Gravitation

About: Gravitation is a research topic. Over the lifetime, 29306 publications have been published within this topic receiving 821510 citations.

Dynamical evolution of boson stars: Perturbing the ground state.

Abstract: This is the first paper in a series in which we study the dynamical evolution of self-gravitating complex scalar field configurations (boson stars) in numerical relativity. Boson stars have equilibrium configurations corresponding to different levels of excitation of the scalar fields (i.e., different numbers of nodes). In this paper we report on the dynamical evolution of the perturbed ground-state boson stars. The major results are the following. (i) Under finite perturbations (with possibly finite changes in the total mass $M$ and the particle number $N$), the ground-state configurations of a boson star consist of a stable branch and an unstable branch. The transition point corresponds to a critical mass of $M=0.633(\frac{{M}_{\mathrm{Planck}}^{2}}{m})$, where $m$ is the mass of the scalar field, depending slightly on the type of perturbation considered. This extends the previous result obtained by other authors that there are two such branches under infinitesimal perturbations with fixed $M$ and $N$. (ii) The configurations on the stable branch, when perturbed, will oscillate, emit scalar field radiation with a characteristic frequency, and settle down into a new configuration with less mass and a larger radius than the initial perturbed configuration. The quasinormal frequency and the decay rate have been studied. The decay rate is an increasing function of the oscillation amplitude. (iii) The configurations on the unstable branch, when perturbed, either collapse to a black hole or migrate to and eventually settle down on the stable branch, depending on the type of perturbation. This behavior has been seen in initial configurations with both positive and negative binding energies. These results have implications on the actual existence and the formation of boson stars in an astrophysical environment.

Some special solutions of the equations of axially symmetric gravitational fields

Abstract: The problem of axially symmetric fields was first treated by Weyl, who succeeded in obtaining solutions for a static field in terms of the Newtonian potential of a distribution of matter in an associated canonical space. He also solved the more general problem involving the electric field. Levi Civita, by slightly different methods, obtained solutions differing from those of Weyl in one respect, and discussed fully the case in which the field is produced by an infinite cylinder. R. Bach has discussed the special case of two spheres and has calculated their mutual attraction. Bach also considered the field of a slowly rotating sphere, and obtained approximate solutions, taking the Schwarz child solution as his zero-th approximation. The same field was discussed earlier by Leuse and Thirring, who considered, the linear terms, only, in the gravitational equation. Kornel Lanczos has also considered a special case of stationary fields and applied the results to cosmological problems. The more general case of gravitational fields produced by matter in stationary rotation has been treated by W. R. Andress and E. Akeley. Both these authors obtain approximate solutions of the general problem, and the latter treats at length the field of a rotating fluid. The object of this paper is to present some special, but exact, solutions which the author obtained some years ago and, also, two methods of successive approximation for obtaining solutions of a more general type, which behave in an assigned manner at infinity and on a surface of revolution enclosing the rotating matter to which the field is due. Our solutions include as special cases the solutions of Weyl, Levi Civita and others which pertain to static fields. Also, the approximate solutions for stationary fields obtained by Leuse and Thirring, Bach and Andress are contained in our solutions when appropriate choice of boundary conditions is made and higher order terms are neglected.

Perturbations of a Rotating Black Hole

Abstract: Decoupled, separable equations describing perturbations of a Kerr black hole are derived. These equations can be used to study black-hole processes involving scalar, electromagnetic, neutrino or gravitational fields. A number of astrophysical applications are made: Misner's idea that gravitational synchrotron radiation might explain Weber's observations is shown to be untenable; rotating black holes are shown to be stable against small perturbations; energy amplification by "superradiant scattering" of waves off a rotating black hole is computed; the "spin down" (loss of angular momentum) of a rotating black hole caused by a stationary non-axisymmetric perturbation is calculated.

Black Saturn

Abstract: Using the inverse scattering method we construct an exact stationary asymptotically flat 4+1-dimensional vacuum solution describing Black Saturn: a spherical black hole surrounded by a black ring Angular momentum keeps the configuration in equilibrium Black saturn reveals a number of interesting gravitational phenomena: (1) The balanced solution exhibits 2-fold continuous non-uniqueness for fixed mass and angular momentum; (2) Remarkably, the 4+1d Schwarzschild black hole is not unique, since the black ring and black hole of black saturn can counter-rotate to give zero total angular momentum at infinity, while maintaining balance; (3) The system cleanly demonstrates rotational frame-dragging when a black hole with vanishing Komar angular momentum is rotating as the black ring drags the surrounding spacetime Possible generalizations include multiple rings of saturn as well as doubly spinning black saturn configurations