Letter: Differential Invariants of the Kerr Vacuum

The norms associated with the gradients of the two non-differential invariants of the Kerr vacuum are examined. Whereas both locally single out the horizons, their global behavior is more interesting. Both reflect the background angular momentum as the volume of space allowing a timelike gradient decreases with increasing angular momentum becoming zero in the degenerate and naked cases. These results extend directly to the Kerr-Newman geometry.     

Letter: Slowly Rotating, Compact Fluid Sources Embedded in Kerr Empty Space-Time

Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to and including quadratic terms in an angular velocity parameter using Darmois junction conditions. The boundary behaviour of the metric tensor and partial derivatives is used to develop a series solution of Einstein's equation's for the rotating fluid. The boundary of the rotating source is expressed explicitly in terms of sinusoidal functions of the polar angle. As an example of the analysis the Schwarzschild interior solution is endowed with rotation and the equation of the fluid boundary is generated together with surface behaviour of the fluid density and angular velocity.     

Letter: The Radial Infall of a Highly Relativistic Point Particle into a Kerr Black Hole Along the Symmetry Axis

In this Letter we consider the radial infall along the symmetry axis of an ultra-relativistic point particle into a rotating Kerr black hole. We use the Sasaki-Nakamura formalism to compute the waveform, energy spectra and total energy radiated during this process. We discuss possible connections between these results and the black hole-black hole collision at the speed of light process.     

Parametrization of the Kerr Solution

From the Kerr solution of Ernst equation under Ehlers and unitary transformations, we build a parametrized Kerr solution depending on three parameters, namely the mass, the angular momentum of the source and an adimensional parameter m ₁. Varying m ₁ produces a topological deformation of the ergosphere.     

Addendum: Hawking Radiation of Photons in a Variable-Mass Kerr Black Hole

Hawking evaporation of photons in a variable-mass Kerr space-time is investigated by using a method of the generalized tortoise coordinate transformation. The blackbody radiant spectrum of photons displays a new spin-rotation coupling effect obviously dependent on different helicity states of photons.     

Back-reaction of the Kerr black hole. A thermodynamical approach

A thermodynamical approach is used to solve the back-reaction problem of the Kerr black hole; the dressed mass, the dressed angular momentum, and the dressed entropy are calculated.     

Spherical Photon Orbits Around a Kerr Black Hole

Two circular photon orbits are known to exist in the equatorial plane of the Kerr black hole. In this paper, we investigate so-called spherical photon orbits—orbits with constant coordinate radii that are not confined to the equatorial plane. A one-parameter class of solutions is found, which includes the circular orbits as special cases. The properties of these spherical orbits are then analyzed, with the aim of classifying them by qualitative differences in their behavior. Finally, representative orbits from each class are plotted out, including a zero-angular momentum photon orbit and one with non-fixed azimuthal direction.     

Collisional Invariants for the Phonon Boltzmann Equation

For the phonon Boltzmann equation with only pair collisions we characterize the set of all collisional invariants under some mild conditions on the dispersion relation.     

Letter: Wave Equations for the Perturbations of a Charged Black Hole

A pair of simple wave equations is presented for the symmetric gravitational and electromagnetic perturbations of a charged black hole. One of the equations is uncoupled, and the other has a source term given by the solution of the first equation. The derivation is presented in full detail for either axially symmetric or stationary perturbations, and is quite straightforward. This result is expected to have important applications in astrophysical models.     

Letter: Quasinormal Modes of the Electrically Charged Dilaton Black Hole

We sketch the results of calculations of the quasinormal frequencies of the electrically charged dilaton black hole. At the earlier phase of evaporation (Q is less than 0.7–0.8M), the dilaton black hole rings with the complex frequencies which differ negligibly from those of the Reissner-Nordström black hole. The spectrum of the frequencies weakly depends upon the dilaton coupling.     

Temperature and thermodynamic geometry of the Kerr-Sen black hole

This paper studies the thermodynamic properties of the Kerr-Sen black hole from the viewpoint of geometry.It calculates the temperature and heat capacity of the black hole,Weinhold metric and Ruppeiner metric are also obtained respectively.It finds that they are both curved and the curvature scalar of Weinhold curvature implies no information about the phase transition while the Ruppeiner one does.But they both carry no information about the second-order phase transition point reproduced from the capacity.Besides,the Legendre invariant metric of the Kerr-Sen black hole has been discussed and its scalar curvature gives the information about the second-order phase transition point.     

Late-time evolution of massive Dirac fields in the Kerr background

The late-time tail of massive Dirac fields in Kerr spacetime is investigated by using the black hole Green function. It is shown that in the intermediate late times there are two kinds of new properties. The one is that the asymptotic behaviour of the massive Dirac fields is dominated by a decaying tail without any oscillation, which is different from the oscillatory decaying tails of the massive scalar field; the other is that the dumping exponent for the massive Dirac field depends not only on the multiple number of the wave mode and the mass of the Dirac particle but also on the rotating parameter of the black hole.     

Extrinsic Curvature Embedding Diagrams

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the extrinsic curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is embedded in the higher dimensional curved space. Simple examples are given to illustrate the idea.     

Non-thermal Hawking radiation from the Kerr black hole

We present a short and direct derivation of Hawking radiation by using the Damour-Ruffini method, as taking into account the self-gravitational interaction from the Kerr black hole. It is found that the radiation is not exactly thermal, and because the derivation obeys conservation laws, the non-thermal Hawking radiation can carry information from the black hole. So it can be used to explain the black hole information paradox, and the process satisfies unitary.     

Invariants of the Riemann tensor: A classical approach

This paper describes the start of an investigation into the application of classical invariant theory to scalar polynomial invariants of the Riemann tensor. In particular, the classical methods of enumerating invariants are discussed with the aim, not achieved in this paper, of verifying Sneddon's result, obtained by explicit calculation of the invariants that the dimension of a Hilbert basis is 38.     

Non-thermal Hawking radiation from the Kerr black hole

We present a short and direct derivation of Hawking radiation by using the Damour-Ruffini method, as taking into account the self-gravitational interaction from the Kerr black hole. It is found that the radiation is not exactly thermal, and because the derivation obeys conservation laws, the non-thermal Hawking radiation can carry information from the black hole. So it can be used to explain the black hole information paradox, and the process satisfies unitary.     

Tunnelling effect of the non-stationary Kerr black hole

Extending Parikh and Wilczek＇s work to the non-stationary black hole, we study the Hawking radiation of the non-stationary Kerr black hole by the Hamilto-Jacobi method. The result shows that the radiation spectrum is not purely thermal and the tunnelling probability is related to the change of Bekenstein Hawking entropy, which gives a correction to the Hawking thermal radiation of the black hole.     

Letter: Gravitational Thermodynamics of a Vaidya Black Hole

The path integral approach is applied to the statistical thermodynamics of a radiating Vaidya black hole. The entropy still satisfies the Bekenstein-Hawking formula, except for a negligible term. The entropy production, as a measurement of the irreversibility, is also obtained.     

Letter: Solutions of All One-Dimensional Wave Equations with Time Independent Potential and Separable Variables

Solutions, in terms of special functions, of all wave equations u _xx – u _tt = V(x) u(t,x), characterised by eight inequivalent time independent potentials and by variables separation, have been found. The real valueness and the properties of the solutions produced by computer algebra programs are not always manifest and in this work we provide ready to use solutions. We discuss especially the potential (m ₁ + m ₂ sinh x)cosh^–2x. Such potential approximates the Schwarzschild black hole potential and its use for determining black holes quasi-normal modes is hinted to.     

Entropy Correction for Kerr Black Hole

In this paper, we discuss leading-order corrections to the entropy of Kerr black hole due to thermal fluctuations in the finite cavity. Then temperature is constant, the solution of the black hole is obtained within a cavity, that is, the solution of the spacetime after considering the radiation of the black hole. Therefore, we derive that the location of the black hole horizon and specific heat are the functions of temperature and the radius of the cavity.Corrections to entropy also are related to the radius of the cavity. Through calculation, we obtain conditions of taking the value of the cavity‘s radius. We provide a new way for studying the corrections of complicated spacetimes.