Perfect mirrors and the self-accelerating box paradox

We consider the question raised by Unruh and Wald of whether mirrored boxes can self-accelerate in flat spacetime (the ``self-accelerating box paradox''). From the point of view of the box, which perceives the acceleration as an impressed gravitational field, this is equivalent to asking whether the box can be supported by the buoyant force arising from its immersion in a perceived bath of thermal (Unruh) radiation. The perfect mirrors we study are of the type that rely on light internal degrees of freedom which adjust to and reflect impinging radiation. We suggest that a minimum of one internal mirror degree of freedom is required for each bulk field degree of freedom reflected. A short calculation then shows that such mirrors necessarily absorb enough heat from the thermal bath that their increased mass prevents them from floating on the thermal radiation. For this type of mirror the paradox is therefore resolved. We also observe that this failure of boxes to ``float'' invalidates one of the assumptions going into the Unruh-Wald analysis of entropy balances involving boxes lowered adiabatically toward black holes. Nevertheless, their broad argument can be maintained until the box reaches a new regime in which box-antibox pairs dominate over massless fields as contributions to thermal radiation.Comment: 11 pages, Revtex4, changes made in response to referee and to enhance clarity, discussion of massive fields correcte

On the Status of Highly Entropic Objects

It has been proposed that the entropy of any object must satisfy fundamental (holographic or Bekenstein) bounds set by the object's size and perhaps its energy. However, most discussions of these bounds have ignored the possibility that objects violating the putative bounds could themselves become important components of Hawking radiation. We show that this possibility cannot a priori be neglected in existing derivations of the bounds. Thus this effect could potentially invalidate these derivations; but it might also lead to observational evidence for the bounds themselves.Comment: 6 pages, RevTex, a few editorial change

Ten Proofs of the Generalized Second Law

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are described and critiqued. Each proof provides valuable insights which should be useful for constructing future, more complete proofs. Rather than merely summarizing previous research, this review offers new perspectives, and strategies for overcoming limitations of the existing proofs. A long introductory section addresses some choices that must be made in any formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should one use the global or the apparent horizon? Is it necessary to assume any entropy bounds? If the area has quantum fluctuations, should the GSL apply to the average area? The definition and implications of the classical, hydrodynamic, semiclassical and full quantum gravity regimes are also discussed. A lack of agreement regarding how to define the "quasi-stationary" regime is addressed by distinguishing it from the "quasi-steady" regime.Comment: 60 pages, 2 figures, 1 table. v2: corrected typos and added a footnote to match the published versio

Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy

We consider a general, classical theory of gravity with arbitrary matter fields in $n$ dimensions, arising from a diffeomorphism invariant Lagrangian, \bL. We first show that \bL always can be written in a ``manifestly covariant" form. We then show that the symplectic potential current $(n-1)$-form, $\th$, and the symplectic current $(n-1)$-form, \om, for the theory always can be globally defined in a covariant manner. Associated with any infinitesimal diffeomorphism is a Noether current $(n-1)$-form, \bJ, and corresponding Noether charge $(n-2)$-form, \bQ. We derive a general ``decomposition formula" for \bQ. Using this formula for the Noether charge, we prove that the first law of black hole mechanics holds for arbitrary perturbations of a stationary black hole. (For higher derivative theories, previous arguments had established this law only for stationary perturbations.) Finally, we propose a local, geometrical prescription for the entropy, $S_{dyn}$, of a dynamical black hole. This prescription agrees with the Noether charge formula for stationary black holes and their perturbations, and is independent of all ambiguities associated with the choices of \bL, $\th$, and \bQ. However, the issue of whether this dynamical entropy in general obeys a ``second law" of black hole mechanics remains open. In an appendix, we apply some of our results to theories with a nondynamical metric and also briefly develop the theory of stress-energy pseudotensors.Comment: 30 pages, LaTe

All the Four Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory

We present the explicit form for all the four dimensional, static, spherically symmetric solutions in $(4+n)$-d Abelian Kaluza-Klein theory by performing a subset of $SO(2,n)$ transformations corresponding to four $SO(1,1)$ boosts on the Schwarzschild solution, supplemented by $SO(n)/SO(n-2)$ transformations. The solutions are parameterized by the mass $M$, Taub-Nut charge $a$, $n$ electric $\vec{\cal Q}$ and $n$ magnetic $\vec{\cal P}$ charges. Non-extreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstr\" om or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while non-supersymmetric extreme ones have a global space-time of extreme Reissner-Nordstr\" om black holes.Comment: 8 pages, uses RevTex, improved version to appear in Phys. Rev. Let

A Proof of the Generalized Second Law for Two-Dimensional Black Holes

We investigate the generalized second law for two-dimensional black holes in equilibrium (Hartle-Hawking) and nonequilibrium (Unruh) with the heat bath surrounding the black holes. We obtain a simple expression for the change of total entropy in terms of covariant thermodynamic variables, which is valid not only for the Hartle-Hawking state but also for the Unruh state up to leading order, without assuming a quasi-stationary evolution of the black holes. Using this expression, it is shown that the rate of local entropy production is non-negative in the two-dimensional black hole systems.Comment: 15 pages, boundary condition of static black hole is added to clarify the situation, abstract and section 4 (concluding remarks) is rewritten, and minor corrections, references adde

Treadmill exercise activates subcortical neural networks and improves walking after a stroke

BACKGROUND AND PURPOSE: Stroke often impairs gait thereby reducing mobility and fitness and promoting chronic disability. Gait is a complex sensorimotor function controlled by integrated cortical, subcortical, and spinal networks. The mechanisms of gait recovery after stroke are not well understood. This study examines the hypothesis that progressive task-repetitive treadmill exercise (T-EX) improves fitness and gait function in subjects with chronic hemiparetic stroke by inducing adaptations in the brain (plasticity).METHODS: A randomized controlled trial determined the effects of 6-month T-EX (n=37) versus comparable duration stretching (CON, n=34) on walking, aerobic fitness and in a subset (n=15/17) on brain activation measured by functional MRI.RESULTS: T-EX significantly improved treadmill-walking velocity by 51% and cardiovascular fitness by 18% (11% and -3% for CON, respectively; P<0.05). T-EX but not CON affected brain activation during paretic, but not during nonparetic limb movement, showing 72% increased activation in posterior cerebellar lobe and 18% in midbrain (P<0.005). Exercise-mediated improvements in walking velocity correlated with increased activation in cerebellum and midbrain.CONCLUSIONS: T-EX improves walking, fitness and recruits cerebellum-midbrain circuits, likely reflecting neural network plasticity. This neural recruitment is associated with better walking. These findings demonstrate the effectiveness of T-EX rehabilitation in promoting gait recovery of stroke survivors with long-term mobility impairment and provide evidence of neuroplastic mechanisms that could lead to further refinements in these paradigms to improve functional outcomes

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein-Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Comment: 14 pages, one figure. Dedicated to Rafael Sorkin's birthda

Wormholes and Flux Tubes in 5D Kaluza-Klein Theory

In this paper spherically symmetric solutions to 5D Kaluza-Klein theory, with ``electric'' and/or ``magnetic'' fields are investigated. It is shown that the global structure of the spacetime depends on the relation between the ``electrical'' and ``magnetic'' Kaluza-Klein fields. For small ``magnetic'' field we find a wormhole-like solution. As the strength of the ``magnetic'' field is increased relative to the strength of the ``electrical'' field, the wormhole-like solution evolves into a finite or infinite flux tube depending on the strengths of the two fields. For the large ``electric'' field case we conjecture that this solution can be considered as the mouth of a wormhole, with the $G_{55}$, $G_{5t}$ and $G_{5\phi}$ components of the metric acting as the source of the exotic matter necessary for the formation of the wormhole's mouth. For the large ``magnetic'' field case a 5D flux tube forms, which is similar to the flux tube between two monopoles in Type-II superconductors, or the hypothesized color field flux tube between two quarks in the QCD vacuum.Comment: 12 pages, 5 eps.figures, REVTEX, Discussion about null surfaces ammended. References added. To be published in PR

STATIC FOUR-DIMENSIONAL ABELIAN BLACK HOLES IN KALUZA-KLEIN THEORY

Static, four-dimensional (4-d) black holes (BH's) in ($4+n$)-d Kaluza-Klein (KK) theory with Abelian isometry and diagonal internal metric have at most one electric ($Q$) and one magnetic ($P$) charges, which can either come from the same $U(1)$-gauge field (corresponding to BH's in effective 5-d KK theory) or from different ones (corresponding to BH's with $U(1)_M\times U(1)_E$ isometry of an effective 6-d KK theory). In the latter case, explicit non-extreme solutions have the global space-time of Schwarzschild BH's, finite temperature, and non-zero entropy. In the extreme (supersymmetric) limit the singularity becomes null, the temperature saturates the upper bound $T_H=1/4\pi\sqrt{|QP|}$, and entropy is zero. A class of KK BH's with constrained charge configurations, exhibiting a continuous electric-magnetic duality, are generated by global $SO(n)$ transformations on the above classes of the solutions.Comment: 11 pages, 2 Postscript figures. uses RevTeX and psfig.sty (for figs) paper and figs also at ftp://dept.physics.upenn.edu/pub/Cvetic/UPR-645-