Session T8: Exact Solutions and Analyses of Spacetimes

Spacetime Dynamics from Spin Dynamics: Scalar and Pseudoscalar Fields

Two fundamental unresolved issues in gravitational physics are the origin of the cosmological constant (dark energy) and the origin of mass. It is remarkable that these two seemingly disparate quantities appear to have the same order of magnitude: the cosmological constant is of order $\Lambda \sim (5meV)^4$ and the neutrino mixing parameters suggest neutrino masses also on the order $m_\nu \sim 5meV$. Since all matter particles are represented by spinor fields, it seems natural to inquire whether the gravitational interaction of the spinor fields can illuminate the situation. To this end, a theory of gravity where the Lagrangian density is taken to be quadratic in the spin curvature is being studied. Relaxing the Schrodinger condition allows the introduction of new fields into the spin connection. This results in the spin curvature containing not only spacetime curvature but also torsion as well as contributions from other fields. If we add only a scalar field the theory generates mass for the spinors but its cosmological solution oscillates. On the other hand, if we add only a pseudoscalar field the cosmological solution accelerates but yields no mass for the spinors. Here I discuss the situation where both a scalar and pseudoscalar are included in the theory.   

Jet Formation in Super-massive Black Holes

An exact solution to the force-free magnetosphere of a Kerr black hole is discussed within the context of the Blandford- Znajek mechanism. The resulting null current vector field of the solution is decomposed into two future pointing timelike vector fields, one of which is able to extract energy from to black hole to the asymptotic regions. We conclude the discussion by considering the astrophysical implications and limitations of this exact solution.   

Oppenheimer-Snyder Collapse in AdS Spacetime

Since Oppenheimer and Snyder first studied the collapse of stars under their own weight in 1939, many other studies on gravitational collapse have been performed. In this project, we study the gravitational collapse of pressureless dust in AdS spacetime. This project compares and contrasts the redshift of null rays emitted from an infalling dust cloud in this Schwarzschild AdS spacetime to that of an ordinary Schwarzschild spacetime.   

A new form of the five-dimensional Myers-Perry rotating black hole metric

Painleve'-Gullstrand coordinates are convenient for presenting the Schwarzschild solution because of their flat constant-time hypersurfaces. Generalizations of these coordinates suitable for the rotating Kerr black hole have been presented by Doran and, more recently, Natario. These coordinate systems feature a time coordinate identical to the proper time of zero-angular-momentum observers that are dropped from infinity. Here, the methods of Natario and Doran are extended to the five-dimensional rotating black hole found by Myers and Perry. The result is a new formulation of the Myers-Perry metric. The properties and physical significance of these new coordinates are discussed.   

Hair on near-extremal Reissner-Nordstr{\o}m AdS black holes

We discuss hairy black hole solutions with scalar hair of mass $m$ and (small) electromagnetic coupling $q^2$, near extremality. Hair forms below a critical temperature $T_c$ and for $q^2 > q_c^2$ where $q_c^2$ is determined by the AdS$_2$ geometry of the horizon and can be negative. At the critical point $q^2 = q_c^2$, the critical temperature vanishes; there is no instability below $q_c^2$. We perform explicit analytic calculations of $T_c$, the condensate and the conductivity for $m^2 =-2$, in which case $q_c^2 = - \frac{1}{4}$. We show that the gap in units of $T_c$ diverges as $T_c \to 0$. We find no discontinuity in the behavior of the system across $q^2 = 0$.   

Quantum Stabilization of General-Relativistic Variable-Density Degenerate Stars

A previous investigation by one of the authors showed that the critical mass of a constant-density neutron star can become greater than eight solar masses under conditions of neutron condensation to form a separate phase of composite bosons, provided the scattering length of the bosons was on the order of a picometer. That analysis employed Newtonian gravity, but general relativity provides a more fundamental analysis. Using general relativity, a Klein-Gordon Lagrangian density with Gross-Pitaevskii term for the bosons, and an effective-field approximation for neutrons, we have determined the equilibrium states of a collapsed star in a spherically symmetric variable-density single phase comprising a ground-state boson condensate and degenerate gas of noninteracting neutrons. Our calculations show that boson scattering lengths of about 20 picometers can prevent collapse to stellar black holes.   

A Challenge to Entropic Gravity

In a recent publication, Erik Verlinde attempts to show that gravity should be viewed not as a fundamental force, but rather as an emergent thermodynamic phenomenon arising from an unspecified microscopic theory via equipartition and holography. We present a challenge to his reformulation of gravity. A detailed examination of Verlinde's derivation leads to a number of questions that severely weaken the claim that such a theory correctly reproduces Newton's laws or Einstein gravity. In particular, we find that neither Newtonian gravity nor the Einstein equations are uniquely determined using Verlinde's postulates.   

Deduction of Einstein equation from homogeneity of Riemann spacetime

The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. \\[4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).