arXiv subjects

Martin O'Loughlin

Publications and source records attributed to Martin O'Loughlin.

At least 19 recordsLinked to original sources

arXiv2019

Geodesic congruences, impulsive gravitational waves and gravitational memory

In this paper we introduce a new approach to the study of the effects that an impulsive wave, containing a mixture of material sources and gravitational waves, has on a geodesic congruence that traverses it. We find that the effect of the wave on the congruence is a discontinuity in the B-tensor of the congruence. Our results thus provide a detector independent and covariant characterization of gravitational memory.

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arXiv2016

Horizon Shells: Classical Structure at the Horizon of a Black Hole

We address the question of the uniqueness of the Schwarzschild black hole by considering the following question: How many meaningful solutions of the Einstein equations exist that agree with the Schwarzschild solution (with a fixed mass m) everywhere except maybe on a codimension one hypersurface? The perhaps surprising answer is that the solution is unique (and uniquely the Schwarzschild solution everywhere in spacetime) *unless* the hypersurface is the event horizon of the Schwarzschild black hole, in which case there are actually an infinite number of distinct solutions. We explain this result and comment on some of the possible implications for black hole physics.

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arXiv2015

Horizon Shells and BMS-like Soldering Transformations

We revisit the theory of null shells in general relativity, with a particular emphasis on null shells placed at horizons of black holes. We study in detail the considerable freedom that is available in the case that one solders two metrics together across null hypersurfaces (such as Killing horizons) for which the induced metric is invariant under translations along the null generators. In this case the group of soldering transformations turns out to be infinite dimensional, and these solderings create non-trivial horizon shells containing both massless matter and impulsive gravitational wave components. We also rephrase this result in the language of Carrollian symmetry groups. To illustrate this phenomenon we discuss in detail the example of shells on the horizon of the Schwarzschild black hole (with equal interior and exterior mass), uncovering a rich classical structure at the horizon and deriving an explicit expression for the general horizon shell energy-momentum tensor. In the special case of BMS-like soldering supertranslations we find a conserved shell-energy that is strikingly similar to the standard expression for asymptotic BMS supertranslation charges, suggesting a direct relation between the physical properties of these horizon shells and the recently proposed BMS supertranslation hair of a black hole.

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arXiv2015

Wave equations on the linear mass Vaidya metric

We discuss the near singularity region of the linear mass Vaidya metric. In particular we investi- gate the structure in the numerical solutions for the scattering of scalar and electromagnetic metric perturbations from the singularity. In addition to directly integrating the full wave-equation, we use the symmetry of the metric to reduce the problem to that of an ODE. We observe that, around the total evaporation point, quasi-normal like oscillations appear, indicating that this may be an interesting model for the description of the end-point of black hole evaporation.

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arXiv2013

A linear mass Vaidya metric at the end of black hole evaporation

We discuss the near singularity region of the linear mass Vaidya metric for massless particles with non-zero angular momentum. In particular we look at massless geodesics with non-zero angular momentum near the vanishing point of a special subclass of linear mass Vaidya metrics. We also investigate this same structure in the numerical solutions for the scattering of massless scalars from the singularity. Finally we make some comments on the possibility of using this metric as a semi-classical model for the end-point of black hole evaporation.

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arXiv2013

Micro Black Hole Production and Evaporation

It has been conjectured that Micro Black Holes (MBH) may be formed in the presence of large extra dimensions. These MBHs have very small mass and they decay almost instantaneously. Taking into consideration quantum effects, they should Hawking radiate mainly to Standard Model particles, this radiation then gets modified by the non trivial geometry around the MBHs; the so called greybody factors which filter the Hawking radiation. To test the validity of MBH models, one needs to investigate it experimentally. A primary tool in this investigation is simulation of the MBH formation and evaporation, including all theoretical work that has been performed up to now. BlackMax and CHARYBDIS2 are the most modern and realistic simulators currently available. However they still suffer from a lack of important parameters. In this article we will discuss the primary work that we have done to study the possible changes that can be implemented in the simulations.

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arXiv2011

Aspects of Plane Wave (Matrix) String Dynamics

We analyse two issues that arise in the context of (matrix) string theories in plane wave backgrounds, namely (1) the use of Brinkmann- versus Rosen-variables in the quantum theory for general plane waves (which we settle conclusively in favour of Brinkmann variables), and (2) the regularisation of the quantum dynamics for a certain class of singular plane waves (discussing the benefits and limitations of regularisations of the plane-wave metric itself).

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arXiv2010

The non-Abelian gauge theory of matrix big bangs

We study at the classical and quantum mechanical level the time-dependent Yang-Mills theory that one obtains via the generalisation of discrete light-cone quantisation to singular homogeneous plane waves. The non-Abelian nature of this theory is known to be important for physics near the singularity, at least as far as the number of degrees of freedom is concerned. We will show that the quartic interaction is always subleading as one approaches the singularity and that close enough to t=0 the evolution is driven by the diverging tachyonic mass term. The evolution towards asymptotically flat space-time also reveals some surprising features.

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arXiv2008

DLCQ and Plane Wave Matrix Big Bang Models

We study the generalisations of the Craps-Sethi-Verlinde matrix big bang model to curved, in particular plane wave, space-times, beginning with a careful discussion of the DLCQ procedure. Singular homogeneous plane waves are ideal toy-models of realistic space-time singularities since they have been shown to arise universally as their Penrose limits, and we emphasise the role played by the symmetries of these plane waves in implementing the flat space Seiberg-Sen DLCQ prescription for these curved backgrounds. We then analyse various aspects of the resulting matrix string Yang-Mills theories, such as the relation between strong coupling space-time singularities and world-sheet tachyonic mass terms. In order to have concrete examples at hand, in an appendix we determine and analyse the IIA singular homogeneous plane wave - null dilaton backgrounds.

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arXiv2008

Multiple M2-Branes and Plane Waves

We propose a natural generalisation of the BLG multiple M2-brane action to membranes in curved plane wave backgrounds, and verify in two different ways that the action correctly captures the non-trivial space-time geometry. We show that the M2 to D2 reduction of the theory along a non-trivial direction in field space is equivalent to the D2-brane world-volume Yang-Mills theory with a non-trivial (null-time dependent) dilaton in the corresponding IIA background geometry. As another consistency check of this proposal we show that the properties of metric 3-algebras ensure the equivalence of the Rosen coordinate version of this action (time-dependent metric on the space of 3-algebra valued scalar fields, no mass terms) and its Brinkmann counterpart (constant couplings but time-dependent mass terms). We also establish an analogous result for deformed Yang-Mills theories in any dimension which, in particular, demonstrates the equivalence of the Rosen and Brinkmann forms of the plane wave matrix string action.

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arXiv2007

Half BPS states in AdS_5 x Y^{p,q}

We study a class of solutions of IIB Supergravity which are asymptotically AdS_5 x Y^{p,q}. They have an R x SO(4) x SU(2) x U(1) isometry and preserve half of the 8 supercharges of the background geometry. They are described by a set of second order differential equations that we have found and analysed in a previous paper, where we studied 1/8 BPS states in the maximally supersymmetric AdS_5 x S^5 background. These geometries correspond to certain chiral primary operators of the N=1 superconformal quiver theories, dual to IIB theory on AdS_5 x Y^{p,q}. We also show how to recover the AdS_5 x Y^{p,q} backgrounds by suitably doubling the number of preserved supersymmetries. We then solve the differential equations perturbatively in a large AdS_5 radius expansion, imposing asymptotic AdS_5 x Y^{p,q} boundary conditions. We compute the global baryonic and mesonic charges, including the R-charge. As for the computation of the mass, i.e. the conformal dimension D of the dual field theory operators, which is notoriously subtle in asymptotically AdS backgrounds, we adopt the general formalism due to Wald and collaborators, which gives a finite result, and verify the relation D=3 R / 2, demanded by the N=1 superconformal algebra.

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arXiv2005

Singularities and closed time-like curves in type IIB 1/2 BPS geometries

We study in detail the moduli space of solutions discovered in LLM relaxing the constraint that guarantees the absence of singularities. The solutions fall into three classes, non-singular, null-singular and time machines with a time-like naked singularity. We study the general features of these metrics and prove that there are actually just two generic classes of space-times - those with null singularities are in the same class as the non-singular metrics. AdS/CFT seems to provide a dual description only for the first of these two types of space-time in terms of a unitary CFT indicating the possible existence of a chronology protection mechanism for this class of geometries.

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arXiv2005

On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves

As a step towards understanding the properties of string theory in time-dependent and singular spacetimes, we study the divergence of density operators for string ensembles in singular scale-invariant plane waves, i.e. those plane waves that arise as the Penrose limits of generic power-law spacetime singularities. We show that the scale invariance implies that the Hagedorn behaviour of bosonic and supersymmetric strings in these backgrounds, even with the inclusion of RR or NS fields, is the same as that of strings in flat space. This is in marked contrast to the behaviour of strings in the BFHP plane wave which exhibit quantitatively and qualitatively different thermodynamic properties.

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arXiv2004

Two and three loop alpha' corrections to T-duality: Kasner and Schwarzschild

Two and three loop alpha' corrections are calculated for Kasner and Schwarzschild metrics, and their T-duals, in the bosonic string theory. These metrics are used to obtain the two and three loop alpha' corrections to T-duality. It is noted in particular that the inclusion of alpha' corrections and the requirement of consistency with the alpha'-corrected T-duality for the Kasner and Schwarzschild metrics enables one to fix uniquely the covariant form of the T-duality rules at three loops. As a generalization of the T-dual of the Schwarzschild geometry a class of massless geometries is presented.

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arXiv2004

The Universality of Penrose Limits near Space-Time Singularities

We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic power-law singularities of this type the oscillator frequencies of the resulting homogeneous singular plane wave turn out to lie in a range which is known to allow for an analytic extension of string modes through the singularity. The discussion is phrased in terms of the recently obtained covariant characterisation of the Penrose limit; the relation with null geodesic deviation is explained in detail.

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arXiv2003

Boundary actions in Ponzano-Regge discretization, Quantum groups and AdS(3)

Boundary actions for three-dimensional quantum gravity in the discretized formalism of Ponzano-Regge are studied with a view towards understanding the boundary degrees of freedom. These degrees of freedom postulated in the holography hypothesis are supposed to be characteristic of quantum gravity theories. In particular it is expected that some of these degrees of freedom reside on black hole horizons. This paper is a study of these ideas in the context of a theory of quantum gravity that requires no additional structure such as supersymmetry or special gravitational backgrounds. Lorentzian as well as Euclidean regimes are examined. Some surprising relationships to Liouville theory and string theory in AdS(3) are found.

gr-qc↗

arXiv2003

Penrose Limits and Spacetime Singularities

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ is the restriction of the null geodesic deviation matrix (curvature tensor) of the original spacetime metric to the null geodesic, evaluated in a comoving frame. We also consider the Penrose limits of spacetime singularities and show that for a large class of black hole, cosmological and null singularities (of Szekeres-Iyer ``power-law type''), including those of the FRW and Schwarzschild metrics, the result is a singular homogeneous plane wave with profile $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.

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arXiv2003

Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves

We prove that M-theory plane waves with extra supersymmetries are necessarily homogeneous (but possibly time-dependent), and we show by explicit construction that such time-dependent plane waves can admit extra supersymmetries. To that end we study the Penrose limits of Goedel-like metrics, show that the Penrose limit of the M-theory Goedel metric (with 20 supercharges) is generically a time-dependent homogeneous plane wave of the anti-Mach type, and display the four extra Killings spinors in that case. We conclude with some general remarks on the Killing spinor equations for homogeneous plane waves.

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