RNAdS. We then investigate the effect of this coupling on the quasinormal modes. We find that there exists a critical value of the coupling which triggers the instability of the RNAdS. We also find that as the charge of the RNAdS is increased towards its extremal value, the critical value of the derivative coupling is decreased.
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