Extrinsic Curvature and the Einstein Constraints

The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors which involves a weight function. In stationary spacetimes, there is a natural choice of the weight function such that the transverse traceless part of the extrinsic curvature (or canonical momentum) vanishes.Comment: 8 pages, no figures; added new section; significant polishing of tex

Corotating and irrotational binary black holes in quasi-circular orbits

A complete formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in general, true equilibrium binary configurations. However, when the timescale for orbital decay is much longer than the orbital period, a binary can be considered to be in quasi-equilibrium. If each black hole is assumed to be in quasi-equilibrium, then a complete set of boundary conditions for all initial data variables can be developed. These boundary conditions are applied on the apparent horizon of each black hole, and in fact force a specified surface to be an apparent horizon. A global assumption of quasi-equilibrium is also used to fix some of the freely specifiable pieces of the initial data and to uniquely fix the asymptotic boundary conditions. This formalism should allow for the construction of completely general quasi-equilibrium black hole binary initial data.Comment: 13 pages, no figures, revtex4; Content changed slightly to reflect fact that regularized shift solutions do satisfy the isometry boundary condition

Boulware state and semiclassical thermodynamics of black holes in a cavity

A black hole, surrounded by a reflecting shell, acts as an effective star-like object with respect to the outer region that leads to vacuum polarization outside, where the quantum fields are in the Boulware state. We find the quantum correction to the Hawking temperature, taking into account this circumstance. It is proportional to the integral of the trace of the total quantum stress-energy tensor over the whole space from the horizon to infinity. For the shell, sufficiently close to the horizon, the leading term comes from the boundary contribution of the Boulware state.Comment: 7 pages. To appear in Phys. Rev.

Dilaton black holes in grand canonical ensemble near the extreme state

Dilaton black holes with a pure electric charge are considered in a framework of a grand canonical ensemble near the extreme state. It is shown that there exists such a subset of boundary data that the Hawking temperature smoothly goes to zero to an infinite value of a horizon radius but the horizon area and entropy are finite and differ from zero. In string theory the existence of a horizon in the extreme limit is due to the finiteness of a system only.Comment: 8 pages, RevTex 3.0. Presentation improved, discussion on metrics in string theory simplified. To be published in Phys.Rev.

A Linear-Nonlinear Formulation of Einstein Equations for the Two-Body Problem in General Relativity

A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of the dynamical variables into i) a fixed conformal 3-geometry, ii) a conformal factor possessing nonlinear dynamics and iii) transverse-traceless perturbations of the conformal 3-geometry.Comment: 7 pages, no figure

Two-dimensional quantum-corrected black hole in a finite size cavity

We consider the gravitation-dilaton theory (not necessarily exactly solvable), whose potentials represent a generic linear combination of an exponential and linear functions of the dilaton. A black hole, arising in such theories, is supposed to be enclosed in a cavity, where it attains thermal equilibrium, whereas outside the cavity the field is in the Boulware state. We calculate quantum corrections to the Hawking temperature $T_{H}$, with the contribution from the boundary taken into account. Vacuum polarization outside the shell tend to cool the system. We find that, for the shell to be in the thermal equilibrium, it cannot be placed too close to the horizon. The quantum corrections to the mass due to vacuum polarization vanish in spite of non-zero quantum stresses. We discuss also the canonical boundary conditions and show that accounting for the finiteness of the system plays a crucial role in some theories (e.g., CGHS), where it enables to define the stable canonical ensemble, whereas consideration in an infinite space would predict instability.Comment: 21 pages. In v.2 misprints corrected. To appear in Phys. Rev.

Action of Singular Instantons of Hawking-Turok Type

Using Kaluza-Klein technique we show that the singularity of Hawking-Turok type has a fixed point (bolt) contribution to the action in addition to the usual boundary contribution. Interestingly by adding this contribution we can obtain a simple expression for the total action which is feasible for both regular and singular instantons. Our result casts doubt on the constraint proposed by Turok in the recent calculation in which Vilenkin's instantons are regarded as a limit of certain constrained instantons.Comment: 14 pages, LaTe

The Momentum Constraints of General Relativity and Spatial Conformal Isometries

Transverse-tracefree (TT-) tensors on $({\bf R}^3,g_{ab})$, with $g_{ab}$ an asymptotically flat metric of fast decay at infinity, are studied. When the source tensor from which these TT tensors are constructed has fast fall-off at infinity, TT tensors allow a multipole-type expansion. When $g_{ab}$ has no conformal Killing vectors (CKV's) it is proven that any finite but otherwise arbitrary set of moments can be realized by a suitable TT tensor. When CKV's exist there are obstructions -- certain (combinations of) moments have to vanish -- which we study.Comment: 16 page

Thermal partition function of photons and gravitons in a Rindler wedge

The thermal partition function of photons in any covariant gauge and gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed using a local $\zeta$-function regularization approach. The correct Planckian leading order temperature dependence $T^4$ is obtained in both cases. For the photons, the existence of a surface term giving a negative contribution to the entropy is confirmed, as earlier obtained by Kabat, but this term is shown to be gauge dependent in the four-dimensional case and, therefore is discarded. It is argued that similar terms could appear dealing with any integer spin $s\geq 1$ in the massless case and in more general manifolds. Our conjecture is checked in the case of a graviton in the harmonic gauge, where different surface terms also appear, and physically consistent results arise dropping these terms. The results are discussed in relation to the quantum corrections to the black hole entropy.Comment: 29 pages, RevTeX, no figures. Minor errors corrected and a few comments changed since first submission. To be published on Phys.Rev.

Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.Comment: 37 pages; 2 figure