Everything, unless stated otherwise, is in Meeting Room 3. Seminars will be 15 minutes long, with a couple of minutes of questions after each and then a couple of minutes to install the subsequent speaker.

TUESDAY APRIL 3.

9:30--11:00 REGISTRATION AND COFFEE, CMS CORE.

11:15 BRIEF WELCOME AND LOGISTICS SPEECH. Dr Edward Anderson (DAMTP and Peterhouse Cambridge).

I. CLASSICAL FORMALISM.

Chair: Professor Malcolm MacCallum (Queen Mary University of London).

11:30-11:45 Professor Donald Lynden-Bell, Institute of Astronomy and Clare College Cambridge.

"Energy and Angular Momentum Density of Stationary Gravitational Fields."

Observers in a stationary space-time can estimate the material energy density and the kinetic energy-density of that material. This is more than the total mass, the difference being the gravitational potential energy. By use of a non-locally-defined conformal factor, the difference is expressed in terms of squares of 'field' quantities to get expressions analogous to Maxwell's $E^2/8\pi$. The relevant results are published in two papers one in CQG and one in Phys Rev D 2007.

11:50-12:05 Dr Julian Barbour, Retired.

"The Principles of Relational Dynamics."

The word 'relational' occurs with ever increasing frequency in the quantum-gravity literature. It is easy to say what one means by a relational variable -- in particle mechanics, for example, an interparticle separation is one. However, the definition of a relational theory is another matter; here there is much confusion. Since general relativity is said to be a relational (background-independent) theory and that this has far-reaching implications for quantum gravity, it is important to know what a relational theory is. In this talk I will present what I believe are the defining principles of a relational theory and show that a generally covariant theory is not necessarily relational.

12:10-12:25 Dr Edward Anderson, DAMTP and Peterhouse Cambridge.

"New formulation of gauge theories prior to variation: alternative to ADM formulation of GR."

I give a general working for how to vary auxiliary variables in gauge theories. As a first application, I show that lapse and shift can be regarded not as multipliers but as velocities of cyclic coordinates that I term {\it instant} and {\it grid}. Thus I obtain an alternative to the ADM formulation of GR. I use this to obtain the `relational' action for GR [1] from the spacetime perspective, and to extend it to the case with boundary terms. As a second application, I show how certain pairs of multipliers can be regarded rather as one auxiliary and its velocity. This (and subsequent analysis) gives a clear interpretation of the alternative theory [2] and of the ABFKO formulation of the GR initial value problem [3]. (this work is forthcoming in 2 preprints).

[1] J.B. Barbour, B.Z. Foster and N. \'{O} Murchadha, Class. Quantum Grav. 19 3217 (2002), gr-qc/0012089; E. Anderson, Studies in History and Philosophy of Modern Physics, 38 15 (2007), gr-qc/0511070. [2] E. Anderson, J.B. Barbour, B.Z. Foster and N. \'{O} Murchadha, Class. Quantum Grav. 20 157 (2003), gr-qc/0211022. [3] E. Anderson, J.B. Barbour, B.Z. Foster, B. Kelleher and N. \'{O} Murchadha, Class. Quantum Grav 22 1795 (2005).

12:30-12:45 Professor Brian Edgar, Linköping's University (Sweden).

"The new potential for the Weyl tensor in $n$ dimensions: gauge and second order equation, by S. Brian Edgar and Jose M.M. Senovilla."

Although the Lanczos potential (a $(2,1)$ form, $ L_{ab}{}^c$) for the Weyl tensor does not exist in dimensions greater than four, a new potential (a $(2,3)$ form, $ P_{ab}{}^{cde}$, which coincides with the double dual of $ L_{ab}{}^c$ in four dimensions) has recently been shown to exist in all dimensions greater than four. In this talk we discuss the structure of its second order differential equation which is obtained from the Bianchi identities, and the related question of gauge.

12:50-2:15 LUNCH.

Pay for your own, in the CMS Cafeteria or elsewhere.

II. QUANTUM GRAVITY

Chair: Dr Edward Anderson (DAMTP and Peterhouse Cambridge).

2:15-2:30 Dr Jorma Louko, University of Nottingham.

"Polymer quantisation of the Hydrogen atom."

In the polymer Hilbert space of loop quantum gravity, singular phase space functions of the type $1/\sqrt{|x|}$ have been promoted into quantum operators by a prescription, due to Thiemann, that uses the commutator of $\sqrt{|x|}$ and a suitable translation operator. We investigate this prescription in polymer quantisation of the $s$-wave sector of the Hydrogen atom. The lowest energy eigenvalues are in excellent agreement with those of the conventional Schr\"odinger quantisation (and the experiment) already when the scale of fundamental discreteness is two orders of magnitude below the Rydberg scale. (Work in collaboration with Viqar Husain and Oliver Winkler.)

2:35-2:50 Oliver Robertshaw, University of Southampton

"Lie point symmetries and the geodesic approximation for the Schrodinger-Newton equations."

The Schrodinger-Newton equations are the Schrodinger equation, with an additional gravitational potential term satisfying Poisson's equation. Such a system was originally proposed in order to investigate whether gravity could bring about an (objective) wavefunction collapse of quantum objects.

The Lie point symmetries of this system admit, amongst others, a Galilean transformation. This can be used to put an approximate solution, corresponding to widely separated `lumps' of probability, into uniform motion. These lumps are found to move like point particles under a mutual inverse-square attraction.

2:55-3:10 Yuri P. Laptev, People's Friendship University, Moscow (Russia).

"Gravitationally Bound Quantum Systems."

Primordial black holes (mini-holes) can capture elementary particles due to gravitational interaction. Bound quantum systems maintaining a particle in orbit around a mini-hole are called graviatoms [1]. The graviatoms prove to exist only under some conditions, which are satisfied for systems containing leptons and mesons. Electromagnetic and gravitational radiations of charged particles in the graviatoms are comparable with Hawking’s mini-hole radiation. The graviatoms containing neutrinos have macroscopic dimensions. Baryon interaction with mini-holes is describable in the framework of quantum accretion.

[1] Yu.P. Laptev, M.L. Fil’chenkov, gr-qc/0606019; published in "Astronomical and Astrophysical Transactions", 25, (2006), 33--42, "Electromagnetic and Gravitational Radiation of Graviatoms". Additional references: 1. M.L. Fil'chenkov, Quantum radiation of charged particle in a Schwarzschild field, Astron. Nachr. 311 (1990), 223--225. 2. M.L. Fil'chenkov, Yu.P. Laptev, Graviatom dipole Radiation, Gravitation and Cosmology, 12 (2006), 65--68.

3:15-3:30 Dr George Jaroszkiewicz, University of Nottingham.

"Quantized Detector Network approach to Relativity."

We discuss an approach to relativistic quantum mechanics based on observers and quantized apparatus signals, bypassing the concept of system under observation. Labstates are the quantum states of the theory, and these encode the signal dynamics of apparatus, including those aspects conventionally discussed in terms of relativistic spacetimes, such as lightcone structure and causality.

3:35-3:50 Stefan Zohren, Imperial College London.

"The emergence of background geometry from quantum fluctuations."

We show how the quantization of two-dimensional gravity leads to an (Euclidean) quantum space-time where the average geometry is that of constant negative curvature and where the Hartle-Hawking boundary condition arises naturally.

3:55-4:10 Eyo Ita, DAMTP Cambridge.

Abstract: There is a special state which can be said to solve the full theory of a finite theory of quantum gravity, the holy grail of theoretical physics for most of the previous century. The state does so in the sense that it identically satisfies the quantum version of the constraints of general relativity to all orders devoid of quantum corrections. This state is known as the Kodama state, and arises from a special relation of pure gravity with cosmological constant term. Since the state is also semiclassical, by also satisfying the classical version of the constraints, it exhibits a semiclassical-quantum correspondence (SQC). For more general models, namely gravity coupled to lower spin matter fields, the SQC might be broken causing the resulting quantum theory to be non finite. An interesting question is whether there exist states satisfying the SQC when there are matter fields in addition to gravity present. We will illustrate a new method of restoring the SQC in order to produce ‘generalized’ Kodama states and a corresponding finite quantum theory of gravity for this case. This is the first step in a new method for obtaining a finite quantum theory of gravity coupled to a general combination of fields in the full (non minisuperspace) theory.

4:15-4:45 COFFEE BREAK

III. BLACK HOLES.

Chair: Dr Jorma Louko (University of Nottingham).

4:45-5:00 Dr Brien Nolan, Dublin City University (Ireland).

"A quick and easy instability result for black hole inner horizons."

In the region between the outer (event) horizon and the inner (Cauchy) horizon of a `static' spherical black hole space-time, the radius $r$ provides a natural time coordinate. We show that the $L^2$ norm of a massless scalar field on surfaces of constant $r$ blows up in the approach to the Cauchy horizon.

5:05-5:20 Dr Elizabeth Winstanley, University of Sheffield.

"Hawking radiation from rotating brane black holes."

We review recent work on the Hawking radiation, on the brane, of scalars, gauge bosons and fermions from rotating higher dimensional black holes. In particular, we are interested in the emission of particles, energy and angular momentum. This data will be essential for the accurate simulation of potential black hole events at the LHC.

5:25-5:40 Dr H.K. Kunduri, University of Nottingham.

"Anti de Sitter Black Holes."

Five dimensional black holes in anti de Sitter space are of interest as they may have a tractable quantum description via the gauge-gravity correspondnce. After a short review of known black holes, I will discuss two directions where progress has been made in finding evidence for more general solutions.

5:45-6:00 George Kottanattu, University of Nottingham.

"Static spherically symmetric SU(3) geon black holes."

Geon-type black holes are a loosely defined class of single-exterior black-and-white hole spacetimes modelled on the example of the ``$RP^3$ geon'' of Friedman et al (gr-qc/9305017). The holes possess an unconventional topology behind the horizons, and this topology in known to be detectable by distant observers via the Hawking effect of quantum fields. Up to date the family is known to admit geons of the vacuum, abelian and SU(2) kind (Louko et al, gr-qc/0412012); in this talk I will address and present preliminary results concerning static spherically symmetric SU(3) geon black holes.

6:05-6:20 Dr. Sam Dolan, University College Dublin (Ireland).

"Quasi-Bound States on Black Hole Backgrounds"

The well-known Quasi-Normal Modes (QNMs) are solutions to linearised wave equations on black hole spacetimes. QNMs obey two boundary conditions: they are ingoing at the horizon, and outgoing (and divergent) at infinity. In this talk, I will discuss a related, but less-studied, set of solutions (the "Quasi-Bound States") that are ingoing at the horizon, but tend to zero at infinity. Generically, these bound states arise whenever the wave equation has a non-zero rest mass. Like the QNMs, the QBSs have a discrete complex energy spectrum, and decay with time. In this talk, I will show that Leaver's continued-fraction method (originally used for determining QNM frequencies) can be adapted to compute the bound state spectrum of the massive scalar wave equation on the Kerr background.

7:00-9:30 CQG-SPONSORED RECEPTION.

There will be food, wine and soft drinks.

WEDNESDAY APRIL 4

IV. NUMERICAL RELATIVITY AND GRAVITATIONAL WAVES

Chair: Dr John Stewart (DAMTP and Kings College Cambridge).

9:30-9:45 Dr Ian Hawke, University of Southampton.

"Numerical simulations of gravitational collapse."

Recent simulations of gravitational collapse without symmetries will be discussed, including the gravitational waves emitted when a neutron star collapses to a black hole, the robust features of gravitational wave forms in iron-core collapse, and the seemingly generic appearance of the low T/W instability.

9:50-10:05 Trevor Sidery, University of Southampton.

"Superfluid Turbulence in Neutron Stars."

In this talk I will outline the motivations and challenges in investigating the effect of turbulence in neutron star interiors.

10:10-10:25 David Hilditch, University of Southampton.

"Asymptotically null slices in numerical relativity."

In numerical relativity there is a trade off between pushing the outer boundary far out and resolving outgoing gravitational radiation. We describe spacelike slices which can be combined with a radial stretch or compactification so that the outer boundary may be put very far out without losing outgoing waves. We present numerical evolution of such slices.

10:30-10:45 Dr Thomas Cokelaer, Cardiff University, on behalf of the LIGO Scientific Collaboration.

"Search for binary coalescences in LIGO's third and fourth science runs."

The LIGO Scientific Collaboration has analysed the data from the third and fourth science runs searching for binary black holes, binary neutron stars and binaries consisting of primordial black holes. In this talk we will report on the results of this analysis.

10:50-11:05 Dr B.S. Sathyaprakash

"Extending the mass reach of LISA with higher harmonics in inspirals (Arun, Iyer, Sathyaprakash and Sinha)"

In this talk we will discuss how higher signal harmonics might help in extending the mass reach and help LISA to search for binaries consisting of black holes that are most commonly found in galactic nuclei.

11:10-11:25 Alf Tang, Imperial College London.

"Detect cosmic gravitational-wave background with LISA in Bayesian approach."

Cosmic gravitational-wave background is a powerful tool to study fundamental physics. The difficulty is that the cosmological sources are randomly distributed across the sky and the signals are incoherent, producing a continuum which is entangled with instrumental noise. In this talk, firstly I will introduce different scenarios able to generate the background, and show the predicted spectra. Then from Fourier transform and Gaussian distribution, I will illustrate the formula describing the instrumental noise power spectrum, and show how to subtract the acceleration noise power with the formula. Finally, I will suggest an algorithm based on Bayesian statistics to obtain information on cosmic gravitational-wave background.

11:30-11:50 COFFEE BREAK

V. MATHEMATICAL RELATIVITY

Chair: Dr Mihalis Dafermos (DPMMS Cambridge) if he is back from Kuwait, else Dr. Carsten Gundlach (University of Southampton).

11:50-12:05 William Clavering, Queen Mary University of London.

"The mass of a gravitating system at finite infinity."

We review the proposal to study gravitational systems at `finite infinity' and consider Hawking's formula for the mass in this context. Analysis of several exact solutions is carried out including cosmological black holes and the spherically symmetric scalar field.

12:10-12:25 Gustav Holzegel, DAMTP Cambridge.

"Positive Mass and Isoperimetric Inequalities."

I will revisit Brill's proof of positive mass for regular, three-dimensional, time-symmetric, axisymmetric initial-data and generalize his method in various directions. In particular, I will show how to include an apparent horizon in the initial-data and prove the Riemannian Penrose inequality for a wide number of cases in an elementary manner. For four-dimensional initial-data admitting a generalized form of axisymmetry, an elementary proof of positive mass and (in the black hole case) of a Riemannian Penrose inequality is also given.

12:30-12:45 Ifigeneia Klaoudatou, University of the Aegean (Greece).

"Classification of cosmological singularities in isotropic universes."

We present some of our recent results on the classification of cosmological singularities of isotropic universes using the Hubble parameter, the scale factor and the Bel Robinson energy. We show how a bounded Bel Robinson energy is used to prove a completeness theorem for closed isotropic universes. We also find how the existence of closed trapped surfaces can be traced in the behaviour of Bel Robinson energy. Most of the above results are illustrated through representative cosmological models.

12:50-1:05 Thomas Bäckdahl, Linköping's University (Sweden).

"Axisymmetric stationary spacetimes with arbitrary multipole moments."

In general relativity, multipole moments gives a coordinate independent description of stationary spacetimes. Although the notion of multipole moments was developed in the seventies, there are still some open questions. The major remaining problem is, whether there exist spacetimes with arbitrary a priori specified multipole moments. In this talk, this problem is studied for the axisymmetric case. A necessary and sufficient condition on the multipole moments is given for existence of a solution. Thus proving that the multipole moments completely characterise the axisymmetric stationary solutions. "

1:10 - 2:30 LUNCH BREAK

VI. MATHEMATICAL AND CLASSICAL GR.

Chair: Dr Carsten Gundlach (University of Southampton).

2:30-2:45 Narit Pidokrajt, Stockholm University (Sweden).

"Thermogeometric structures of black holes."

Thermodynamics of black holes is studied by means of Ruppeiner geometry, which is a Riemannian geometry of the thermodynamic state space of the system under consideration. The Ruppeiner geometry is believed to measure the complexity of underlying statistical mechanics in that its curvature singularities are a signal of critical behaviour, whereas the flat Ruppeiner geometry corresponds to a system which is non-interacting like the ideal gas. Applications of this method to black hole (BH) physics include BHs in 2D, 3D as well as Einstein-Maxwell, Myers-Perry and Gibbons-Maeda dilaton BHs. The most physically significant case so far is the Ruppeiner geometry of Myers-Perry BHs in D>5 where the curvature singularities correspond to thermodynamic instability as predicted earlier in the literature.

2:50-3:05 Prakash Sarnobat, Loughborough University.

"The Wahlquist exterior II: Interpretation of multipole moments."

The Wahlquist solution is the only known bounded exact rotating fluid, yet it possesses an unusual shape to its boundary. We are now able to explain this. The slow rotation limit of the interior is taken, and we show that it is possible to generate invariant boundary data in Weyl coordinates; this enables one to use the Ernst potential formalism for the exterior and perform up to second order Cauchy matching. We then perform an asymptotic matching to the interior multipole expansion of the field originating from two point masses. They tidally distort the fluid into a prolate spheroid.

3:10-3:25 Cristian Luebbe, Oxford.

"Isotropic singularities."

The key idea of this talk is whether a singularity can be removed by suitable conformal rescaling of the metric. Such singularities are known as isotropic singularities. We will investigate the possibilities of extensions of a metric in the conformal class through a given singularity. We introduce conformal geodesics and the tractor formalism and use them to derive an existence theorem from bounded tractor curvature.

3:30-3:45 Jonathan Middleton, DAMTP Cambridge.

"On The Stability Of Isotropic Cosmological Singularities In Higher-Order Gravity"

We show that, in quadratic Lagrangian theories of gravity, isotropic cosmological singularities are stable to the presence of small scalar, vector and tensor inhomogeneities. Unlike in general relativity, a particular exact isotropic solution is shown to be the stable attractor on approach to the initial cosmological singularity. This solution is also known to act as an attractor in Bianchi universes of types I, II and IX, reinforcing the hypothesis that small inhomogeneous and anisotropic perturbations of this attractor form part of the general cosmological solution to the field equations of quadratic gravity. We also consider the more complicated behaviour in theories in which the Lagrangian contains more general terms of the form $(R_{ab}R^{ab})^n$.

3:50-4:00 Julian Sonner, DAMTP Cambridge,

Dilaton-Axion Domain Walls and Fake Supergravity

Dynamical systems methods are used to investigate domain-wall solutions of a two-parameter family of models in which gravity is coupled to an axion, and to a dilaton with an exponential potential of either sign. A complete global analysis is presented for (i) constant axion and (ii) flat walls, including a study of bifurcations, and a new exact domain-wall solution with non-constant axion. We reconsider `fake supergravity' issues in light of these results with applications to potentials with anti-de Sitter vacua. We also show by example that `adapted' truncation to a single-scalar model is sometimes inconsistent, and we propose a `generalized' fake supergravity formalism that applies in some such cases.

4:05-4:20 COFFEE BREAK AND MEETING OF CQG BEST STUDENT TALK PRIZE PANNEL

VII. COSMOLOGY.

Chair: TBA.

4:20-4:35 Dr Ilia Musco, Queen Mary University of London.

"Initial conditions for primordial black hole formation."

We study Primordial Black Hole (PBH) formation in the early universe. We specify initial conditions in terms of a curvature profile, which represents large amplitude metric perturbations away from the homogeneous Friedmann Robertson Walker model. Using an asymptotic quasi-homogeneous solution, we relate the curvature profile with the density and velocity perturbations, which at an early enough time, when the length scale of the configuration is much larger than the cosmological horizon, can be treated as small perturbations of the background values. We use two parametric description of the curvature profiles and follow numerically the evolution of the initial configurations. (Published on Class. Quant. Grav. 24 (2007) 1405.)

4:40-4:55 Mr Michael Gerrard, visiting researcher collaborating with Dr. Tim Sumner of Imperial College.

"The Effect of a Fifth Large-Scale Space-Time Dimension on Orbital Dynamics"

The introduction of a fifth large-scale space-time dimension to the equations of orbital dynamics produces results that are in good agreement with the observed flat rotational curves of galaxies. This analysis does not require the modification of Newtonian Dynamics (as proposed by Milgrom within MOND Theory), only its extension from four to five dimensions. The universal acceleration constant a0 used within MOND Theory and the transition from classical Newtonian dynamics to the MOND regime emerge naturally (and without the introduction of arbitrary fitting functions) if this five-dimensional analysis is adopted.

The talk is based on the paper by Michael Gerrard and Tim Sumner, gr-qc/0605080.

5:00-5:15 Dr Vojtech Pravda, Institute of Mathematics of the Academy of Sciences of the Czech Republic.

"(No) Goldberg-Sachs theorem in higher dimensions."

We will discuss possible generalization of the Goldberg-Sachs theorem to higher dimensions. According to this theorem in 4 dimensions multiple principal null directions (PNDs) of a vacuum algebraically special spacetime are geodetic and shearfree. In higher dimensions we show that in algebraically special vacuum spacetimes multiple PNDs are also geodetic in "generic" case. However, special cases with non-geodetic PNDs also exist and we present explicit examples for arbitrary dimension n>6. Unlike in the four-dimensional case, shear is non-vanishing in most cases in higher dimensions. For example vacuum type III and N expanding spacetimes have always shearing multiple PND. In odd dimensions shear is always non-zero for twisting geodetic PNDs (e.g. Myers-Perry for n = 5).

M. Ortaggio, V. Pravda, A. Pravdova, Ricci identities in higher dimensions, Class. Quant. Grav. 24 (2007) 1657. V. Pravda, A. Pravdova, M. Ortaggio, in preparation, (to be on arXiv at the time of Britgrav). A. Coley, R. Milson, V. Pravda, A. Pravdova, Classification of the Weyl Tensor in Higher Dimensions, Class. Quant. Grav. 21 (2004) L35. V. Pravda, A. Pravdova, A. Coley, R. Milson, Bianchi identities in higher dimensions, Class. Quant. Grav. 21 (2004) 2873.

5:20-5:35 Dr Christian Boehmer, Portsmouth.

"Does the cosmological constant imply the existence of a minimum mass?"

I show that in the framework of classical general relativity the presence of a positive cosmological constant implies the existence of a minimal mass and of a minimal density in nature. These results rigorously follow from the generalised Buchdahl inequality in the presence of a cosmological term. Published in: Phys. Lett. B630 (2005) 73-77.

5:40 The CQG BEST Student Talk Prize is awarded, and there is a brief farewell speech.