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We study the time evolution of the test scalar and electromagnetic fields perturbations in configurations of phantom wormholes surrounded by dark energy with state parameter $omega< -1$. We observe obvious signals of echoes reflecting wormholes properties and disclose the physical reasons behind such phenomena. In particular, we find that the dark energy equation of state has a clear imprint in echoes in wave perturbations. When $omega$ approaches the phantom divide $omega=-1$ from below, the delay time of echoes becomes longer. The echo of gravitational wave is likely to be detected in the near future, the signature of the dark energy equation of state in the echo spectrum can serve as a local measurement of the dark energy.
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A possible candidate for the late time accelerated expanding Universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., $omega(r)=p(r)/rho(r)$. We shall impose that phantom energy is concentrated in the neighborhood of the throat, to ensure the flaring out condition, and several models are analyzed. We shall also consider the possibility that these phantom wormholes be sustained by their own quantum fluctuations. The energy density of the graviton one loop contribution to a classical energy in a phantom wormhole background and the finite one loop energy density are considered as a self-consistent source for these wormhole geometries. The latter semi-classical approach prohibits solutions with a constant equation of state parameter, which further motivates the imposition of a radial dependent parameter, $omega(r)$, and only permits solutions with a steep positive slope proportional to the radial derivative of the equation of state parameter, evaluated at the throat. The size of the wormhole throat as a function of the relevant parameters is also explored.
We present the first numerical construction of the scalar Schwarzschild Green function in the time-domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront propagates through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large l-limit of quasinormal modes. We show that the four-fold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A two-fold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including null infinity, and argue that, even with ideal instruments, only a finite number of echoes can be observed. Putting these pieces together, we provide a heuristic expression that approximates the Green function with a few free parameters. Accurate calculations and approximations of the Green function are the most general way of solving for wave propagation in curved spacetimes and should be useful in a variety of studies such as the computation of the self-force on a particle.
The realm of strong classical gravity and perhaps even quantum gravity are waiting to be explored. In this letter we consider the recently detected triple system composed of two stars and a non-accreting black hole. Using published observations of this system we conduct the most sensitive test to date for whether the black hole is actually a wormhole by looking for orbital perturbations due to an object on the other side of the wormhole. The mass limit obtained on the perturber is $sim4$ orders of magnitude better than for observations of S2 orbiting the supermassive black hole at Sgr A*. We also consider how observations of a pulsar could test for whether the black hole in a pulsar-black hole binary is a wormhole. A pulsar in a similar orbit to S2 would be $sim10$ orders of magnitude more sensitive than observations of S2. For a nominal pulsar-black hole binary of stellar masses, with orbital size similar to that of the Hulse-Taylor binary pulsar, one year of observations could set a mass limit on a perturber that is $sim6$ orders of magnitude better than observations of a pulsar around Sgr~A*. A range of limits between the pulsar-Sgr~A* and Hulse-Taylor cases could be obtained for a possible population of pulsar-black hole binaries that may exist near the galactic center.
The effect of the Gauss-Bonnet term on the existence and dynamical stability of thin-shell wormholes as negative tension branes is studied in the arbitrary dimensional spherically, planar, and hyperbolically symmetric spacetimes. We consider radial perturbations against the shell for the solutions which have the Z${}_2$ symmetry and admit the general relativistic limit. It is shown that the Gauss-Bonnet term shrinks the parameter region admitting static wormholes. The effect of the Gauss-Bonnet term on the stability depends on the spacetime symmetry. For planar symmetric wormholes, the Gauss-Bonnet term does not affect their stability. If the coupling constant is positive but small, the Gauss-Bonnet term tends to destabilize spherically symmetric wormholes, while it stabilizes hypebolically symmetric wormholes. The Gauss-Bonnet term can destabilize hypebolically symmetric wormholes as a non-perturbative effect, however, spherically symmetric wormholes cannot be stable.
Searches for gravitational wave echoes in the aftermath of mergers and/or formation of astrophysical black holes have recently opened a novel and surprising window into the quantum nature of their horizons. Similar to astro- and helioseismology, study of the spectrum of quantum black holes provides a promising method to understand their inner structure, what we call $textit{quantum black hole seismology}$. We provide a detailed numerical and analytic description of this spectrum in terms of the properties of the Kerr spacetime and quantum black hole horizons, showing that it drastically differs from their classical counterparts. Our most significant findings are the following: (1) If the temperature of quantum black hole is $lesssim 2 times$ Hawking temperature, then it will not suffer from ergoregion instability (although the bound is looser at smaller spins). (2) We find how quantum black hole spectra pinpoint the microscopic properties of quantum structure. For example, the detailed spacing of spectral lines can distinguish whether quantum effects appear through compactness (i.e., exotic compact objects) or frequency (i.e., modified dispersion relation). (3) We find out that the overtone quasinormal modes may strongly enhance the amplitude of echo in the low-frequency region. (4) We show the invariance of the spectrum under the generalized Darboux transformation of linear perturbations, showing that it is a genuine covariant observable.
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