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Register a new userWhat is the topology of a Schwarzschild black hole?
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Authors
Edmundo M. Monte
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We investigate the topology of Schwarzschilds black hole through the immersion of this space-time in spaces of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschilds black hole.
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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.
We study linear gravitational perturbations of Schwarzschild spacetime by solving numerically Regge-Wheeler-Zerilli equations in time domain using hyperboloidal surfaces and a compactifying radial coordinate. We stress the importance of including the asymptotic region in the computational domain in studies of gravitational radiation. The hyperboloidal approach should be helpful in a wide range of applications employing black hole perturbation theory.
Acoustic black hole is becoming an attractive topic in recent years, for it open-up new direction for experimental explorations of black holes in laboratories. In this work, the gravitational bending of acoustic Schwarzschild black hole is investigated. We resort to the approach developed by Gibbons and Werner, in which the gravitational bending is calculated using the Gauss-Bonnet theorem in geometrical topology. In this approach, the gravitational bending is directly connected with the topological properties of curved spacetime. The deflection angle of light for acoustic Schwarzschild black hole is calculated and carefully analyzed in this work. The results show that the gravitational bending effect in acoustic black hole is enhanced, compared with those in conventional Schwarzschild black hole. This observation indicates that the acoustic black holes may be more easily detectable in gravitational bending and weak gravitational lensing observations. Keywords: Gravitational Bending; Gauss-Bonnet Theorem; Acoustic Schwarzschild Black Hole
We present results from calculations of the orbital evolution in eccentric binaries of nonrotating black holes with extreme mass-ratios. Our inspiral model is based on the method of osculating geodesics, and is the first to incorporate the full gravitational self-force (GSF) effect, including conservative corrections. The GSF information is encapsulated in an analytic interpolation formula based on numerical GSF data for over a thousand sample geodesic orbits. We assess the importance of including conservative GSF corrections in waveform models for gravitational-wave searches.
Following the initial work of Calcagni et al. on the black holes in multi-fractional theories, we focus on the Schwarzschild black hole in multi-fractional theory with q-derivatives. After presenting its Hawking and Hayward temperatures in detail, we verify these results by appealing to the well-known Hamilton-Jacobi and null geodesic methods of the tunnelling approach to Hawking radiation. A special emphasis is placed on the difference between the geometric and fractional frames.
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