Black Holes in Einstein-Aether Theory

We study black hole solutions in general relativity coupled to a unit timelike vector field dubbed the "aether". To be causally isolated a black hole interior must trap matter fields as well as all aether and metric modes. The theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four coupling coefficients. We find that the full three-parameter family of local spherically symmetric static solutions is always regular at a metric horizon, but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic flatness imposes another condition, leaving a one-parameter family of regular black holes. These solutions are compared to the Schwarzschild solution using numerical integration for a special class of coupling coefficients. They are very close to Schwarzschild outside the horizon for a wide range of couplings, and have a spacelike singularity inside, but differ inside quantitatively. Some quantities constructed from the metric and aether oscillate in the interior as the singularity is approached. The aether is at rest at spatial infinity and flows into the black hole, but differs significantly from the the 4-velocity of freely-falling geodesics.Comment: 22 pages, 6 figures; v2: minor editing; v3: corrected overall sign in twist formula and an error in the equation for the aether stress tensor. Results unchanged since correct form was used in calculations; v4: corrected minor typ

Action and Hamiltonian for eternal black holes

We present the Hamiltonian, quasilocal energy, and angular momentum for a spacetime region spatially bounded by two timelike surfaces. The results are applied to the particular case of a spacetime representing an eternal black hole. It is shown that in the case when the boundaries are located in two different wedges of the Kruskal diagram, the Hamiltonian is of the form $H = H_+ - H_-$, where $H_+$ and $H_-$ are the Hamiltonian functions for the right and left wedges respectively. The application of the obtained results to the thermofield dynamics description of quantum effects in black holes is briefly discussed.Comment: 24 pages, Revtex, 5 figures (available upon request

3D integrated superconducting qubits

As the field of superconducting quantum computing advances from the few-qubit stage to larger-scale processors, qubit addressability and extensibility will necessitate the use of 3D integration and packaging. While 3D integration is well-developed for commercial electronics, relatively little work has been performed to determine its compatibility with high-coherence solid-state qubits. Of particular concern, qubit coherence times can be suppressed by the requisite processing steps and close proximity of another chip. In this work, we use a flip-chip process to bond a chip with superconducting flux qubits to another chip containing structures for qubit readout and control. We demonstrate that high qubit coherence ($T_1$, $T_{2,\rm{echo}} > 20\,\mu$s) is maintained in a flip-chip geometry in the presence of galvanic, capacitive, and inductive coupling between the chips

Equivalence of black hole thermodynamics between a generalized theory of gravity and the Einstein theory

We analyze black hole thermodynamics in a generalized theory of gravity whose Lagrangian is an arbitrary function of the metric, the Ricci tensor and a scalar field. We can convert the theory into the Einstein frame via a "Legendre" transformation or a conformal transformation. We calculate thermodynamical variables both in the original frame and in the Einstein frame, following the Iyer--Wald definition which satisfies the first law of thermodynamics. We show that all thermodynamical variables defined in the original frame are the same as those in the Einstein frame, if the spacetimes in both frames are asymptotically flat, regular and possess event horizons with non-zero temperatures. This result may be useful to study whether the second law is still valid in the generalized theory of gravity.Comment: 14 pages, no figure

A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is ``rotating''--i.e., is such that the stationary Killing field is not everywhere normal to the horizon--must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, $P$. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.Comment: 24 pages, no figures, v2: footnotes and references added, v3: numerous minor revision

Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting

The BTZ stationary black hole solution is considered and its mass and angular momentum are calculated by means of Noether theorem. In particular, relative conserved quantities with respect to a suitably fixed background are discussed. Entropy is then computed in a geometric and macroscopic framework, so that it satisfies the first principle of thermodynamics. In order to compare this more general framework to the prescription by Wald et al. we construct the maximal extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion about the different features of the two methods for computing entropy is finally developed.Comment: PlainTEX, 16 pages. Revised version 1.

On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions

All known stationary black hole solutions in higher dimensions possess additional rotational symmetries in addition to the stationary Killing field. Also, for all known stationary solutions, the event horizon is a Killing horizon, and the surface gravity is constant. In the case of non-degenerate horizons (non-extremal black holes), a general theorem was previously established [gr-qc/0605106] proving that these statements are in fact generally true under the assumption that the spacetime is analytic, and that the metric satisfies Einstein's equation. Here, we extend the analysis to the case of degenerate (extremal) black holes. It is shown that the theorem still holds true if the vector of angular velocities of the horizon satisfies a certain "diophantine condition," which holds except for a set of measure zero.Comment: 30pp, Latex, no figure

Area-charge inequality for black holes

The inequality between area and charge $A\geq 4\pi Q^2$ for dynamical black holes is proved. No symmetry assumption is made and charged matter fields are included. Extensions of this inequality are also proved for regions in the spacetime which are not necessarily black hole boundaries.Comment: 21 pages, 2 figure

Roughness Scaling in Cyclical Surface Growth

The scaling behavior of cyclical growth (e.g. cycles of alternating deposition and desorption primary processes) is investigated theoretically and probed experimentally. The scaling approach to kinetic roughening is generalized to cyclical processes by substituting the time by the number of cycles $n$. The roughness is predicted to grow as $n^{\beta}$ where $\beta$ is the cyclical growth exponent. The roughness saturates to a value which scales with the system size $L$ as $L^{\alpha}$, where $\alpha$ is the cyclical roughness exponent. The relations between the cyclical exponents and the corresponding exponents of the primary processes are studied. Exact relations are found for cycles composed of primary linear processes. An approximate renormalization group approach is introduced to analyze non-linear effects in the primary processes. The analytical results are backed by extensive numerical simulations of different pairs of primary processes, both linear and non-linear. Experimentally, silver surfaces are grown by a cyclical process composed of electrodeposition followed by 50% electrodissolution. The roughness is found to increase as a power-law of $n$, consistent with the scaling behavior anticipated theoretically. Potential applications of cyclical scaling include accelerated testing of rechargeable batteries, and improved chemotherapeutic treatment of cancerous tumors

Black Hole Entropy is Noether Charge

We consider a general, classical theory of gravity in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian. In any such theory, to each vector field, $\xi^a$, on spacetime one can associate a local symmetry and, hence, a Noether current $(n-1)$-form, ${\bf j}$, and (for solutions to the field equations) a Noether charge $(n-2)$-form, ${\bf Q}$. Assuming only that the theory admits stationary black hole solutions with a bifurcate Killing horizon, and that the canonical mass and angular momentum of solutions are well defined at infinity, we show that the first law of black hole mechanics always holds for perturbations to nearby stationary black hole solutions. The quantity playing the role of black hole entropy in this formula is simply $2 \pi$ times the integral over $\Sigma$ of the Noether charge $(n-2)$-form associated with the horizon Killing field, normalized so as to have unit surface gravity. Furthermore, we show that this black hole entropy always is given by a local geometrical expression on the horizon of the black hole. We thereby obtain a natural candidate for the entropy of a dynamical black hole in a general theory of gravity. Our results show that the validity of the ``second law" of black hole mechanics in dynamical evolution from an initially stationary black hole to a final stationary state is equivalent to the positivity of a total Noether flux, and thus may be intimately related to the positive energy properties of the theory. The relationship between the derivation of our formula for black hole entropy and the derivation via ``Euclidean methods" also is explained.Comment: 16 pages, EFI 93-4