Exact Fermi coordinates for anti-de Sitter and other spacetimes
This paper has been withdrawn by the authors, an improved version with the title "Exact Fermi coordinates for a class of spacetimes", arXiv:0912.2779, replaces it.
gr-qc↗
arXiv subjects
David Klein
Publications and source records attributed to David Klein.
Exact Fermi coordinates for a class of spacetimes
We find exact Fermi coordinates for timelike geodesic observers for a class of spacetimes that includes anti-de Sitter spacetime, de Sitter spacetime, the constant density interior Schwarzschild spacetime with positive, zero, and negative cosmological constant, and the Einstein static universe. Maximal charts for Fermi coordinates are discussed.
math-ph↗
Timelike Killing Fields and Relativistic Statistical Mechanics
For spacetimes with timelike Killing fields, we introduce a "Fermi-Walker-Killing" coordinate system and use it to prove a Liouville Theorem for an appropriate volume element of phase space for a statistical mechanical system of particles. We derive an exact relativistic formula for the Helmholtz free energy of an ideal gas and compare it, for a class of spacetimes, to its Newtonian analog, derived both independently and as the Newtonian limit of our formula. We also find the relativistic thermodynamic equation of state. Specific examples are given in Kerr spacetime.
gr-qc↗
Frame dragging anomalies for rotating bodies
Examples of axially symmetric solutions to Einstein's field equations are given that exhibit anomalous "negative frame dragging" in the sense that zero angular momentum test particles acquire angular velocities in the opposite direction of rotation from the source of the metric.
gr-qc↗
A simple criterion for nonrotating reference frames
We prove a theorem that gives an easily verifiable necessary and sufficient condition for a reference frame with fixed spacelike coordinates to be nonrotating in the sense of Walker. Applications are discussed.
gr-qc↗
Causality violating geodesics in Bonnor's rotating dust metric
We exhibit timelike geodesic paths for a metric, introduced by Bonnor [11] and considered also by Steadman [13], and show that coordinate time runs backward along a portion of these geodesics.
gr-qc↗
General Transformation Formulas for Fermi-Walker Coordinates
We calculate the transformation and inverse transformation, in the form of Taylor expansions, from arbitrary coordinates to Fermi-Walker coordinates in tubular neighborhoods of arbitrary timelike paths for general spacetimes. Explicit formulas for coefficients and the Jacobian matrix are given.
gr-qc↗
A Statistical Mechanical Problem in Schwarzschild Spacetime
We use Fermi coordinates to calculate the canonical partition function for an ideal gas in a circular geodesic orbit in Schwarzschild spacetime. To test the validity of the results we prove theorems for limiting cases. We recover the Newtonian gas law subject only to tidal forces in the Newtonian limit. Additionally we recover the special relativistic gas law as the radius of the orbit increases to infinity. We also discuss how the method can be extended to the non ideal gas case.
gr-qc↗