Confluent Heun functions and the physics of black holes: Resonant frequencies,Hawking radiation and scattering of scalar waves

We apply the confluent Heun functions to study the resonant frequencies (quasispectrum), the Hawking radiation and the scattering process of scalar waves, in a class of spacetimes, namely, the ones generated by a Kerr–Newman–Kasuya spacetime (dyon black hole) and a Reissner–Nordström black hole surrounded by a magnetic field (Ernst spacetime). In both spacetimes, the solutions for the angular and radial parts of the corresponding Klein–Gordon equations are obtained exactly, for massive and massless fields, respectively. The special cases of Kerr and Schwarzschild black holes are analyzed and the solutions obtained, as well as in the case of a Schwarzschild black hole surrounded by a magnetic field. In all these special situations, the resonant frequencies, Hawking radiation and scattering are studied.     

Astrophysical applications of the gravitational searchlight

The astrophysical consequences of the blue-shifted radiation emitted in the forward direction by a source moving in an equatorial orbit with radius slightly in excess of 1.5 times the Schwarzschild radius of a highly collapsed central object are examined with special reference to quasistellar objects.     

Conformal scalar propagation and Hawking radiation

The construction of the conformal scalar propagator which has been obtained in the preceding two projects as an analytic function of the Schwarzschild black-hole space-time is completed with a boundary condition imposed by the physical context through contour integration in the exterior vicinity of the event horizon. It is shown that, as a consequence of the semi-classical character which the emitted quanta have in that exterior vicinity, the particle production by the Schwarzschild black hole which was formally established in the preceding project is identical to thermal Hawking radiation. By extension, it is established that such a particle production corresponds to a spectrum which detracts from thermality by the amount predicted by Parikh and Wilczek if energy conservation is properly imposed as a constraint on scalar propagation. The results obtained herein support the case made by Hawking on the relation between quantum propagation and observation of particles produced by a black hole.     

Radiation bursts from particles in the field of compact, impenetrable, astrophysical objects

The radiation emitted by charged, scalar particles in a Schwarzschild field with maximal acceleration corrections is calculated classically and in the tree approximation of quantum field theory. In both instances the particles emit radiation that has characteristics similar to those of gamma-ray bursters.     

Absorption and defocusing of electromagnetic radiation by a Schwarzschild black hole

A comparison of electromagnetic radiation absorbed by a black hole and that emitted at infinity is made for selected circular orbits of a charged particle in a Schwarzschild geometry. Radiation intensity and beaming processes for geodesic as well as ultra-relativistic unbound orbits are compared and contrasted with the special relativistic results of classical electrodynamics.     

Radiation from hot spots orbiting an extreme Reissner-Nordström black hole

The general-relativistic effects of an extreme Reissner-Nordström black hole on the flux of radiation emitted by a hot spot orbiting the hole with a thin accretion disk are investigated. The light curves, the redshift factor, and the solid angle against the spot orbit position are given. The results are then compared with those of a spot orbiting a Schwarzschild black hole.     

Gravity/CFT correspondence for three-dimensional Einstein gravity with a conformal scalar field

We study the three-dimensional Einstein gravity conformally coupled to a scalar field. Solutions of this theory are geometries with vanishing scalar curvature. We consider solutions with a constant scalar field which corresponds to an infinite Newton?s constant. There is a class of solutions with possible curvature singularities which asymptotic symmetries are given by two copies of the Virasoro algebra. We argue that the central charge of the corresponding CFT is infinite. Furthermore, we construct a family of Schwarzschild solutions which can be conformally mapped to the Martínez–Zanelli solution of Einstein?s equations with a negative cosmological constant coupled to conformal scalar field.     

Black holes in which the electrostatic or scalar equation is solvable in closed form

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerate horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordström black holes in higher dimensions.     

Metric for an Oblate Earth

In linearized general relativity the metric ofa body is described by a scalar potential and athree-vector potential. We here present a simpletransformation derivation of the linearized metric interms of these potentials, and calculate the exactscalar and vector potentials for a field with oblatespheroidal symmetry. The results for the externalpotentials do not depend on details of the densitydistribution inside the earth; both the scalar and vectorpotentials are fully determined by the total mass, thetotal angular momentum, and a radial parameter, all ofwhich are accurately known from observation. The scalar potential is accurate to roughly10^-6 and the vector potential, which hasnever been accurately measured, should be accurate toabout 10^-5. Applications include an accuratetreatmen t of the details of the motion of satellites, and theprecession of a gyroscope in earth orbit.     

Gravitational Waves from a Pseudo-Newtonian Kerr Field with Halos

A close relation between gravitational waveforms and the types of trajectories in a superposed field between a pseudo-Newtonian Kerr black hole and quadrupolar halos is shown in detail. The gravitational waveforms emitted from circular, KAM tori and chaotic orbits must be periodic, quasiperiodic and stochastic, respectively. The chaotic motion can maximally enhance both the amplitudes and the energy emission rates of the waves.     

Lorentz invariance violation in modified gravity

We consider an environmentally dependent violation of Lorentz invariance in scalar–tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.     

The Kirchhoff gauge

We discuss the Kirchhoff gauge in classical electrodynamics. In this gauge, the scalar potential satisfies an elliptical equation and the vector potential satisfies a wave equation with a nonlocal source. We find the solutions of both equations and show that, despite of the unphysical character of the scalar potential, the electric and magnetic fields obtained from the scalar and vector potentials are given by their well-known retarded expressions. We note that the Kirchhoff gauge pertains to the class of gauges known as the velocity gauge.     

Scalar resonant frequencies and Hawking effect of an f(R) global monopole

Massive scalar fields are considered in the gravitational field produced by a Schwarzschild black hole with a global monopole in f(R) gravity.The exact solution of the radial part of the Klein-Gordon equation in this background is obtained and is given in terms of the general Heun functions.We apply the properties of the general Heun functions to study the Hawking radiation and the resonant frequencies of scalar particles.     

Exact solutions of Einstein's field equations for a massive point-particle with scalar point-charge

The exact static and spherically symmetric solution of Einstein's field equations for a massive point-particle with a scalar point-charge as source of a massless scalar field is derived in Schwarzschild coordinates. There exists no longer a Schwarzschild horizon. Only at the point-particle metric and scalar field are singular (naked singularity).     

Compact boson stars

We consider compact boson stars that arise for a V-shaped scalar field potential. They represent a one parameter family of solutions of the scaled Einstein–signum–Gordon equations. We analyze the physical properties of these solutions and determine their domain of existence. Along their physically relevant branch emerging from the compact Q-ball solution, their mass increases with increasing radius. Employing arguments from catastrophe theory we argue that this branch is stable, until the maximal value of the mass is reached. There the mass and size are on the order of magnitude of the Schwarzschild limit, and thus the spiraling respectively oscillating behaviour, well known for compact stars, sets in.     

Hawking Temperature of a Static Black Hole in Harmonic Coordinates

Hawking radiation is usually studied in standard coordinates. In this paper, we calculate the Hawking temperature of a Schwarzschild black hole in harmonic coordinates, as well as that of a Reissner-Nordström black hole. The action of a scalar field near the event horizon can be formulated exactly without omitting some high-order terms. We show dimensional reduction for Hawking temperature is also valid for harmonic coordinates, and verify further that the results are independent on concrete coordinates. With the help of Lorentz transformation, our work might also serve as a basis to investigate the thermal radiation from a moving black hole.     

Quantum dynamics of relativistic bosons through nonminimal vector square potentials

The dynamics of relativistic bosons (scalar and vectorial) through nonminimal vector square (well and barrier) potentials is studied in the Duffin–Kemmer–Petiau (DKP) formalism. We show that the problem can be mapped in effective Schrödinger equations for a component of the DKP spinor. An oscillatory transmission coefficient is found and there is total reflection. Additionally, the energy spectrum of bound states is obtained and reveals the Schiff–Snyder–Weinberg effect, for specific conditions the potential lodges bound states of particles and antiparticles.     

Cosmological Implication of the Trace Anomaly

We establish a connection between the trace anomaly and thermal radiation in the standard cosmology. This is done by solving the covariant conservation equation of the stress tensor associated with a conformally invariant quantum scalar field. The solution corresponds to thermal radiation with a temperature which is given in terms of a cut-off time excluding the spacetime regions very close to the initial singularity. We discuss the interrelation between this result and the result obtained in a two-dimensional Schwarzschild spacetime.