arXiv subjects
Publications and source records attributed to R. B. Mann.
Planar black holes with Galilean asymptotics have been proposed as the holographic dual of a non-relativistic conformal field theory at finite temperature. I show that these objects can undergo a phase transition at low temperature to a new type of soliton with the same asymptotic structure. The strength of the chemical potential is induced by the scale of the soliton.
It has recently been discovered that for certain rates of mode-exchange collisions analytic solutions can be found for a Hamiltonian describing the two-mode Bose-Einstein condensate. We proceed to study the behavior of the system using perturbation theory if the coupling constants only approximately match these parameter constraints. We find that the model is robust to such perturbations. We study the effects of degeneracy on the perturbations and find that the induced changes differ greatly from the non-degenerate case. We also model inelastic collisions that result in particle loss or condensate decay as external perturbations and use this formalism to examine the effects of three-body recombination and background collisions.
All elementary Hamiltonians in nature are expected to be invariant under rotation. Despite this restriction, we usually assume that any arbitrary measurement or unitary time evolution can be implemented on a physical system, an assumption whose validity is not obvious. We introduce two different schemes by which any arbitrary unitary time evolution and measurement can be implemented with desired accuracy by using rotationally invariant Hamiltonians that act on the given system and two ancillary systems serving as reference frames. These frames specify the z and x directions and are independent of the desired time evolution. We also investigate the effects of quantum fluctuations that inevitably arise due to usage of a finite system as a reference frame and estimate how fast these fluctuations tend to zero when the size of the reference frame tends to infinity. Moreover we prove that for a general symmetry any symmetric quantum operations can be implemented just by using symmetric interactions and ancillas in the symmetric states.
We consider the tunnelling of charged spin-(1/2) fermions from a Kerr-Newman black hole and demonstrate that the expected Hawking temperature is recovered. We discuss certain technical subtleties related to the obtention of this result.
We investigate the tunnelling of spin 1/2 particles through event horizons. We first apply the tunnelling method to Rindler spacetime and obtain the Unruh temperature. We then apply fermion tunnelling to a general non-rotating black hole metric and show that the Hawking temperature is recovered.
We show that the internal stationary state of a black hole for massless Dirac fields can be represented by an entangled state of collapsing matter and infalling Hawking radiation. This implies that the Horowitz-Maldacena conjecture for the black hole final state originally proposed for the massless scalar fields is also applicable to fermionic fields as well. For an initially mixed state we find that the measure of mixedness is expected to decrease under evaporation.
We investigate the quantum evolution of the metric operators for Bianchi-Type I model universes in the Heisenberg picture in order to remove the need to consider the wave function of the universe and interpret its "spin" variables. The calculation is analogous to that of the Zitterbewegung of the Dirac electron. We consider the behavior of the metric near the classical singularity, and consider the curvature there. Although factor ordering questions preclude the presentation of an unambiguous result for the curvature invariants, it does seem that the classical $t^{-4}$ divergence of the Kretschmann scalar is not removed by quantization.
We consider the problem of the motion of $N$ bodies in a self-gravitating system in two spacetime dimensions. We point out that this system can be mapped onto the quantum-mechanical problem of an N-body generalization of the problem of the H$_{2}^{+}$ molecular ion in one dimension. The canonical gravitational N-body formalism can be extended to include electromagnetic charges. We derive a general algorithm for solving this problem, and show how it reduces to known results for the 2-body and 3-body systems.
We study the solutions of the Euclidean-signature Einstein equations (gravitational instantons) whose line-element takes the Kerr-bolt form, characterized by three real parameters: a size, a NUT charge, and a spin rate. The exclusion of singularities eliminates most combinations of these parameters, leaving only separated solution-manifolds between which continuous transitions are impossible (The angular velocity divided by the temperature is forced to be a rational multiple of $2π$). This ``quantization'' prevents the free variations presupposed by an equation like $T dS=dM + ΩdJ$, and thereby renders the first law true, false, meaningless, or tautological, depending on how one approaches it.
We consider the spacetime structure of Kerr-Gödel black holes, analyzing their parameter space Kerr-Gödel in detail. We apply the tunnelling method to compute their temperature and compare the results to previous calculations obtained via other methods. We claim that it is not possible to have the CTC horizon in between the two black hole horizons and include a discussion of issues that occur when the radius of the CTC horizon is smaller than the radius of both black hole horizons.
We consider the problem of (1+1)-dimensional quantum gravity coupled to particles. Working with the canonically reduced Hamiltonian, we obtain its post-Newtonian expansion for two identical particles. We quantize the (1+1)-dimensional Newtonian system first, after which explicit energy corrections to second order in 1/c are obtained. We compute the perturbed wavefunctions and show that the particles are bound less tightly together than in the Newtonian case.
We study gravitationally collapsing models of pressureless dust, fluids with pressure, and the generalized Chaplygin gas (GCG) shell in (2+1)-dimensional spacetimes. Various collapse scenarios are investigated under a variety of the background configurations such as anti-de Sitter(AdS) black hole, de Sitter (dS) space, flat and AdS space with a conical deficit. As with the case of a disk of dust, we find that the collapse of a dust shell coincides with the Oppenheimer-Snyder type collapse to a black hole provided the initial density is sufficiently large. We also find -- for all types of shell -- that collapse to a naked singularity is possible under a broad variety of initial conditions. For shells with pressure this singularity can occur for a finite radius of the shell. We also find that GCG shells exhibit diverse collapse scenarios, which can be easily demonstrated by an effective potential analysis.
Two approaches to renormalization-group improvement are examined: the substitution of the solutions of running couplings, masses and fields into perturbatively computed quantities is compared with the systematic sum of all the leading log (LL), next-to-leading log (NLL) etc. contributions to radiatively corrected processes, with n-loop expressions for the running quantities being responsible for summing N^{n}LL contributions. A detailed comparison of these procedures is made in the context of the effective potential V in the 4-dimensional O(4) massless $λϕ^{4}$ model, showing the distinction between these procedures at two-loop order when considering the NLL contributions to the effective potential V.
Non-abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher dimensional (2-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-abelian generalizations of the Yang-Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in (2+1) dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields - the $ΣΦEA$ model - can be formulated both as a standard gauge theory and as a higher gauge theory. Since the model has a very rich structure - it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson-Friedman-Walker cosmological-like expanding geometries - this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in (2+1) dimensions coupled to matter in an entirely new framework.
We analyze the entanglement between two modes of a free Dirac field as seen by two relatively accelerated parties. The entanglement is degraded by the Unruh effect and asymptotically reaches a non-vanishing minimum value in the infinite acceleration limit. This means that the state always remains entangled to a degree and can be used in quantum information tasks, such as teleportation, between parties in relative uniform acceleration. We analyze our results from the point of view afforded by the phenomenon of entanglement sharing and in terms of recent results in the area of multi-qubit complementarity.
We investigate the equal-mass 3-body system in general relativistic lineal gravity in the presence of a cosmological constant $Λ$. The cosmological vacuum energy introduces features that do not have a non-relativistic counterpart, inducing a competing expansion/contraction of spacetime that competes with the gravitational self-attraction of the bodies. We derive a canonical expression for the Hamiltonian of the system and discuss the numerical solution of the resulting equations of motion. As for the system with $Λ=0$, we find that the structure of the phase space yields a rich variety of interesting dynamics that can be divided into three distinct regions: annulus, pretzel, and chaotic; the first two being regions of quasi-periodicity while the latter is a region of chaos. However unlike the $Λ=0$ case, we find that a negative cosmological constant considerably diminishes the amount of chaos in the system, even beyond that of the $Λ=0$ non-relativistic system. By contrast, a positive cosmological constant considerably enhances the amount of chaos, typically leading to KAM breakdown.
We demonstrate the stability under subsequent-to-leading logarithm corrections of the quartic scalar-field coupling constant $λ$ and the running Higgs boson mass obtained from the (initially massless) effective potential for radiatively broken electroweak symmetry in the single-Higgs-Doublet Standard Model. Such subsequent-to-leading logarithm contributions are systematically extracted from the renormalization group equation considered beyond one-loop order. We show $λ$ to be the dominant coupling constant of the effective potential for the radiatively broken case of electroweak symmetry. We demonstrate the stability of $λ$ and the running Higgs boson mass through five orders of successively subleading logarithmic corrections to the scalar-field-theory projection of the effective potential for which all coupling constants except the dominant coupling constant $λ$ are disregarded. We present a full next-to-leading logarithm potential in the three dominant Standard Model coupling constants ($t$-quark-Yukawa, $α_s$, and $λ$) from these coupling constants' contribution to two loop $β$- and $γ$-functions. Finally, we demonstrate the manifest order-by-order stability of the physical Higgs boson mass in the 220-231 GeV range. In particular, we obtain a 231 GeV physical Higgs boson mass inclusive of the $t$-quark-Yukawa and $α_s$ coupling constants to next-to-leading logarithm order, and inclusive of the smaller $SU(2)\times U(1)$ gauge coupling constants to leading logarithm order.
We generalize the quasilocal definition of the stress energy tensor of Einstein gravity to the case of third order Lovelock gravity, by introducing the surface terms that make the action well-defined. We also introduce the boundary counterterm that removes the divergences of the action and the conserved quantities of the solutions of third order Lovelock gravity with zero curvature boundary at constant $t$ and $r$. Then, we compute the charged rotating solutions of this theory in $n+1$ dimensions with a complete set of allowed rotation parameters. These charged rotating solutions present black hole solutions with two inner and outer event horizons, extreme black holes or naked singularities provided the parameters of the solutions are chosen suitable. We compute temperature, entropy, charge, electric potential, mass and angular momenta of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We find a Smarr-type formula and perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable. This is commensurate with the fact that there is no Hawking-Page phase transition for black objects with zero curvature horizon.